%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP624+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:08:12 AM UTC 2025
% Result : Theorem 1.22s 1.38s
% Output : Proof 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP624+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:27:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.22/1.38 % SZS status Theorem
% 1.22/1.38 % SZS output start Proof
% 1.22/1.38 tff(k1_binop_1_type, type, (
% 1.22/1.38 k1_binop_1: ( $i * $i * $i ) > $i)).
% 1.22/1.38 tff(tptp_fun_C_2_type, type, (
% 1.22/1.38 tptp_fun_C_2: $i)).
% 1.22/1.38 tff(tptp_fun_B_1_type, type, (
% 1.22/1.38 tptp_fun_B_1: $i)).
% 1.22/1.38 tff(u1_group_1_type, type, (
% 1.22/1.38 u1_group_1: $i > $i)).
% 1.22/1.38 tff(g1_group_1_type, type, (
% 1.22/1.38 g1_group_1: ( $i * $i ) > $i)).
% 1.22/1.38 tff(k2_autgroup_type, type, (
% 1.22/1.38 k2_autgroup: $i > $i)).
% 1.22/1.38 tff(tptp_fun_A_0_type, type, (
% 1.22/1.38 tptp_fun_A_0: $i)).
% 1.22/1.38 tff(k1_autgroup_type, type, (
% 1.22/1.38 k1_autgroup: $i > $i)).
% 1.22/1.38 tff(k2_binop_1_type, type, (
% 1.22/1.38 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 1.22/1.38 tff(u1_struct_0_type, type, (
% 1.22/1.38 u1_struct_0: $i > $i)).
% 1.22/1.38 tff(k7_funct_2_type, type, (
% 1.22/1.38 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 1.22/1.38 tff(l1_group_1_type, type, (
% 1.22/1.38 l1_group_1: $i > $o)).
% 1.22/1.38 tff(v1_group_1_type, type, (
% 1.22/1.38 v1_group_1: $i > $o)).
% 1.22/1.38 tff(m1_relset_1_type, type, (
% 1.22/1.38 m1_relset_1: ( $i * $i * $i ) > $o)).
% 1.22/1.38 tff(k2_zfmisc_1_type, type, (
% 1.22/1.38 k2_zfmisc_1: ( $i * $i ) > $i)).
% 1.22/1.38 tff(m2_relset_1_type, type, (
% 1.22/1.38 m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.22/1.38 tff(v1_funct_2_type, type, (
% 1.22/1.38 v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.22/1.38 tff(v1_funct_1_type, type, (
% 1.22/1.38 v1_funct_1: $i > $o)).
% 1.22/1.38 tff(v4_group_1_type, type, (
% 1.22/1.38 v4_group_1: $i > $o)).
% 1.22/1.38 tff(v3_group_1_type, type, (
% 1.22/1.38 v3_group_1: $i > $o)).
% 1.22/1.38 tff(v3_struct_0_type, type, (
% 1.22/1.38 v3_struct_0: $i > $o)).
% 1.22/1.38 tff(m2_fraenkel_type, type, (
% 1.22/1.38 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 1.22/1.38 tff(k4_autgroup_type, type, (
% 1.22/1.38 k4_autgroup: $i > $i)).
% 1.22/1.38 tff(tptp_fun_C_3_type, type, (
% 1.22/1.38 tptp_fun_C_3: ( $i * $i ) > $i)).
% 1.22/1.38 tff(tptp_fun_D_4_type, type, (
% 1.22/1.38 tptp_fun_D_4: ( $i * $i ) > $i)).
% 1.22/1.38 tff(m1_subset_1_type, type, (
% 1.22/1.38 m1_subset_1: ( $i * $i ) > $o)).
% 1.22/1.38 tff(m1_fraenkel_type, type, (
% 1.22/1.38 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 1.22/1.38 tff(v1_xboole_0_type, type, (
% 1.22/1.38 v1_xboole_0: $i > $o)).
% 1.22/1.38 tff(l1_struct_0_type, type, (
% 1.22/1.38 l1_struct_0: $i > $o)).
% 1.22/1.38 tff(v1_fraenkel_type, type, (
% 1.22/1.38 v1_fraenkel: $i > $o)).
% 1.22/1.38 tff(1,plain,
% 1.22/1.38 ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k1_binop_1(k2_autgroup(A!0), B!1, C!2)) <=> (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.22/1.38 inference(commutativity,[status(thm)],[])).
% 1.22/1.38 tff(2,plain,
% 1.22/1.38 (^[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)))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(3,plain,
% 1.22/1.38 (![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))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[2])).
% 1.22/1.38 tff(4,plain,
% 1.22/1.38 (![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))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(5,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')).
% 1.22/1.38 tff(6,plain,
% 1.22/1.38 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.22/1.38 tff(7,plain,(
% 1.22/1.38 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.22/1.38 inference(skolemize,[status(sab)],[6])).
% 1.22/1.38 tff(8,plain,
% 1.22/1.38 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.22/1.38 tff(9,plain,
% 1.22/1.38 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))),
% 1.22/1.38 inference(quant_inst,[status(thm)],[])).
% 1.22/1.38 tff(10,plain,
% 1.22/1.38 (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.22/1.38 tff(11,plain,
% 1.22/1.38 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(12,plain,
% 1.22/1.38 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[11])).
% 1.22/1.38 tff(13,plain,
% 1.22/1.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), rewrite((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(14,plain,
% 1.22/1.38 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[13])).
% 1.22/1.38 tff(15,plain,
% 1.22/1.38 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(16,plain,
% 1.22/1.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), rewrite(((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 1.22/1.38 inference(bind,[status(th)],[])).
% 1.22/1.38 tff(17,plain,
% 1.22/1.38 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 1.22/1.38 inference(quant_intro,[status(thm)],[16])).
% 1.22/1.38 tff(18,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ((v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_autgroup')).
% 1.22/1.38 tff(19,plain,
% 1.22/1.38 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.22/1.38 tff(20,plain,
% 1.22/1.38 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.22/1.38 tff(21,plain,(
% 1.22/1.38 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | (v1_funct_1(k2_autgroup(A)) & v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))),
% 1.22/1.38 inference(skolemize,[status(sab)],[20])).
% 1.22/1.38 tff(22,plain,
% 1.22/1.38 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.22/1.38 tff(23,plain,
% 1.22/1.38 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 1.22/1.38 tff(24,plain,
% 1.22/1.38 ((((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(25,plain,
% 1.22/1.38 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(26,plain,
% 1.22/1.38 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(27,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t15_autgroup')).
% 1.22/1.38 tff(28,plain,
% 1.22/1.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.22/1.38 tff(29,plain,
% 1.22/1.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[28, 25])).
% 1.22/1.38 tff(30,plain,
% 1.22/1.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.22/1.38 tff(31,plain,
% 1.22/1.38 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (k1_binop_1(k2_autgroup(A), B, C) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B)))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[30, 25])).
% 1.22/1.38 tff(32,plain,
% 1.22/1.38 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))))),
% 1.22/1.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.22/1.38 tff(33,plain,
% 1.22/1.38 (l1_group_1(A!0)),
% 1.22/1.38 inference(and_elim,[status(thm)],[32])).
% 1.22/1.38 tff(34,plain,
% 1.22/1.38 (v4_group_1(A!0)),
% 1.22/1.38 inference(and_elim,[status(thm)],[32])).
% 1.22/1.38 tff(35,plain,
% 1.22/1.38 (v3_group_1(A!0)),
% 1.22/1.38 inference(and_elim,[status(thm)],[32])).
% 1.22/1.38 tff(36,plain,
% 1.22/1.38 (v1_group_1(A!0)),
% 1.22/1.38 inference(and_elim,[status(thm)],[32])).
% 1.22/1.38 tff(37,plain,
% 1.22/1.38 (~v3_struct_0(A!0)),
% 1.22/1.38 inference(and_elim,[status(thm)],[32])).
% 1.22/1.38 tff(38,plain,
% 1.22/1.38 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(39,plain,
% 1.22/1.38 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.38 inference(rewrite,[status(thm)],[])).
% 1.22/1.38 tff(40,plain,
% 1.22/1.38 ((~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) <=> (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(41,plain,
% 1.22/1.39 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[40])).
% 1.22/1.39 tff(42,plain,
% 1.22/1.39 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[41, 39])).
% 1.22/1.39 tff(43,plain,
% 1.22/1.39 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[42])).
% 1.22/1.39 tff(44,plain,
% 1.22/1.39 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[43, 38])).
% 1.22/1.39 tff(45,plain,
% 1.22/1.39 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(46,plain,
% 1.22/1.39 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~((~v1_funct_1(k2_autgroup(A))) | (~v1_funct_2(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(k2_autgroup(A), k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.22/1.39 tff(47,plain,
% 1.22/1.39 (~((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[46, 37, 36, 35, 34, 33, 23])).
% 1.22/1.39 tff(48,plain,
% 1.22/1.39 (((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(49,plain,
% 1.22/1.39 (m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 1.22/1.39 tff(50,plain,
% 1.22/1.39 ((~(m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(51,plain,
% 1.22/1.39 ((~(m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)) <=> m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 1.22/1.39 tff(52,plain,
% 1.22/1.39 (m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[51, 10])).
% 1.22/1.39 tff(53,plain,
% 1.22/1.39 (((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(54,plain,
% 1.22/1.39 (v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[53, 47])).
% 1.22/1.39 tff(55,plain,
% 1.22/1.39 (((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) | v1_funct_1(k2_autgroup(A!0))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(56,plain,
% 1.22/1.39 (v1_funct_1(k2_autgroup(A!0))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[55, 47])).
% 1.22/1.39 tff(57,plain,
% 1.22/1.39 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(58,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[57])).
% 1.22/1.39 tff(59,plain,
% 1.22/1.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), rewrite((v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))) <=> (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(60,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[59])).
% 1.22/1.39 tff(61,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(62,plain,
% 1.22/1.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(63,plain,
% 1.22/1.39 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[62])).
% 1.22/1.39 tff(64,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g1_group_1')).
% 1.22/1.39 tff(65,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.22/1.39 tff(66,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[65, 61])).
% 1.22/1.39 tff(67,plain,(
% 1.22/1.39 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (v1_group_1(g1_group_1(A, B)) & l1_group_1(g1_group_1(A, B))))),
% 1.22/1.39 inference(skolemize,[status(sab)],[66])).
% 1.22/1.39 tff(68,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.22/1.39 tff(69,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[68, 58])).
% 1.22/1.39 tff(70,plain,
% 1.22/1.39 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(71,plain,
% 1.22/1.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(72,plain,
% 1.22/1.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~((~v1_group_1(g1_group_1(A, B))) | (~l1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.22/1.39 tff(73,plain,
% 1.22/1.39 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[72, 69, 56, 54])).
% 1.22/1.39 tff(74,plain,
% 1.22/1.39 (~((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[73, 52])).
% 1.22/1.39 tff(75,plain,
% 1.22/1.39 (((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(76,plain,
% 1.22/1.39 (l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.22/1.39 tff(77,plain,
% 1.22/1.39 (((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.22/1.39 inference(tautology,[status(thm)],[])).
% 1.22/1.39 tff(78,plain,
% 1.22/1.39 (v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[77, 74])).
% 1.22/1.39 tff(79,plain,
% 1.22/1.39 (^[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))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(80,plain,
% 1.22/1.39 (![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)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[79])).
% 1.22/1.39 tff(81,plain,
% 1.22/1.39 (![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)))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(82,plain,
% 1.22/1.39 (^[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)))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(83,plain,
% 1.22/1.39 (![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)))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[82])).
% 1.22/1.39 tff(84,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')).
% 1.22/1.39 tff(85,plain,
% 1.22/1.39 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.22/1.39 tff(86,plain,
% 1.22/1.39 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.22/1.39 tff(87,plain,(
% 1.22/1.39 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.22/1.39 inference(skolemize,[status(sab)],[86])).
% 1.22/1.39 tff(88,plain,
% 1.22/1.39 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[87, 80])).
% 1.22/1.39 tff(89,plain,
% 1.22/1.39 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(90,plain,
% 1.22/1.39 (((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) <=> ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(91,plain,
% 1.22/1.39 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.22/1.39 inference(monotonicity,[status(thm)],[90])).
% 1.22/1.39 tff(92,plain,
% 1.22/1.39 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[91, 89])).
% 1.22/1.39 tff(93,plain,
% 1.22/1.39 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(94,plain,
% 1.22/1.39 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.22/1.39 tff(95,plain,
% 1.22/1.39 (g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[94, 88, 78, 76])).
% 1.22/1.39 tff(96,plain,
% 1.22/1.39 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(97,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[96])).
% 1.22/1.39 tff(98,plain,
% 1.22/1.39 (^[A: $i, B: $i] : rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(99,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[98])).
% 1.22/1.39 tff(100,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(transitivity,[status(thm)],[99, 97])).
% 1.22/1.39 tff(101,plain,
% 1.22/1.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(102,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[101])).
% 1.22/1.39 tff(103,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(104,plain,
% 1.22/1.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))))),
% 1.22/1.39 inference(bind,[status(th)],[])).
% 1.22/1.39 tff(105,plain,
% 1.22/1.39 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 1.22/1.39 inference(quant_intro,[status(thm)],[104])).
% 1.22/1.39 tff(106,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i, D: $i] : ((g1_group_1(A, B) = g1_group_1(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_group_1')).
% 1.22/1.39 tff(107,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.22/1.39 tff(108,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.22/1.39 tff(109,plain,(
% 1.22/1.39 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | ((A = C) & (B = D))))),
% 1.22/1.39 inference(skolemize,[status(sab)],[108])).
% 1.22/1.39 tff(110,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[109, 102])).
% 1.22/1.39 tff(111,plain,
% 1.22/1.39 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[110, 100])).
% 1.22/1.39 tff(112,plain,
% 1.22/1.39 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))),
% 1.22/1.39 inference(rewrite,[status(thm)],[])).
% 1.22/1.39 tff(113,plain,
% 1.22/1.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D))))))),
% 1.22/1.39 inference(quant_inst,[status(thm)],[])).
% 1.22/1.39 tff(114,plain,
% 1.22/1.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i, D: $i] : ((~(g1_group_1(A, B) = g1_group_1(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 1.22/1.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.22/1.39 tff(115,plain,
% 1.22/1.39 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[114, 111, 56, 54])).
% 1.22/1.39 tff(116,plain,
% 1.22/1.39 (![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))),
% 1.22/1.39 inference(unit_resolution,[status(thm)],[115, 52])).
% 1.22/1.39 tff(117,plain,
% 1.22/1.39 (((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))) <=> ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | (~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(118,plain,
% 1.22/1.40 ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(119,plain,
% 1.22/1.40 ((~![C: $i, D: $i] : ((~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(C, D))) | (~((~(k1_autgroup(A!0) = C)) | (~(k2_autgroup(A!0) = D)))))) | (~(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)) = g1_group_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.22/1.40 tff(120,plain,
% 1.22/1.40 (~((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[119, 116, 95])).
% 1.22/1.40 tff(121,plain,
% 1.22/1.40 (((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.22/1.40 inference(tautology,[status(thm)],[])).
% 1.22/1.40 tff(122,plain,
% 1.22/1.40 (k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[121, 120])).
% 1.22/1.40 tff(123,plain,
% 1.22/1.40 (u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) = k2_autgroup(A!0)),
% 1.22/1.40 inference(symmetry,[status(thm)],[122])).
% 1.22/1.40 tff(124,plain,
% 1.22/1.40 (k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(k2_autgroup(A!0), B!1, C!2)),
% 1.22/1.40 inference(monotonicity,[status(thm)],[123])).
% 1.22/1.40 tff(125,plain,
% 1.22/1.40 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(126,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[125])).
% 1.22/1.40 tff(127,plain,
% 1.22/1.40 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(128,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[127])).
% 1.22/1.40 tff(129,plain,
% 1.22/1.40 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(130,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[129])).
% 1.22/1.40 tff(131,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(transitivity,[status(thm)],[130, 128])).
% 1.22/1.40 tff(132,plain,
% 1.22/1.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(133,plain,
% 1.22/1.40 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[132])).
% 1.22/1.40 tff(134,plain,
% 1.22/1.40 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(135,plain,
% 1.22/1.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(136,plain,
% 1.22/1.40 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[135])).
% 1.22/1.40 tff(137,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_autgroup')).
% 1.22/1.40 tff(138,plain,
% 1.22/1.40 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.22/1.40 tff(139,plain,
% 1.22/1.40 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.22/1.40 tff(140,plain,(
% 1.22/1.40 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(skolemize,[status(sab)],[139])).
% 1.22/1.40 tff(141,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.22/1.40 tff(142,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[141, 131])).
% 1.22/1.40 tff(143,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[142, 126])).
% 1.22/1.40 tff(144,plain,
% 1.22/1.40 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(145,plain,
% 1.22/1.40 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(146,plain,
% 1.22/1.40 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[145])).
% 1.22/1.40 tff(147,plain,
% 1.22/1.40 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 1.22/1.40 inference(transitivity,[status(thm)],[146, 144])).
% 1.22/1.40 tff(148,plain,
% 1.22/1.40 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(149,plain,
% 1.22/1.40 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.22/1.40 tff(150,plain,
% 1.22/1.40 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[149, 37, 36, 35, 34, 33, 143])).
% 1.22/1.40 tff(151,plain,
% 1.22/1.40 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 1.22/1.40 inference(and_elim,[status(thm)],[32])).
% 1.22/1.40 tff(152,plain,
% 1.22/1.40 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(153,plain,
% 1.22/1.40 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(154,plain,
% 1.22/1.40 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.22/1.40 tff(155,plain,
% 1.22/1.40 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[154, 151, 150])).
% 1.22/1.40 tff(156,plain,
% 1.22/1.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))))), (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))))), rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(157,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[156])).
% 1.22/1.40 tff(158,plain,
% 1.22/1.40 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(159,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[158])).
% 1.22/1.40 tff(160,plain,
% 1.22/1.40 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))),
% 1.22/1.40 inference(bind,[status(th)],[])).
% 1.22/1.40 tff(161,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.40 inference(quant_intro,[status(thm)],[160])).
% 1.22/1.40 tff(162,plain,
% 1.22/1.40 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.40 inference(transitivity,[status(thm)],[161, 159])).
% 1.22/1.40 tff(163,plain,
% 1.22/1.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))))), trans(monotonicity(rewrite(((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) <=> ((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))), trans(monotonicity(rewrite((m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))) <=> (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))), (((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))), rewrite(((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))), (((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))), ((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))) <=> (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))), rewrite((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) <=> (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))), ((((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))) <=> (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))))),
% 1.22/1.41 inference(bind,[status(th)],[])).
% 1.22/1.41 tff(164,plain,
% 1.22/1.41 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.41 inference(quant_intro,[status(thm)],[163])).
% 1.22/1.41 tff(165,plain,
% 1.22/1.41 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(166,plain,
% 1.22/1.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))), rewrite(((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) <=> ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), (![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) <=> ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))))),
% 1.22/1.41 inference(bind,[status(th)],[])).
% 1.22/1.41 tff(167,plain,
% 1.22/1.41 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 1.22/1.41 inference(quant_intro,[status(thm)],[166])).
% 1.22/1.41 tff(168,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) => ((B = k2_autgroup(A)) <=> ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![D: $i] : (m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_autgroup')).
% 1.22/1.41 tff(169,plain,
% 1.22/1.41 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.22/1.41 tff(170,plain,
% 1.22/1.41 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | ((B = k2_autgroup(A)) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[169, 165])).
% 1.22/1.41 tff(171,plain,(
% 1.22/1.41 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)) & m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A)))) | (((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))) & ((B = k2_autgroup(A)) | (m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) & (~((~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))))))),
% 1.22/1.41 inference(skolemize,[status(sab)],[170])).
% 1.22/1.41 tff(172,plain,
% 1.22/1.41 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[171, 164])).
% 1.22/1.41 tff(173,plain,
% 1.22/1.41 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C)))))) | (~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A)))))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[172, 162])).
% 1.22/1.41 tff(174,plain,
% 1.22/1.41 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[173, 157])).
% 1.22/1.41 tff(175,plain,
% 1.22/1.41 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(176,plain,
% 1.22/1.41 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(177,plain,
% 1.22/1.41 (^[B: $i] : trans(monotonicity(monotonicity(monotonicity(rewrite((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) <=> (~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0)))))))), monotonicity(rewrite(((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) <=> ((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))), ((~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))), (((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))) <=> ((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))), ((~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) <=> (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))), rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))), (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.42 inference(bind,[status(th)],[])).
% 1.22/1.42 tff(178,plain,
% 1.22/1.42 (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))) <=> ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.22/1.42 inference(quant_intro,[status(thm)],[177])).
% 1.22/1.42 tff(179,plain,
% 1.22/1.42 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[178])).
% 1.22/1.42 tff(180,plain,
% 1.22/1.42 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.42 inference(transitivity,[status(thm)],[179, 176])).
% 1.22/1.42 tff(181,plain,
% 1.22/1.42 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[180])).
% 1.22/1.42 tff(182,plain,
% 1.22/1.42 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))))),
% 1.22/1.42 inference(transitivity,[status(thm)],[181, 175])).
% 1.22/1.42 tff(183,plain,
% 1.22/1.42 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(184,plain,
% 1.22/1.42 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A), k1_autgroup(A)), k1_autgroup(A))) | (~((~((B = k2_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~m2_fraenkel(tptp_fun_D_4(B, A), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), tptp_fun_D_4(B, A), tptp_fun_C_3(B, A))))))) | (~((~(B = k2_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (k2_binop_1(k1_autgroup(A), k1_autgroup(A), k1_autgroup(A), B, C, D) = k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), D, C))))))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.22/1.42 tff(185,plain,
% 1.22/1.42 (![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[184, 37, 36, 35, 34, 33, 174])).
% 1.22/1.42 tff(186,plain,
% 1.22/1.42 (((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(187,plain,
% 1.22/1.42 (((~v1_funct_1(k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(188,plain,
% 1.22/1.42 ((~(~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(189,plain,
% 1.22/1.42 (($false | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(190,plain,
% 1.22/1.43 ((~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(191,plain,
% 1.22/1.43 ((~$true) <=> $false),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(192,plain,
% 1.22/1.43 (($true | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> $true),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(193,plain,
% 1.22/1.43 ((k2_autgroup(A!0) = k2_autgroup(A!0)) <=> $true),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(194,plain,
% 1.22/1.43 (((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> ($true | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[193])).
% 1.22/1.43 tff(195,plain,
% 1.22/1.43 (((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0)))))) <=> $true),
% 1.22/1.43 inference(transitivity,[status(thm)],[194, 192])).
% 1.22/1.43 tff(196,plain,
% 1.22/1.43 ((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) <=> (~$true)),
% 1.22/1.43 inference(monotonicity,[status(thm)],[195])).
% 1.22/1.43 tff(197,plain,
% 1.22/1.43 ((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) <=> $false),
% 1.22/1.43 inference(transitivity,[status(thm)],[196, 191])).
% 1.22/1.43 tff(198,plain,
% 1.22/1.43 (((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))) <=> ($false | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[197, 190])).
% 1.22/1.43 tff(199,plain,
% 1.22/1.43 (((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))) <=> (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[198, 189])).
% 1.22/1.43 tff(200,plain,
% 1.22/1.43 ((~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) <=> (~(~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[199])).
% 1.22/1.43 tff(201,plain,
% 1.22/1.43 ((~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[200, 188])).
% 1.22/1.43 tff(202,plain,
% 1.22/1.43 (((~v1_funct_1(k2_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[201])).
% 1.22/1.43 tff(203,plain,
% 1.22/1.43 (((~v1_funct_1(k2_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0)))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[202, 187])).
% 1.22/1.43 tff(204,plain,
% 1.22/1.43 (((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))))),
% 1.28/1.43 inference(monotonicity,[status(thm)],[203])).
% 1.28/1.43 tff(205,plain,
% 1.28/1.43 (((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))),
% 1.28/1.43 inference(transitivity,[status(thm)],[204, 186])).
% 1.28/1.43 tff(206,plain,
% 1.28/1.43 ((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~((~((k2_autgroup(A!0) = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(k2_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(k2_autgroup(A!0), A!0), tptp_fun_C_3(k2_autgroup(A!0), A!0))))))) | (~((~(k2_autgroup(A!0) = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))),
% 1.28/1.43 inference(quant_inst,[status(thm)],[])).
% 1.28/1.43 tff(207,plain,
% 1.28/1.43 ((~![B: $i] : ((~v1_funct_1(B)) | (~((~((B = k2_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~m2_fraenkel(tptp_fun_D_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), tptp_fun_D_4(B, A!0), tptp_fun_C_3(B, A!0))))))) | (~((~(B = k2_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), B, C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C)))))))) | (~m2_relset_1(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(B, k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~m2_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 1.28/1.43 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.28/1.43 tff(208,plain,
% 1.28/1.43 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))),
% 1.28/1.43 inference(unit_resolution,[status(thm)],[207, 185, 56, 49, 54])).
% 1.28/1.43 tff(209,plain,
% 1.28/1.43 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))),
% 1.28/1.43 inference(rewrite,[status(thm)],[])).
% 1.28/1.43 tff(210,plain,
% 1.28/1.43 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1))))),
% 1.28/1.43 inference(quant_inst,[status(thm)],[])).
% 1.28/1.43 tff(211,plain,
% 1.28/1.43 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), C, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, C))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 1.28/1.44 tff(212,plain,
% 1.28/1.44 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[211, 208, 155])).
% 1.28/1.44 tff(213,plain,
% 1.28/1.44 (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 1.28/1.44 inference(and_elim,[status(thm)],[32])).
% 1.28/1.44 tff(214,plain,
% 1.28/1.44 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 1.28/1.44 inference(or_elim,[status(thm)],[213])).
% 1.28/1.44 tff(215,plain,
% 1.28/1.44 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(216,plain,
% 1.28/1.44 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(217,plain,
% 1.28/1.44 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.28/1.44 tff(218,plain,
% 1.28/1.44 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[217, 214, 150])).
% 1.28/1.44 tff(219,plain,
% 1.28/1.44 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(220,plain,
% 1.28/1.44 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(221,plain,
% 1.28/1.44 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, D) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), D, B!1)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.28/1.44 tff(222,plain,
% 1.28/1.44 (k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[221, 218, 212])).
% 1.28/1.44 tff(223,plain,
% 1.28/1.44 (((~(k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~(k2_autgroup(A!0) = u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.44 inference(tautology,[status(thm)],[])).
% 1.28/1.44 tff(224,plain,
% 1.28/1.44 (k1_autgroup(A!0) = u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[223, 120])).
% 1.28/1.44 tff(225,plain,
% 1.28/1.44 (u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) = k1_autgroup(A!0)),
% 1.28/1.44 inference(symmetry,[status(thm)],[224])).
% 1.28/1.44 tff(226,plain,
% 1.28/1.44 (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k2_binop_1(k1_autgroup(A!0), k1_autgroup(A!0), k1_autgroup(A!0), k2_autgroup(A!0), B!1, C!2)),
% 1.28/1.44 inference(monotonicity,[status(thm)],[225, 225, 225, 123])).
% 1.28/1.44 tff(227,plain,
% 1.28/1.44 (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 1.28/1.44 inference(transitivity,[status(thm)],[226, 222])).
% 1.28/1.44 tff(228,plain,
% 1.28/1.44 ((k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) <=> (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k1_binop_1(k2_autgroup(A!0), B!1, C!2))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[227, 124])).
% 1.28/1.44 tff(229,plain,
% 1.28/1.44 ((k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) <=> (k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.28/1.44 inference(transitivity,[status(thm)],[228, 1])).
% 1.28/1.44 tff(230,plain,
% 1.28/1.44 ((k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)) <=> (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 1.28/1.44 inference(symmetry,[status(thm)],[229])).
% 1.28/1.44 tff(231,plain,
% 1.28/1.44 ((~(k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) <=> (~(k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[230])).
% 1.28/1.44 tff(232,plain,
% 1.28/1.44 (~(k1_binop_1(k2_autgroup(A!0), B!1, C!2) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.28/1.44 inference(or_elim,[status(thm)],[213])).
% 1.28/1.44 tff(233,plain,
% 1.28/1.44 (~(k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.28/1.44 tff(234,plain,
% 1.28/1.44 (m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[225])).
% 1.28/1.44 tff(235,plain,
% 1.28/1.44 (m1_subset_1(C!2, k1_autgroup(A!0)) <=> m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.44 inference(symmetry,[status(thm)],[234])).
% 1.28/1.44 tff(236,plain,
% 1.28/1.44 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(237,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[236])).
% 1.28/1.44 tff(238,plain,
% 1.28/1.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(239,plain,
% 1.28/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[238])).
% 1.28/1.44 tff(240,plain,
% 1.28/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(241,plain,
% 1.28/1.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(242,plain,
% 1.28/1.44 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[241])).
% 1.28/1.44 tff(243,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 1.28/1.44 tff(244,plain,
% 1.28/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.28/1.44 tff(245,plain,
% 1.28/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[244, 240])).
% 1.28/1.44 tff(246,plain,(
% 1.28/1.44 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.28/1.44 inference(skolemize,[status(sab)],[245])).
% 1.28/1.44 tff(247,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[246, 239])).
% 1.28/1.44 tff(248,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[247, 237])).
% 1.28/1.44 tff(249,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(250,plain,
% 1.28/1.44 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(251,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[250])).
% 1.28/1.44 tff(252,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[251, 249])).
% 1.28/1.44 tff(253,plain,
% 1.28/1.44 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(254,plain,
% 1.28/1.44 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.28/1.44 tff(255,plain,
% 1.28/1.44 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[254, 37, 36, 35, 34, 33, 248])).
% 1.28/1.44 tff(256,plain,
% 1.28/1.44 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(257,plain,
% 1.28/1.44 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[256])).
% 1.28/1.44 tff(258,plain,
% 1.28/1.44 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(259,plain,
% 1.28/1.44 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(260,plain,
% 1.28/1.44 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[259])).
% 1.28/1.44 tff(261,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 1.28/1.44 tff(262,plain,
% 1.28/1.44 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.28/1.44 tff(263,plain,
% 1.28/1.44 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[262, 258])).
% 1.28/1.44 tff(264,plain,(
% 1.28/1.44 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(skolemize,[status(sab)],[263])).
% 1.28/1.44 tff(265,plain,
% 1.28/1.44 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[264, 257])).
% 1.28/1.44 tff(266,plain,
% 1.28/1.44 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(267,plain,
% 1.28/1.44 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(268,plain,
% 1.28/1.44 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.28/1.44 tff(269,plain,
% 1.28/1.44 (l1_struct_0(A!0)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[268, 33, 265])).
% 1.28/1.44 tff(270,plain,
% 1.28/1.44 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(271,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[270])).
% 1.28/1.44 tff(272,plain,
% 1.28/1.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(273,plain,
% 1.28/1.44 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[272])).
% 1.28/1.44 tff(274,plain,
% 1.28/1.44 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(275,plain,
% 1.28/1.44 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(276,plain,
% 1.28/1.44 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[275])).
% 1.28/1.44 tff(277,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 1.28/1.44 tff(278,plain,
% 1.28/1.44 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.28/1.44 tff(279,plain,
% 1.28/1.44 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[278, 274])).
% 1.28/1.44 tff(280,plain,(
% 1.28/1.44 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.28/1.44 inference(skolemize,[status(sab)],[279])).
% 1.28/1.44 tff(281,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[280, 273])).
% 1.28/1.44 tff(282,plain,
% 1.28/1.44 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[281, 271])).
% 1.28/1.44 tff(283,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(284,plain,
% 1.28/1.44 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(285,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[284])).
% 1.28/1.44 tff(286,plain,
% 1.28/1.44 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.28/1.44 inference(transitivity,[status(thm)],[285, 283])).
% 1.28/1.44 tff(287,plain,
% 1.28/1.44 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(288,plain,
% 1.28/1.44 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.28/1.44 tff(289,plain,
% 1.28/1.44 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[288, 37, 282])).
% 1.28/1.44 tff(290,plain,
% 1.28/1.44 (~v1_xboole_0(u1_struct_0(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[289, 269])).
% 1.28/1.44 tff(291,plain,
% 1.28/1.44 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(292,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[291])).
% 1.28/1.44 tff(293,plain,
% 1.28/1.44 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(294,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[293])).
% 1.28/1.44 tff(295,plain,
% 1.28/1.44 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(296,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[295])).
% 1.28/1.44 tff(297,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[296, 294])).
% 1.28/1.44 tff(298,plain,
% 1.28/1.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(299,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[298])).
% 1.28/1.44 tff(300,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(301,plain,
% 1.28/1.44 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(302,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[301])).
% 1.28/1.44 tff(303,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 1.28/1.44 tff(304,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.28/1.44 tff(305,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[304, 300])).
% 1.28/1.44 tff(306,plain,(
% 1.28/1.44 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(skolemize,[status(sab)],[305])).
% 1.28/1.44 tff(307,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[306, 299])).
% 1.28/1.44 tff(308,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[307, 297])).
% 1.28/1.44 tff(309,plain,
% 1.28/1.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[308, 292])).
% 1.28/1.44 tff(310,plain,
% 1.28/1.44 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(311,plain,
% 1.28/1.44 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(312,plain,
% 1.28/1.44 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.28/1.44 tff(313,plain,
% 1.28/1.44 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[312, 309, 290, 255])).
% 1.28/1.44 tff(314,plain,
% 1.28/1.44 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(315,plain,
% 1.28/1.44 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[314, 313])).
% 1.28/1.44 tff(316,plain,
% 1.28/1.44 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.28/1.44 inference(tautology,[status(thm)],[])).
% 1.28/1.44 tff(317,plain,
% 1.28/1.44 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[316, 218])).
% 1.28/1.44 tff(318,plain,
% 1.28/1.44 (m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[317, 315])).
% 1.28/1.44 tff(319,plain,
% 1.28/1.44 (m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[318, 235])).
% 1.28/1.44 tff(320,plain,
% 1.28/1.44 (m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[225])).
% 1.28/1.44 tff(321,plain,
% 1.28/1.44 (m1_subset_1(B!1, k1_autgroup(A!0)) <=> m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.44 inference(symmetry,[status(thm)],[320])).
% 1.28/1.44 tff(322,plain,
% 1.28/1.44 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(323,plain,
% 1.28/1.44 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[322, 313])).
% 1.28/1.44 tff(324,plain,
% 1.28/1.44 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.28/1.44 inference(tautology,[status(thm)],[])).
% 1.28/1.44 tff(325,plain,
% 1.28/1.44 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[324, 155])).
% 1.28/1.44 tff(326,plain,
% 1.28/1.44 (m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[325, 323])).
% 1.28/1.44 tff(327,plain,
% 1.28/1.44 (m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[326, 321])).
% 1.28/1.44 tff(328,plain,
% 1.28/1.44 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(329,plain,
% 1.28/1.44 (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[328, 8])).
% 1.28/1.45 tff(330,plain,
% 1.28/1.45 (^[A: $i] : refl(((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(331,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[330])).
% 1.28/1.45 tff(332,plain,
% 1.28/1.45 (^[A: $i] : rewrite(((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(333,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[332])).
% 1.28/1.45 tff(334,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(335,plain,
% 1.28/1.45 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_group_1(A) => (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(336,plain,
% 1.28/1.45 (![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[335])).
% 1.28/1.45 tff(337,axiom,(![A: $i] : (l1_group_1(A) => ((v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_group_1')).
% 1.28/1.45 tff(338,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.28/1.45 tff(339,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[338, 334])).
% 1.28/1.45 tff(340,plain,(
% 1.28/1.45 ![A: $i] : ((~l1_group_1(A)) | (v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.28/1.45 inference(skolemize,[status(sab)],[339])).
% 1.28/1.45 tff(341,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[340, 333])).
% 1.28/1.45 tff(342,plain,
% 1.28/1.45 (![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[341, 331])).
% 1.28/1.45 tff(343,plain,
% 1.28/1.45 (((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))) <=> ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(344,plain,
% 1.28/1.45 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(345,plain,
% 1.28/1.45 ((~![A: $i] : ((~l1_group_1(A)) | (~((~v1_funct_1(u1_group_1(A))) | (~v1_funct_2(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_group_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.28/1.45 tff(346,plain,
% 1.28/1.45 (~((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[345, 342, 76])).
% 1.28/1.45 tff(347,plain,
% 1.28/1.45 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(348,plain,
% 1.28/1.45 (m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[347, 346])).
% 1.28/1.45 tff(349,plain,
% 1.28/1.45 ((~(m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(350,plain,
% 1.28/1.45 ((~(m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) <=> m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[349, 348])).
% 1.28/1.45 tff(351,plain,
% 1.28/1.45 (m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[350, 329])).
% 1.28/1.45 tff(352,plain,
% 1.28/1.45 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(353,plain,
% 1.28/1.45 (v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[352, 346])).
% 1.28/1.45 tff(354,plain,
% 1.28/1.45 (((~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m2_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) | v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(355,plain,
% 1.28/1.45 (v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[354, 346])).
% 1.28/1.45 tff(356,plain,
% 1.28/1.45 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(357,plain,
% 1.28/1.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(358,plain,
% 1.28/1.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[357, 356])).
% 1.28/1.45 tff(359,plain,
% 1.28/1.45 (l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[358, 265, 76])).
% 1.28/1.45 tff(360,plain,
% 1.28/1.45 (^[A: $i, B: $i, C: $i] : refl(((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(361,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[360])).
% 1.28/1.45 tff(362,plain,
% 1.28/1.45 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(363,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[362])).
% 1.28/1.45 tff(364,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(365,plain,
% 1.28/1.45 (^[A: $i, B: $i, C: $i] : rewrite((m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(366,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[365])).
% 1.28/1.45 tff(367,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 1.28/1.45 tff(368,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.28/1.45 tff(369,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[368, 364])).
% 1.28/1.45 tff(370,plain,(
% 1.28/1.45 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.28/1.45 inference(skolemize,[status(sab)],[369])).
% 1.28/1.45 tff(371,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[370, 363])).
% 1.28/1.45 tff(372,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[371, 361])).
% 1.28/1.45 tff(373,plain,
% 1.28/1.45 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(374,plain,
% 1.28/1.45 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(375,plain,
% 1.28/1.45 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.28/1.45 tff(376,plain,
% 1.28/1.45 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[375, 372, 255])).
% 1.28/1.45 tff(377,plain,
% 1.28/1.45 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(378,plain,
% 1.28/1.45 (~v1_xboole_0(k1_autgroup(A!0))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[377, 376])).
% 1.28/1.45 tff(379,plain,
% 1.28/1.45 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(380,plain,
% 1.28/1.45 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[379])).
% 1.28/1.45 tff(381,plain,
% 1.28/1.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), rewrite(((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))) <=> (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))), (((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B)))))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))), (((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(382,plain,
% 1.28/1.45 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[381])).
% 1.28/1.45 tff(383,plain,
% 1.28/1.45 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(384,plain,
% 1.28/1.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A))), (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> (((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))), ((((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(385,plain,
% 1.28/1.45 (![A: $i, B: $i] : (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B)))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[384])).
% 1.28/1.45 tff(386,axiom,(![A: $i, B: $i] : (((((~v1_xboole_0(A)) & v1_funct_1(B)) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) => ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_group_1')).
% 1.28/1.45 tff(387,plain,
% 1.28/1.45 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.28/1.45 tff(388,plain,
% 1.28/1.45 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[387, 383])).
% 1.28/1.45 tff(389,plain,(
% 1.28/1.45 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ((~v3_struct_0(g1_group_1(A, B))) & v1_group_1(g1_group_1(A, B))))),
% 1.28/1.45 inference(skolemize,[status(sab)],[388])).
% 1.28/1.45 tff(390,plain,
% 1.28/1.45 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[389, 382])).
% 1.28/1.45 tff(391,plain,
% 1.28/1.45 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[390, 380])).
% 1.28/1.45 tff(392,plain,
% 1.28/1.45 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(393,plain,
% 1.28/1.45 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(394,plain,
% 1.28/1.45 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | ((~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[393])).
% 1.28/1.45 tff(395,plain,
% 1.28/1.45 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(transitivity,[status(thm)],[394, 392])).
% 1.28/1.45 tff(396,plain,
% 1.28/1.45 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (v1_xboole_0(k1_autgroup(A!0)) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(397,plain,
% 1.28/1.45 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~(v3_struct_0(g1_group_1(A, B)) | (~v1_group_1(g1_group_1(A, B))))))) | (~v1_funct_1(k2_autgroup(A!0))) | (~v1_funct_2(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | (~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.28/1.45 tff(398,plain,
% 1.28/1.45 ((~m1_relset_1(k2_autgroup(A!0), k2_zfmisc_1(k1_autgroup(A!0), k1_autgroup(A!0)), k1_autgroup(A!0))) | v1_xboole_0(k1_autgroup(A!0)) | (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[397, 391, 56, 54])).
% 1.28/1.45 tff(399,plain,
% 1.28/1.45 (~(v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[398, 378, 52])).
% 1.28/1.45 tff(400,plain,
% 1.28/1.45 ((v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(tautology,[status(thm)],[])).
% 1.28/1.45 tff(401,plain,
% 1.28/1.45 (~v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[400, 399])).
% 1.28/1.45 tff(402,plain,
% 1.28/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(403,plain,
% 1.28/1.45 ((v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) <=> (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(404,plain,
% 1.28/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[403])).
% 1.28/1.45 tff(405,plain,
% 1.28/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.28/1.45 inference(transitivity,[status(thm)],[404, 402])).
% 1.28/1.45 tff(406,plain,
% 1.28/1.45 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(407,plain,
% 1.28/1.45 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))) | (~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.28/1.45 tff(408,plain,
% 1.28/1.45 ((~l1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[407, 282, 401])).
% 1.28/1.45 tff(409,plain,
% 1.28/1.45 (~v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[408, 359])).
% 1.28/1.45 tff(410,plain,
% 1.28/1.45 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(411,plain,
% 1.28/1.45 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[410])).
% 1.28/1.45 tff(412,plain,
% 1.28/1.45 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) <=> (~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))))), rewrite((~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))))), rewrite(((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(413,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[412])).
% 1.28/1.46 tff(414,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(415,plain,
% 1.28/1.46 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(416,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[415])).
% 1.28/1.46 tff(417,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_binop_1')).
% 1.28/1.46 tff(418,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.28/1.46 tff(419,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[418, 414])).
% 1.28/1.46 tff(420,plain,(
% 1.28/1.46 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[419])).
% 1.28/1.46 tff(421,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[420, 413])).
% 1.28/1.46 tff(422,plain,
% 1.28/1.46 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[421, 411])).
% 1.28/1.46 tff(423,plain,
% 1.28/1.46 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(424,plain,
% 1.28/1.46 ((v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))))) <=> (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(425,plain,
% 1.28/1.46 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[424])).
% 1.28/1.46 tff(426,plain,
% 1.28/1.46 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[425, 423])).
% 1.28/1.46 tff(427,plain,
% 1.28/1.46 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2)) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))))),
% 1.32/1.47 inference(quant_inst,[status(thm)],[])).
% 1.32/1.47 tff(428,plain,
% 1.32/1.47 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (v1_xboole_0(B) | v1_xboole_0(A) | (k2_binop_1(A, B, C, D, E, F) = k1_binop_1(D, E, F)) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | v1_xboole_0(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))) | (~v1_funct_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~v1_funct_2(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_relset_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), k2_zfmisc_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0)))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 1.32/1.47 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.32/1.47 tff(429,plain,
% 1.32/1.47 ((~m1_subset_1(C!2, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))))) | (k2_binop_1(u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_struct_0(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2) = k1_binop_1(u1_group_1(g1_group_1(k1_autgroup(A!0), k2_autgroup(A!0))), B!1, C!2))),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[428, 422, 409, 355, 353, 351])).
% 1.32/1.47 tff(430,plain,
% 1.32/1.47 ($false),
% 1.32/1.47 inference(unit_resolution,[status(thm)],[429, 327, 319, 233])).
% 1.32/1.47 % SZS output end Proof
% 1.32/1.47 % E exiting
%------------------------------------------------------------------------------