%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP629+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:08:13 AM UTC 2025
% Result : Theorem 90.16s 90.44s
% Output : Proof 90.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP629+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 16:30:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 90.16/90.44 % SZS status Theorem
% 90.16/90.44 % SZS output start Proof
% 90.16/90.44 tff(v1_xboole_0_type, type, (
% 90.16/90.44 v1_xboole_0: $i > $o)).
% 90.16/90.44 tff(u1_struct_0_type, type, (
% 90.16/90.44 u1_struct_0: $i > $i)).
% 90.16/90.44 tff(tptp_fun_A_0_type, type, (
% 90.16/90.44 tptp_fun_A_0: $i)).
% 90.16/90.44 tff(k1_xboole_0_type, type, (
% 90.16/90.44 k1_xboole_0: $i)).
% 90.16/90.44 tff(k1_funct_1_type, type, (
% 90.16/90.44 k1_funct_1: ( $i * $i ) > $i)).
% 90.16/90.44 tff(k2_group_3_type, type, (
% 90.16/90.44 k2_group_3: ( $i * $i * $i ) > $i)).
% 90.16/90.44 tff(k2_group_1_type, type, (
% 90.16/90.44 k2_group_1: $i > $i)).
% 90.16/90.44 tff(tptp_fun_E_24_type, type, (
% 90.16/90.44 tptp_fun_E_24: ( $i * $i * $i ) > $i)).
% 90.16/90.44 tff(k6_autgroup_type, type, (
% 90.16/90.44 k6_autgroup: ( $i * $i ) > $i)).
% 90.16/90.44 tff(k5_relat_1_type, type, (
% 90.16/90.44 k5_relat_1: ( $i * $i ) > $i)).
% 90.16/90.44 tff(tptp_fun_B_1_type, type, (
% 90.16/90.44 tptp_fun_B_1: $i)).
% 90.16/90.44 tff(k3_group_1_type, type, (
% 90.16/90.44 k3_group_1: ( $i * $i ) > $i)).
% 90.16/90.44 tff(k8_funct_2_type, type, (
% 90.16/90.44 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 90.16/90.44 tff(m1_subset_1_type, type, (
% 90.16/90.44 m1_subset_1: ( $i * $i ) > $o)).
% 90.16/90.44 tff(v1_funct_1_type, type, (
% 90.16/90.44 v1_funct_1: $i > $o)).
% 90.16/90.44 tff(k7_funct_2_type, type, (
% 90.16/90.44 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 90.16/90.44 tff(m1_relset_1_type, type, (
% 90.16/90.44 m1_relset_1: ( $i * $i * $i ) > $o)).
% 90.16/90.44 tff(m2_relset_1_type, type, (
% 90.16/90.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 90.16/90.44 tff(v1_funct_2_type, type, (
% 90.16/90.44 v1_funct_2: ( $i * $i * $i ) > $o)).
% 90.16/90.44 tff(m2_fraenkel_type, type, (
% 90.16/90.44 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 90.16/90.44 tff(k4_autgroup_type, type, (
% 90.16/90.44 k4_autgroup: $i > $i)).
% 90.16/90.44 tff(m1_fraenkel_type, type, (
% 90.16/90.44 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 90.16/90.44 tff(v4_group_1_type, type, (
% 90.16/90.44 v4_group_1: $i > $o)).
% 90.16/90.44 tff(v3_group_1_type, type, (
% 90.16/90.44 v3_group_1: $i > $o)).
% 90.16/90.44 tff(l1_group_1_type, type, (
% 90.16/90.44 l1_group_1: $i > $o)).
% 90.16/90.44 tff(v1_group_1_type, type, (
% 90.16/90.44 v1_group_1: $i > $o)).
% 90.16/90.44 tff(v3_struct_0_type, type, (
% 90.16/90.44 v3_struct_0: $i > $o)).
% 90.16/90.44 tff(l1_struct_0_type, type, (
% 90.16/90.44 l1_struct_0: $i > $o)).
% 90.16/90.44 tff(tptp_fun_D_2_type, type, (
% 90.16/90.44 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 90.16/90.44 tff(g1_group_1_type, type, (
% 90.16/90.44 g1_group_1: ( $i * $i ) > $i)).
% 90.16/90.44 tff(u1_group_1_type, type, (
% 90.16/90.44 u1_group_1: $i > $i)).
% 90.16/90.44 tff(r2_hidden_type, type, (
% 90.16/90.44 r2_hidden: ( $i * $i ) > $o)).
% 90.16/90.44 tff(v1_relat_1_type, type, (
% 90.16/90.44 v1_relat_1: $i > $o)).
% 90.16/90.44 tff(v1_fraenkel_type, type, (
% 90.16/90.44 v1_fraenkel: $i > $o)).
% 90.16/90.44 tff(1,plain,
% 90.16/90.44 ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) <=> (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.16/90.44 inference(commutativity,[status(thm)],[])).
% 90.16/90.44 tff(2,plain,
% 90.16/90.44 (^[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)))),
% 90.16/90.44 inference(bind,[status(th)],[])).
% 90.16/90.44 tff(3,plain,
% 90.16/90.44 (![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))),
% 90.16/90.44 inference(quant_intro,[status(thm)],[2])).
% 90.16/90.44 tff(4,plain,
% 90.16/90.44 (![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))),
% 90.16/90.44 inference(rewrite,[status(thm)],[])).
% 90.16/90.44 tff(5,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 90.16/90.44 tff(6,plain,
% 90.16/90.44 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 90.16/90.44 tff(7,plain,(
% 90.16/90.44 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 90.16/90.44 inference(skolemize,[status(sab)],[6])).
% 90.16/90.44 tff(8,plain,
% 90.16/90.44 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 90.16/90.44 tff(9,plain,
% 90.16/90.44 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.16/90.44 inference(quant_inst,[status(thm)],[])).
% 90.16/90.44 tff(10,plain,
% 90.16/90.44 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.44 inference(unit_resolution,[status(thm)],[9, 8])).
% 90.16/90.44 tff(11,plain,
% 90.16/90.44 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k4_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(k4_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))))),
% 90.16/90.44 inference(bind,[status(th)],[])).
% 90.16/90.44 tff(12,plain,
% 90.16/90.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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)))),
% 90.16/90.44 inference(quant_intro,[status(thm)],[11])).
% 90.16/90.44 tff(13,plain,
% 90.16/90.44 (^[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(k4_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(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_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)))))),
% 90.16/90.44 inference(bind,[status(th)],[])).
% 90.16/90.44 tff(14,plain,
% 90.16/90.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 90.16/90.44 inference(quant_intro,[status(thm)],[13])).
% 90.16/90.44 tff(15,plain,
% 90.16/90.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 90.16/90.44 inference(rewrite,[status(thm)],[])).
% 90.16/90.44 tff(16,plain,
% 90.16/90.44 (^[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(k4_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(k4_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(k4_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(k4_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(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 90.16/90.44 inference(bind,[status(th)],[])).
% 90.16/90.44 tff(17,plain,
% 90.16/90.44 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_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(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 90.16/90.44 inference(quant_intro,[status(thm)],[16])).
% 90.16/90.44 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)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 90.16/90.44 tff(19,plain,
% 90.16/90.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 90.16/90.44 tff(20,plain,
% 90.16/90.44 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 90.16/90.44 tff(21,plain,(
% 90.16/90.44 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 90.16/90.44 inference(skolemize,[status(sab)],[20])).
% 90.16/90.44 tff(22,plain,
% 90.16/90.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 90.16/90.44 tff(23,plain,
% 90.16/90.44 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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)))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[22, 12])).
% 90.16/90.44 tff(24,plain,
% 90.16/90.44 ((((~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)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))))) <=> ((~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) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0))))))),
% 90.16/90.44 inference(rewrite,[status(thm)],[])).
% 90.16/90.44 tff(25,plain,
% 90.16/90.44 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A))))))),
% 90.16/90.44 inference(rewrite,[status(thm)],[])).
% 90.16/90.44 tff(26,plain,
% 90.16/90.44 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A))))))),
% 90.16/90.44 inference(rewrite,[status(thm)],[])).
% 90.16/90.44 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] : (m1_subset_1(B, u1_struct_0(A)) => (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_autgroup')).
% 90.16/90.44 tff(28,plain,
% 90.16/90.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A)))))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 90.16/90.44 tff(29,plain,
% 90.16/90.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A)))))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[28, 25])).
% 90.16/90.44 tff(30,plain,
% 90.16/90.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A)))))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[29, 25])).
% 90.16/90.44 tff(31,plain,
% 90.16/90.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k3_group_1(A, B)), k6_autgroup(A, B)) = k6_autgroup(A, k2_group_1(A)))))),
% 90.16/90.44 inference(modus_ponens,[status(thm)],[30, 25])).
% 90.16/90.44 tff(32,plain,
% 90.16/90.44 ((~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) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[31, 24])).
% 90.16/90.45 tff(33,plain,
% 90.16/90.45 (l1_group_1(A!0)),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(34,plain,
% 90.16/90.45 (v4_group_1(A!0)),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(35,plain,
% 90.16/90.45 (v3_group_1(A!0)),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(36,plain,
% 90.16/90.45 (v1_group_1(A!0)),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(37,plain,
% 90.16/90.45 (~v3_struct_0(A!0)),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(38,plain,
% 90.16/90.45 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(39,plain,
% 90.16/90.45 ((v3_struct_0(A!0) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(40,plain,
% 90.16/90.45 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.16/90.45 inference(monotonicity,[status(thm)],[39])).
% 90.16/90.45 tff(41,plain,
% 90.16/90.45 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.16/90.45 inference(transitivity,[status(thm)],[40, 38])).
% 90.16/90.45 tff(42,plain,
% 90.16/90.45 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_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)))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(43,plain,
% 90.16/90.45 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_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(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 90.16/90.45 tff(44,plain,
% 90.16/90.45 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[43, 37, 36, 35, 34, 33, 23])).
% 90.16/90.45 tff(45,plain,
% 90.16/90.45 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(46,plain,
% 90.16/90.45 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[45])).
% 90.16/90.45 tff(47,plain,
% 90.16/90.45 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(48,plain,
% 90.16/90.45 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(49,plain,
% 90.16/90.45 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[48])).
% 90.16/90.45 tff(50,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 90.16/90.45 tff(51,plain,
% 90.16/90.45 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 90.16/90.45 tff(52,plain,
% 90.16/90.45 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 90.16/90.45 tff(53,plain,(
% 90.16/90.45 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(skolemize,[status(sab)],[52])).
% 90.16/90.45 tff(54,plain,
% 90.16/90.45 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[53, 46])).
% 90.16/90.45 tff(55,plain,
% 90.16/90.45 (((~![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)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(56,plain,
% 90.16/90.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(57,plain,
% 90.16/90.45 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 90.16/90.45 tff(58,plain,
% 90.16/90.45 (l1_struct_0(A!0)),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[57, 33, 54])).
% 90.16/90.45 tff(59,plain,
% 90.16/90.45 (^[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))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(60,plain,
% 90.16/90.45 (![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)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[59])).
% 90.16/90.45 tff(61,plain,
% 90.16/90.45 (^[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)))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(62,plain,
% 90.16/90.45 (![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)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[61])).
% 90.16/90.45 tff(63,plain,
% 90.16/90.45 (![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))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(64,plain,
% 90.16/90.45 (^[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)))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(65,plain,
% 90.16/90.45 (![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))))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[64])).
% 90.16/90.45 tff(66,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 90.16/90.45 tff(67,plain,
% 90.16/90.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 90.16/90.45 tff(68,plain,
% 90.16/90.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 90.16/90.45 tff(69,plain,(
% 90.16/90.45 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 90.16/90.45 inference(skolemize,[status(sab)],[68])).
% 90.16/90.45 tff(70,plain,
% 90.16/90.45 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 90.16/90.45 tff(71,plain,
% 90.16/90.45 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[70, 60])).
% 90.16/90.45 tff(72,plain,
% 90.16/90.45 (((~![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))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(73,plain,
% 90.16/90.45 ((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))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(74,plain,
% 90.16/90.45 (((~![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)))))),
% 90.16/90.45 inference(monotonicity,[status(thm)],[73])).
% 90.16/90.45 tff(75,plain,
% 90.16/90.45 (((~![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))))),
% 90.16/90.45 inference(transitivity,[status(thm)],[74, 72])).
% 90.16/90.45 tff(76,plain,
% 90.16/90.45 ((~![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)))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(77,plain,
% 90.16/90.45 ((~![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)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 90.16/90.45 tff(78,plain,
% 90.16/90.45 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[77, 37, 71])).
% 90.16/90.45 tff(79,plain,
% 90.16/90.45 (~v1_xboole_0(u1_struct_0(A!0))),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[78, 58])).
% 90.16/90.45 tff(80,plain,
% 90.16/90.45 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(81,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[80])).
% 90.16/90.45 tff(82,plain,
% 90.16/90.45 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(83,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[82])).
% 90.16/90.45 tff(84,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(transitivity,[status(thm)],[83, 81])).
% 90.16/90.45 tff(85,plain,
% 90.16/90.45 (^[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))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(86,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, 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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[85])).
% 90.16/90.45 tff(87,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, 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)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(88,plain,
% 90.16/90.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> (m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), rewrite((m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), (![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(89,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, 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)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[88])).
% 90.16/90.45 tff(90,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_fraenkel')).
% 90.16/90.45 tff(91,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 90.16/90.45 tff(92,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[91, 87])).
% 90.16/90.45 tff(93,plain,(
% 90.16/90.45 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 90.16/90.45 inference(skolemize,[status(sab)],[92])).
% 90.16/90.45 tff(94,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[93, 86])).
% 90.16/90.45 tff(95,plain,
% 90.16/90.45 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[94, 84])).
% 90.16/90.45 tff(96,plain,
% 90.16/90.45 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(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)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(97,plain,
% 90.16/90.45 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(98,plain,
% 90.16/90.45 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 90.16/90.45 tff(99,plain,
% 90.16/90.45 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[98, 95, 79, 44])).
% 90.16/90.45 tff(100,plain,
% 90.16/90.45 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(101,plain,
% 90.16/90.45 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[100])).
% 90.16/90.45 tff(102,plain,
% 90.16/90.45 (^[A: $i, B: $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) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(103,plain,
% 90.16/90.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[102])).
% 90.16/90.45 tff(104,plain,
% 90.16/90.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(105,plain,
% 90.16/90.45 (^[A: $i, B: $i] : trans(monotonicity(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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, 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_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), ((((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))))),
% 90.16/90.45 inference(bind,[status(th)],[])).
% 90.16/90.45 tff(106,plain,
% 90.16/90.45 (![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 90.16/90.45 inference(quant_intro,[status(thm)],[105])).
% 90.16/90.45 tff(107,axiom,(![A: $i, B: $i] : (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_autgroup')).
% 90.16/90.45 tff(108,plain,
% 90.16/90.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[107, 106])).
% 90.16/90.45 tff(109,plain,
% 90.16/90.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[108, 104])).
% 90.16/90.45 tff(110,plain,(
% 90.16/90.45 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)))),
% 90.16/90.45 inference(skolemize,[status(sab)],[109])).
% 90.16/90.45 tff(111,plain,
% 90.16/90.45 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[110, 103])).
% 90.16/90.45 tff(112,plain,
% 90.16/90.45 (![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[111, 101])).
% 90.16/90.45 tff(113,plain,
% 90.16/90.45 (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0))))),
% 90.16/90.45 inference(and_elim,[status(thm)],[32])).
% 90.16/90.45 tff(114,plain,
% 90.16/90.45 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 90.16/90.45 inference(or_elim,[status(thm)],[113])).
% 90.16/90.45 tff(115,plain,
% 90.16/90.45 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(116,plain,
% 90.16/90.45 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(117,plain,
% 90.16/90.45 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))))),
% 90.16/90.45 inference(monotonicity,[status(thm)],[116])).
% 90.16/90.45 tff(118,plain,
% 90.16/90.45 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)))),
% 90.16/90.45 inference(transitivity,[status(thm)],[117, 115])).
% 90.16/90.45 tff(119,plain,
% 90.16/90.45 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(120,plain,
% 90.16/90.45 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 90.16/90.45 tff(121,plain,
% 90.16/90.45 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 90.16/90.45 inference(unit_resolution,[status(thm)],[120, 37, 36, 35, 34, 33, 114, 112])).
% 90.16/90.45 tff(122,plain,
% 90.16/90.45 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), 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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.45 inference(rewrite,[status(thm)],[])).
% 90.16/90.45 tff(123,plain,
% 90.16/90.45 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.45 inference(quant_inst,[status(thm)],[])).
% 90.16/90.45 tff(124,plain,
% 90.16/90.45 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.16/90.45 inference(modus_ponens,[status(thm)],[123, 122])).
% 90.16/90.46 tff(125,plain,
% 90.16/90.46 (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[124, 121, 99])).
% 90.16/90.46 tff(126,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(127,plain,
% 90.16/90.46 (m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[126, 125])).
% 90.16/90.46 tff(128,plain,
% 90.16/90.46 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(129,plain,
% 90.16/90.46 ((~(m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 90.16/90.46 tff(130,plain,
% 90.16/90.46 (m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[129, 10])).
% 90.16/90.46 tff(131,plain,
% 90.16/90.46 (^[A: $i, B: $i] : refl((m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(132,plain,
% 90.16/90.46 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[131])).
% 90.16/90.46 tff(133,plain,
% 90.16/90.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(134,plain,
% 90.16/90.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[133])).
% 90.16/90.46 tff(135,plain,
% 90.16/90.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(136,plain,
% 90.16/90.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(137,plain,
% 90.16/90.46 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[136])).
% 90.16/90.46 tff(138,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_group_1')).
% 90.16/90.46 tff(139,plain,
% 90.16/90.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 90.16/90.46 tff(140,plain,
% 90.16/90.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 90.16/90.46 tff(141,plain,(
% 90.16/90.46 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_group_1(A, B), u1_struct_0(A)))),
% 90.16/90.46 inference(skolemize,[status(sab)],[140])).
% 90.16/90.46 tff(142,plain,
% 90.16/90.46 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[141, 134])).
% 90.16/90.46 tff(143,plain,
% 90.16/90.46 (![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[142, 132])).
% 90.16/90.46 tff(144,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(145,plain,
% 90.16/90.46 ((m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(146,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 90.16/90.46 inference(monotonicity,[status(thm)],[145])).
% 90.16/90.46 tff(147,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 90.16/90.46 inference(transitivity,[status(thm)],[146, 144])).
% 90.16/90.46 tff(148,plain,
% 90.16/90.46 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)))),
% 90.16/90.46 inference(quant_inst,[status(thm)],[])).
% 90.16/90.46 tff(149,plain,
% 90.16/90.46 ((~![A: $i, B: $i] : (m1_subset_1(k3_group_1(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 90.16/90.46 tff(150,plain,
% 90.16/90.46 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[149, 37, 35, 34, 33, 114, 143])).
% 90.16/90.46 tff(151,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(152,plain,
% 90.16/90.46 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(153,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))))),
% 90.16/90.46 inference(monotonicity,[status(thm)],[152])).
% 90.16/90.46 tff(154,plain,
% 90.16/90.46 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))))),
% 90.16/90.46 inference(transitivity,[status(thm)],[153, 151])).
% 90.16/90.46 tff(155,plain,
% 90.16/90.46 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 90.16/90.46 inference(quant_inst,[status(thm)],[])).
% 90.16/90.46 tff(156,plain,
% 90.16/90.46 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 90.16/90.46 tff(157,plain,
% 90.16/90.46 (m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[156, 37, 36, 35, 34, 33, 112, 150])).
% 90.16/90.46 tff(158,plain,
% 90.16/90.46 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), 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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(159,plain,
% 90.16/90.46 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.16/90.46 inference(quant_inst,[status(thm)],[])).
% 90.16/90.46 tff(160,plain,
% 90.16/90.46 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[159, 158])).
% 90.16/90.46 tff(161,plain,
% 90.16/90.46 (~((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[160, 157, 99])).
% 90.16/90.46 tff(162,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(163,plain,
% 90.16/90.46 (v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[162, 161])).
% 90.16/90.46 tff(164,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(165,plain,
% 90.16/90.46 (v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[164, 125])).
% 90.16/90.46 tff(166,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, B!1))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(167,plain,
% 90.16/90.46 (v1_funct_1(k6_autgroup(A!0, B!1))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[166, 125])).
% 90.16/90.46 tff(168,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(169,plain,
% 90.16/90.46 (v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[168, 161])).
% 90.16/90.46 tff(170,plain,
% 90.16/90.46 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.16/90.46 inference(quant_inst,[status(thm)],[])).
% 90.16/90.46 tff(171,plain,
% 90.16/90.46 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[170, 8])).
% 90.16/90.46 tff(172,plain,
% 90.16/90.46 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(173,plain,
% 90.16/90.46 (m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[172, 161])).
% 90.16/90.46 tff(174,plain,
% 90.16/90.46 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(tautology,[status(thm)],[])).
% 90.16/90.46 tff(175,plain,
% 90.16/90.46 ((~(m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[174, 173])).
% 90.16/90.46 tff(176,plain,
% 90.16/90.46 (m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.16/90.46 inference(unit_resolution,[status(thm)],[175, 171])).
% 90.16/90.46 tff(177,plain,
% 90.16/90.46 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(178,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[177])).
% 90.16/90.46 tff(179,plain,
% 90.16/90.46 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(180,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[179])).
% 90.16/90.46 tff(181,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(182,plain,
% 90.16/90.46 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 90.16/90.46 inference(bind,[status(th)],[])).
% 90.16/90.46 tff(183,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 90.16/90.46 inference(quant_intro,[status(thm)],[182])).
% 90.16/90.46 tff(184,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 90.16/90.46 tff(185,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 90.16/90.46 tff(186,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[185, 181])).
% 90.16/90.46 tff(187,plain,(
% 90.16/90.46 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 90.16/90.46 inference(skolemize,[status(sab)],[186])).
% 90.16/90.46 tff(188,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[187, 180])).
% 90.16/90.46 tff(189,plain,
% 90.16/90.46 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 90.16/90.46 inference(modus_ponens,[status(thm)],[188, 178])).
% 90.16/90.46 tff(190,plain,
% 90.16/90.46 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(191,plain,
% 90.16/90.46 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))))),
% 90.16/90.46 inference(rewrite,[status(thm)],[])).
% 90.16/90.46 tff(192,plain,
% 90.16/90.46 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))))),
% 90.16/90.47 inference(monotonicity,[status(thm)],[191])).
% 90.16/90.47 tff(193,plain,
% 90.16/90.47 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))))),
% 90.16/90.47 inference(transitivity,[status(thm)],[192, 190])).
% 90.16/90.47 tff(194,plain,
% 90.16/90.47 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.16/90.47 inference(quant_inst,[status(thm)],[])).
% 90.16/90.47 tff(195,plain,
% 90.16/90.47 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.16/90.47 inference(modus_ponens,[status(thm)],[194, 193])).
% 90.16/90.47 tff(196,plain,
% 90.16/90.47 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.16/90.47 inference(unit_resolution,[status(thm)],[195, 189])).
% 90.16/90.47 tff(197,plain,
% 90.16/90.47 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))),
% 90.16/90.47 inference(unit_resolution,[status(thm)],[196, 176, 79, 169, 167, 165, 163, 130])).
% 90.16/90.47 tff(198,plain,
% 90.16/90.47 (k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))),
% 90.16/90.47 inference(symmetry,[status(thm)],[197])).
% 90.16/90.47 tff(199,plain,
% 90.16/90.47 (v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) <=> v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.16/90.47 inference(monotonicity,[status(thm)],[198])).
% 90.16/90.47 tff(200,plain,
% 90.16/90.47 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) <=> v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.16/90.47 inference(symmetry,[status(thm)],[199])).
% 90.16/90.47 tff(201,plain,
% 90.16/90.47 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))),
% 90.16/90.47 inference(bind,[status(th)],[])).
% 90.16/90.47 tff(202,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 90.16/90.47 inference(quant_intro,[status(thm)],[201])).
% 90.16/90.47 tff(203,plain,
% 90.16/90.47 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), rewrite((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))))),
% 90.16/90.47 inference(bind,[status(th)],[])).
% 90.16/90.47 tff(204,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 90.16/90.47 inference(quant_intro,[status(thm)],[203])).
% 90.16/90.47 tff(205,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 90.16/90.47 inference(rewrite,[status(thm)],[])).
% 90.16/90.47 tff(206,plain,
% 90.16/90.47 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), rewrite(((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 90.16/90.47 inference(bind,[status(th)],[])).
% 90.16/90.47 tff(207,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 90.16/90.47 inference(quant_intro,[status(thm)],[206])).
% 90.16/90.47 tff(208,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_funct_2')).
% 90.16/90.47 tff(209,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 90.16/90.47 inference(modus_ponens,[status(thm)],[208, 207])).
% 90.16/90.47 tff(210,plain,
% 90.16/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[209, 205])).
% 90.25/90.47 tff(211,plain,(
% 90.25/90.47 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 90.25/90.47 inference(skolemize,[status(sab)],[210])).
% 90.25/90.47 tff(212,plain,
% 90.25/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[211, 204])).
% 90.25/90.47 tff(213,plain,
% 90.25/90.47 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[212, 202])).
% 90.25/90.47 tff(214,plain,
% 90.25/90.47 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.25/90.47 inference(rewrite,[status(thm)],[])).
% 90.25/90.47 tff(215,plain,
% 90.25/90.47 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.25/90.47 inference(quant_inst,[status(thm)],[])).
% 90.25/90.47 tff(216,plain,
% 90.25/90.47 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[215, 214])).
% 90.25/90.47 tff(217,plain,
% 90.25/90.47 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.25/90.47 inference(unit_resolution,[status(thm)],[216, 213])).
% 90.25/90.47 tff(218,plain,
% 90.25/90.47 (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.25/90.47 inference(unit_resolution,[status(thm)],[217, 176, 79, 169, 167, 165, 163, 130])).
% 90.25/90.47 tff(219,plain,
% 90.25/90.47 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(tautology,[status(thm)],[])).
% 90.25/90.47 tff(220,plain,
% 90.25/90.47 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(unit_resolution,[status(thm)],[219, 218])).
% 90.25/90.47 tff(221,plain,
% 90.25/90.47 (v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[220, 200])).
% 90.25/90.47 tff(222,plain,
% 90.25/90.47 ((k6_autgroup(A!0, k2_group_1(A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) <=> (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))),
% 90.25/90.47 inference(commutativity,[status(thm)],[])).
% 90.25/90.47 tff(223,plain,
% 90.25/90.47 ((k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) <=> (k6_autgroup(A!0, k2_group_1(A!0)) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(monotonicity,[status(thm)],[198])).
% 90.25/90.47 tff(224,plain,
% 90.25/90.47 ((k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) <=> (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))),
% 90.25/90.47 inference(transitivity,[status(thm)],[223, 222])).
% 90.25/90.47 tff(225,plain,
% 90.25/90.47 ((k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0))) <=> (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(symmetry,[status(thm)],[224])).
% 90.25/90.47 tff(226,plain,
% 90.25/90.47 ((~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))) <=> (~(k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))))),
% 90.25/90.47 inference(monotonicity,[status(thm)],[225])).
% 90.25/90.47 tff(227,plain,
% 90.25/90.47 (~(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)) = k6_autgroup(A!0, k2_group_1(A!0)))),
% 90.25/90.47 inference(or_elim,[status(thm)],[113])).
% 90.25/90.47 tff(228,plain,
% 90.25/90.47 (~(k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))),
% 90.25/90.47 inference(modus_ponens,[status(thm)],[227, 226])).
% 90.25/90.47 tff(229,plain,
% 90.25/90.47 (m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(monotonicity,[status(thm)],[198])).
% 90.25/90.48 tff(230,plain,
% 90.25/90.48 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(symmetry,[status(thm)],[229])).
% 90.25/90.48 tff(231,plain,
% 90.25/90.48 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(tautology,[status(thm)],[])).
% 90.25/90.48 tff(232,plain,
% 90.25/90.48 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[231, 218])).
% 90.25/90.48 tff(233,plain,
% 90.25/90.48 (m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[232, 230])).
% 90.25/90.48 tff(234,plain,
% 90.25/90.48 (v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(monotonicity,[status(thm)],[198])).
% 90.25/90.48 tff(235,plain,
% 90.25/90.48 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(symmetry,[status(thm)],[234])).
% 90.25/90.48 tff(236,plain,
% 90.25/90.48 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(tautology,[status(thm)],[])).
% 90.25/90.48 tff(237,plain,
% 90.25/90.48 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[236, 218])).
% 90.25/90.48 tff(238,plain,
% 90.25/90.48 (v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[237, 235])).
% 90.25/90.48 tff(239,plain,
% 90.25/90.48 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(240,plain,
% 90.25/90.48 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[239])).
% 90.25/90.48 tff(241,plain,
% 90.25/90.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(242,plain,
% 90.25/90.48 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[241])).
% 90.25/90.48 tff(243,plain,
% 90.25/90.48 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(244,plain,
% 90.25/90.48 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(245,plain,
% 90.25/90.48 (![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[244])).
% 90.25/90.48 tff(246,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_group_1(A)) => m1_subset_1(k2_group_1(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_group_1')).
% 90.25/90.48 tff(247,plain,
% 90.25/90.48 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[246, 245])).
% 90.25/90.48 tff(248,plain,
% 90.25/90.48 (![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[247, 243])).
% 90.25/90.48 tff(249,plain,(
% 90.25/90.48 ![A: $i] : ((~((~v3_struct_0(A)) & l1_group_1(A))) | m1_subset_1(k2_group_1(A), u1_struct_0(A)))),
% 90.25/90.48 inference(skolemize,[status(sab)],[248])).
% 90.25/90.48 tff(250,plain,
% 90.25/90.48 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[249, 242])).
% 90.25/90.48 tff(251,plain,
% 90.25/90.48 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[250, 240])).
% 90.25/90.48 tff(252,plain,
% 90.25/90.48 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(253,plain,
% 90.25/90.48 ((v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(254,plain,
% 90.25/90.48 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 90.25/90.48 inference(monotonicity,[status(thm)],[253])).
% 90.25/90.48 tff(255,plain,
% 90.25/90.48 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 90.25/90.48 inference(transitivity,[status(thm)],[254, 252])).
% 90.25/90.48 tff(256,plain,
% 90.25/90.48 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | (v3_struct_0(A!0) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)))),
% 90.25/90.48 inference(quant_inst,[status(thm)],[])).
% 90.25/90.48 tff(257,plain,
% 90.25/90.48 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k2_group_1(A), u1_struct_0(A)) | (~l1_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[256, 255])).
% 90.25/90.48 tff(258,plain,
% 90.25/90.48 (m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[257, 37, 33, 251])).
% 90.25/90.48 tff(259,plain,
% 90.25/90.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(260,plain,
% 90.25/90.48 ((v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(261,plain,
% 90.25/90.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))))),
% 90.25/90.48 inference(monotonicity,[status(thm)],[260])).
% 90.25/90.48 tff(262,plain,
% 90.25/90.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))))),
% 90.25/90.48 inference(transitivity,[status(thm)],[261, 259])).
% 90.25/90.48 tff(263,plain,
% 90.25/90.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (v3_struct_0(A!0) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 90.25/90.48 inference(quant_inst,[status(thm)],[])).
% 90.25/90.48 tff(264,plain,
% 90.25/90.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m2_fraenkel(k6_autgroup(A, B), u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v1_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)) | m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0)))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[263, 262])).
% 90.25/90.48 tff(265,plain,
% 90.25/90.48 (m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[264, 37, 36, 35, 34, 33, 112, 258])).
% 90.25/90.48 tff(266,plain,
% 90.25/90.48 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(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), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(267,plain,
% 90.25/90.48 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 90.25/90.48 inference(quant_inst,[status(thm)],[])).
% 90.25/90.48 tff(268,plain,
% 90.25/90.48 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[267, 266])).
% 90.25/90.48 tff(269,plain,
% 90.25/90.48 (~((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[268, 265, 99])).
% 90.25/90.48 tff(270,plain,
% 90.25/90.48 (((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(tautology,[status(thm)],[])).
% 90.25/90.48 tff(271,plain,
% 90.25/90.48 (m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[270, 269])).
% 90.25/90.48 tff(272,plain,
% 90.25/90.48 (((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(tautology,[status(thm)],[])).
% 90.25/90.48 tff(273,plain,
% 90.25/90.48 (v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[272, 269])).
% 90.25/90.48 tff(274,plain,
% 90.25/90.48 (((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))),
% 90.25/90.48 inference(tautology,[status(thm)],[])).
% 90.25/90.48 tff(275,plain,
% 90.25/90.48 (v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))),
% 90.25/90.48 inference(unit_resolution,[status(thm)],[274, 269])).
% 90.25/90.48 tff(276,plain,
% 90.25/90.48 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(277,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[276])).
% 90.25/90.48 tff(278,plain,
% 90.25/90.48 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(279,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[278])).
% 90.25/90.48 tff(280,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(transitivity,[status(thm)],[279, 277])).
% 90.25/90.48 tff(281,plain,
% 90.25/90.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) <=> (~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> (~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))))), rewrite((~(~((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))), ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), (((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))) <=> ((C = D) | ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))))), rewrite(((C = D) | ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))) <=> ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))), (((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))) <=> ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))), (![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))) <=> ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))))) <=> (((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))), rewrite((((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B))) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))))) <=> ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(282,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[281])).
% 90.25/90.48 tff(283,plain,
% 90.25/90.48 (^[A: $i, B: $i, C: $i] : rewrite(((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(284,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[283])).
% 90.25/90.48 tff(285,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(286,plain,
% 90.25/90.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite((m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) <=> ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E))))), (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) <=> ![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E))))), ((![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)) <=> (![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)))), rewrite((![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)) <=> ((~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (C = D))), ((![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)) <=> ((~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (C = D)))), ((((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D))) <=> ((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) => ((~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (C = D))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) => ((~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (C = D))) <=> ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D))) <=> ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D))) <=> ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B)) => ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))))),
% 90.25/90.48 inference(bind,[status(th)],[])).
% 90.25/90.48 tff(287,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(quant_intro,[status(thm)],[286])).
% 90.25/90.48 tff(288,axiom,(![A: $i, B: $i, C: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m2_relset_1(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => (![E: $i] : (m1_subset_1(E, A) => (k1_funct_1(C, E) = k1_funct_1(D, E))) => (C = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t113_funct_2')).
% 90.25/90.48 tff(289,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[288, 287])).
% 90.25/90.48 tff(290,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~![E: $i] : ((~m1_subset_1(E, A)) | (k1_funct_1(C, E) = k1_funct_1(D, E)))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[289, 285])).
% 90.25/90.48 tff(291,plain,(
% 90.25/90.48 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))),
% 90.25/90.48 inference(skolemize,[status(sab)],[290])).
% 90.25/90.48 tff(292,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m2_relset_1(C, A, B))) | ![D: $i] : ((C = D) | (~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A)))))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[291, 284])).
% 90.25/90.48 tff(293,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[292, 282])).
% 90.25/90.48 tff(294,plain,
% 90.25/90.48 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))),
% 90.25/90.48 inference(modus_ponens,[status(thm)],[293, 280])).
% 90.25/90.48 tff(295,plain,
% 90.25/90.48 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | ((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(296,plain,
% 90.25/90.48 (((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) <=> ((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.48 inference(rewrite,[status(thm)],[])).
% 90.25/90.48 tff(297,plain,
% 90.25/90.48 (^[D: $i] : rewrite(((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.49 inference(bind,[status(th)],[])).
% 90.25/90.49 tff(298,plain,
% 90.25/90.49 (![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.25/90.49 inference(quant_intro,[status(thm)],[297])).
% 90.25/90.49 tff(299,plain,
% 90.25/90.49 (((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.49 inference(monotonicity,[status(thm)],[298])).
% 90.25/90.49 tff(300,plain,
% 90.25/90.49 (((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.49 inference(transitivity,[status(thm)],[299, 296])).
% 90.25/90.49 tff(301,plain,
% 90.25/90.49 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | ((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | ((~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))))),
% 90.25/90.49 inference(monotonicity,[status(thm)],[300])).
% 90.25/90.49 tff(302,plain,
% 90.25/90.49 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | ((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.25/90.49 inference(transitivity,[status(thm)],[301, 295])).
% 90.25/90.49 tff(303,plain,
% 90.25/90.49 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | ((~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 90.25/90.49 inference(quant_inst,[status(thm)],[])).
% 90.25/90.49 tff(304,plain,
% 90.25/90.49 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | ![D: $i] : ((C = D) | (~((~m1_subset_1(tptp_fun_E_24(D, C, A), A)) | (k1_funct_1(C, tptp_fun_E_24(D, C, A)) = k1_funct_1(D, tptp_fun_E_24(D, C, A))))) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.25/90.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 90.25/90.49 tff(305,plain,
% 90.25/90.49 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.25/90.49 inference(unit_resolution,[status(thm)],[304, 294, 275, 273, 271])).
% 90.25/90.49 tff(306,plain,
% 90.25/90.49 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | ((~v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | (~v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.25/90.49 inference(rewrite,[status(thm)],[])).
% 90.25/90.49 tff(307,plain,
% 90.25/90.49 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | ((~v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.25/90.49 inference(quant_inst,[status(thm)],[])).
% 90.25/90.49 tff(308,plain,
% 90.25/90.49 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = D) | (~((~m1_subset_1(tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(D, tptp_fun_E_24(D, k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | (~v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))),
% 90.25/90.49 inference(modus_ponens,[status(thm)],[307, 306])).
% 90.25/90.49 tff(309,plain,
% 90.25/90.49 ((~v1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)))) | (~v1_funct_2(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))),
% 90.25/90.49 inference(unit_resolution,[status(thm)],[308, 305])).
% 90.25/90.49 tff(310,plain,
% 90.25/90.49 (~((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))),
% 90.25/90.49 inference(unit_resolution,[status(thm)],[309, 238, 233, 228, 221])).
% 90.25/90.49 tff(311,plain,
% 90.25/90.49 (((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))) | m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.25/90.49 inference(tautology,[status(thm)],[])).
% 90.25/90.49 tff(312,plain,
% 90.25/90.49 (m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.25/90.49 inference(unit_resolution,[status(thm)],[311, 310])).
% 90.25/90.49 tff(313,plain,
% 90.25/90.49 (^[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] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))))),
% 90.25/90.49 inference(bind,[status(th)],[])).
% 90.25/90.49 tff(314,plain,
% 90.25/90.49 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.25/90.49 inference(quant_intro,[status(thm)],[313])).
% 90.25/90.49 tff(315,plain,
% 90.25/90.49 (^[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] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))))),
% 90.28/90.49 inference(bind,[status(th)],[])).
% 90.28/90.49 tff(316,plain,
% 90.28/90.49 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.28/90.49 inference(quant_intro,[status(thm)],[315])).
% 90.28/90.49 tff(317,plain,
% 90.28/90.49 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.28/90.49 inference(transitivity,[status(thm)],[316, 314])).
% 90.28/90.49 tff(318,plain,
% 90.28/90.49 (^[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] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))))),
% 90.28/90.50 inference(bind,[status(th)],[])).
% 90.28/90.50 tff(319,plain,
% 90.28/90.50 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.28/90.50 inference(quant_intro,[status(thm)],[318])).
% 90.28/90.50 tff(320,plain,
% 90.28/90.50 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, 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] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))),
% 90.28/90.50 inference(rewrite,[status(thm)],[])).
% 90.28/90.50 tff(321,plain,
% 90.28/90.50 (^[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(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) <=> ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))), ((m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) <=> (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))), rewrite((m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) <=> ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))), ((m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) <=> ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))), (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) <=> ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))))),
% 90.28/90.50 inference(bind,[status(th)],[])).
% 90.28/90.50 tff(322,plain,
% 90.28/90.50 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, 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] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))),
% 90.28/90.50 inference(quant_intro,[status(thm)],[321])).
% 90.28/90.50 tff(323,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] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => ((C = k6_autgroup(A, B)) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_autgroup')).
% 90.28/90.50 tff(324,plain,
% 90.28/90.50 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))),
% 90.28/90.50 inference(modus_ponens,[status(thm)],[323, 322])).
% 90.28/90.50 tff(325,plain,
% 90.28/90.50 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | ((C = k6_autgroup(A, B)) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))))))),
% 90.28/90.50 inference(modus_ponens,[status(thm)],[324, 320])).
% 90.28/90.50 tff(326,plain,(
% 90.28/90.50 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B)))) & ((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))),
% 90.28/90.50 inference(skolemize,[status(sab)],[325])).
% 90.28/90.50 tff(327,plain,
% 90.28/90.50 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.28/90.50 inference(modus_ponens,[status(thm)],[326, 319])).
% 90.28/90.50 tff(328,plain,
% 90.28/90.50 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))),
% 90.28/90.50 inference(modus_ponens,[status(thm)],[327, 317])).
% 90.28/90.50 tff(329,plain,
% 90.28/90.50 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | 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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(rewrite,[status(thm)],[])).
% 90.28/90.50 tff(330,plain,
% 90.28/90.50 ((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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) <=> (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(rewrite,[status(thm)],[])).
% 90.28/90.50 tff(331,plain,
% 90.28/90.50 (^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(bind,[status(th)],[])).
% 90.28/90.50 tff(332,plain,
% 90.28/90.50 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))),
% 90.28/90.50 inference(quant_intro,[status(thm)],[331])).
% 90.28/90.50 tff(333,plain,
% 90.28/90.50 ((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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B))))))))))) <=> (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(monotonicity,[status(thm)],[332])).
% 90.28/90.50 tff(334,plain,
% 90.28/90.50 ((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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B))))))))))) <=> (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(transitivity,[status(thm)],[333, 330])).
% 90.28/90.50 tff(335,plain,
% 90.28/90.50 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))))),
% 90.28/90.50 inference(monotonicity,[status(thm)],[334])).
% 90.28/90.50 tff(336,plain,
% 90.28/90.50 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | 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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B)))))))))),
% 90.28/90.50 inference(transitivity,[status(thm)],[335, 329])).
% 90.28/90.50 tff(337,plain,
% 90.28/90.50 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((C = k6_autgroup(A!0, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))))))))))),
% 90.28/90.50 inference(quant_inst,[status(thm)],[])).
% 90.28/90.50 tff(338,plain,
% 90.28/90.50 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | (~((~((~(C = k6_autgroup(A, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, D) = k2_group_3(A, D, B))))) | (~((C = k6_autgroup(A, B)) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), C, tptp_fun_D_2(C, B, A)) = k2_group_3(A, tptp_fun_D_2(C, B, A), B)))))))))))) | 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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))),
% 90.28/90.50 inference(modus_ponens,[status(thm)],[337, 336])).
% 90.28/90.50 tff(339,plain,
% 90.28/90.50 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))),
% 90.28/90.50 inference(unit_resolution,[status(thm)],[338, 37, 36, 35, 34, 33, 328])).
% 90.28/90.50 tff(340,plain,
% 90.28/90.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0)))))))))),
% 90.28/90.50 inference(rewrite,[status(thm)],[])).
% 90.28/90.50 tff(341,plain,
% 90.28/90.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0)))))))))),
% 90.28/90.51 inference(quant_inst,[status(thm)],[])).
% 90.28/90.51 tff(342,plain,
% 90.28/90.51 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(k2_group_1(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[341, 340])).
% 90.28/90.51 tff(343,plain,
% 90.28/90.51 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))),
% 90.28/90.51 inference(unit_resolution,[status(thm)],[342, 258, 339])).
% 90.28/90.51 tff(344,plain,
% 90.28/90.51 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(345,plain,
% 90.28/90.51 (((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0)))))))) <=> ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(346,plain,
% 90.28/90.51 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))))),
% 90.28/90.51 inference(monotonicity,[status(thm)],[345])).
% 90.28/90.51 tff(347,plain,
% 90.28/90.51 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))),
% 90.28/90.51 inference(transitivity,[status(thm)],[346, 344])).
% 90.28/90.51 tff(348,plain,
% 90.28/90.51 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (k6_autgroup(A!0, k2_group_1(A!0)) = k6_autgroup(A!0, k2_group_1(A!0))))))))),
% 90.28/90.51 inference(quant_inst,[status(thm)],[])).
% 90.28/90.51 tff(349,plain,
% 90.28/90.51 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k2_group_1(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k2_group_1(A!0)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k2_group_1(A!0), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k2_group_1(A!0), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k2_group_1(A!0), A!0), k2_group_1(A!0))))) | (C = k6_autgroup(A!0, k2_group_1(A!0))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[348, 347])).
% 90.28/90.51 tff(350,plain,
% 90.28/90.51 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))),
% 90.28/90.51 inference(unit_resolution,[status(thm)],[349, 265, 343])).
% 90.28/90.51 tff(351,plain,
% 90.28/90.51 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(352,plain,
% 90.28/90.51 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.28/90.51 inference(quant_inst,[status(thm)],[])).
% 90.28/90.51 tff(353,plain,
% 90.28/90.51 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), D) = k2_group_3(A!0, D, k2_group_1(A!0))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[352, 351])).
% 90.28/90.51 tff(354,plain,
% 90.28/90.51 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))),
% 90.28/90.51 inference(unit_resolution,[status(thm)],[353, 350, 312])).
% 90.28/90.51 tff(355,plain,
% 90.28/90.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))))),
% 90.28/90.51 inference(bind,[status(th)],[])).
% 90.28/90.51 tff(356,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(quant_intro,[status(thm)],[355])).
% 90.28/90.51 tff(357,plain,
% 90.28/90.51 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 90.28/90.51 inference(bind,[status(th)],[])).
% 90.28/90.51 tff(358,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(quant_intro,[status(thm)],[357])).
% 90.28/90.51 tff(359,plain,
% 90.28/90.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 90.28/90.51 inference(bind,[status(th)],[])).
% 90.28/90.51 tff(360,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(quant_intro,[status(thm)],[359])).
% 90.28/90.51 tff(361,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(transitivity,[status(thm)],[360, 358])).
% 90.28/90.51 tff(362,plain,
% 90.28/90.51 (^[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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 90.28/90.51 inference(bind,[status(th)],[])).
% 90.28/90.51 tff(363,plain,
% 90.28/90.51 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(quant_intro,[status(thm)],[362])).
% 90.28/90.51 tff(364,plain,
% 90.28/90.51 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = 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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(365,plain,
% 90.28/90.51 (^[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((m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))))),
% 90.28/90.51 inference(bind,[status(th)],[])).
% 90.28/90.51 tff(366,plain,
% 90.28/90.51 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = 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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(quant_intro,[status(thm)],[365])).
% 90.28/90.51 tff(367,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] : (m1_subset_1(B, u1_struct_0(A)) => (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_autgroup')).
% 90.28/90.51 tff(368,plain,
% 90.28/90.51 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[367, 366])).
% 90.28/90.51 tff(369,plain,
% 90.28/90.51 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[368, 364])).
% 90.28/90.51 tff(370,plain,(
% 90.28/90.51 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(skolemize,[status(sab)],[369])).
% 90.28/90.51 tff(371,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[370, 363])).
% 90.28/90.51 tff(372,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[371, 361])).
% 90.28/90.51 tff(373,plain,
% 90.28/90.51 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))),
% 90.28/90.51 inference(modus_ponens,[status(thm)],[372, 356])).
% 90.28/90.51 tff(374,plain,
% 90.28/90.51 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~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] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~v1_group_1(A!0)))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(375,plain,
% 90.28/90.51 ((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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~v1_group_1(A!0)))),
% 90.28/90.51 inference(rewrite,[status(thm)],[])).
% 90.28/90.51 tff(376,plain,
% 90.28/90.51 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~v1_group_1(A!0))))),
% 90.28/90.51 inference(monotonicity,[status(thm)],[375])).
% 90.28/90.51 tff(377,plain,
% 90.28/90.51 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~v1_group_1(A!0)))),
% 90.28/90.52 inference(transitivity,[status(thm)],[376, 374])).
% 90.28/90.52 tff(378,plain,
% 90.28/90.52 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | (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] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)))),
% 90.28/90.52 inference(quant_inst,[status(thm)],[])).
% 90.28/90.52 tff(379,plain,
% 90.28/90.52 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k8_funct_2(u1_struct_0(A), u1_struct_0(A), k6_autgroup(A, k2_group_1(A)), B) = B)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B)) | (~v1_group_1(A!0))),
% 90.28/90.52 inference(modus_ponens,[status(thm)],[378, 377])).
% 90.28/90.52 tff(380,plain,
% 90.28/90.52 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))),
% 90.28/90.52 inference(unit_resolution,[status(thm)],[379, 37, 36, 35, 34, 33, 373])).
% 90.28/90.52 tff(381,plain,
% 90.28/90.52 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.28/90.52 inference(rewrite,[status(thm)],[])).
% 90.28/90.52 tff(382,plain,
% 90.28/90.52 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.28/90.52 inference(quant_inst,[status(thm)],[])).
% 90.28/90.52 tff(383,plain,
% 90.28/90.52 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), B) = B))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.28/90.52 inference(modus_ponens,[status(thm)],[382, 381])).
% 90.28/90.52 tff(384,plain,
% 90.28/90.52 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.28/90.52 inference(unit_resolution,[status(thm)],[383, 380, 312])).
% 90.28/90.52 tff(385,plain,
% 90.28/90.52 (tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.28/90.52 inference(symmetry,[status(thm)],[384])).
% 90.28/90.52 tff(386,plain,
% 90.28/90.52 (tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))),
% 90.28/90.52 inference(transitivity,[status(thm)],[385, 354])).
% 90.28/90.52 tff(387,plain,
% 90.28/90.52 (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.28/90.52 inference(monotonicity,[status(thm)],[386])).
% 90.28/90.52 tff(388,plain,
% 90.28/90.52 (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.28/90.52 inference(symmetry,[status(thm)],[387])).
% 90.28/90.52 tff(389,plain,
% 90.28/90.52 (k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.28/90.52 inference(symmetry,[status(thm)],[354])).
% 90.28/90.52 tff(390,plain,
% 90.28/90.52 (k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.28/90.52 inference(transitivity,[status(thm)],[389, 384])).
% 90.28/90.52 tff(391,plain,
% 90.28/90.52 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0)) <=> m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.28/90.52 inference(monotonicity,[status(thm)],[390])).
% 90.28/90.52 tff(392,plain,
% 90.28/90.52 (m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.28/90.52 inference(symmetry,[status(thm)],[391])).
% 90.28/90.52 tff(393,plain,
% 90.28/90.52 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.28/90.52 inference(modus_ponens,[status(thm)],[312, 392])).
% 90.28/90.52 tff(394,plain,
% 90.28/90.52 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 90.28/90.52 inference(quant_inst,[status(thm)],[])).
% 90.28/90.52 tff(395,plain,
% 90.28/90.52 (m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.28/90.52 inference(unit_resolution,[status(thm)],[394, 8])).
% 90.28/90.52 tff(396,plain,
% 90.28/90.52 ((~(m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.28/90.52 inference(tautology,[status(thm)],[])).
% 90.28/90.52 tff(397,plain,
% 90.28/90.52 ((~(m2_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.28/90.52 inference(unit_resolution,[status(thm)],[396, 271])).
% 90.28/90.52 tff(398,plain,
% 90.28/90.52 (m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 90.28/90.52 inference(unit_resolution,[status(thm)],[397, 395])).
% 90.28/90.52 tff(399,plain,
% 90.28/90.52 (^[A: $i, B: $i, C: $i, D: $i] : refl((v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 90.28/90.52 inference(bind,[status(th)],[])).
% 90.28/90.52 tff(400,plain,
% 90.28/90.52 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 90.28/90.52 inference(quant_intro,[status(thm)],[399])).
% 90.28/90.52 tff(401,plain,
% 90.28/90.52 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 90.30/90.52 inference(bind,[status(th)],[])).
% 90.30/90.52 tff(402,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 90.30/90.52 inference(quant_intro,[status(thm)],[401])).
% 90.30/90.52 tff(403,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 90.30/90.52 inference(rewrite,[status(thm)],[])).
% 90.30/90.52 tff(404,plain,
% 90.30/90.52 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 90.30/90.52 inference(bind,[status(th)],[])).
% 90.30/90.52 tff(405,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 90.30/90.52 inference(quant_intro,[status(thm)],[404])).
% 90.30/90.52 tff(406,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 90.30/90.52 tff(407,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 90.30/90.52 inference(modus_ponens,[status(thm)],[406, 405])).
% 90.30/90.52 tff(408,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 90.30/90.52 inference(modus_ponens,[status(thm)],[407, 403])).
% 90.30/90.52 tff(409,plain,(
% 90.30/90.52 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 90.30/90.52 inference(skolemize,[status(sab)],[408])).
% 90.30/90.52 tff(410,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 90.30/90.52 inference(modus_ponens,[status(thm)],[409, 402])).
% 90.30/90.52 tff(411,plain,
% 90.30/90.52 (![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 90.30/90.52 inference(modus_ponens,[status(thm)],[410, 400])).
% 90.30/90.52 tff(412,plain,
% 90.30/90.52 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.30/90.52 inference(rewrite,[status(thm)],[])).
% 90.30/90.52 tff(413,plain,
% 90.30/90.52 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.30/90.52 inference(rewrite,[status(thm)],[])).
% 90.30/90.52 tff(414,plain,
% 90.30/90.52 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.30/90.52 inference(monotonicity,[status(thm)],[413])).
% 90.30/90.52 tff(415,plain,
% 90.30/90.52 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.30/90.52 inference(transitivity,[status(thm)],[414, 412])).
% 90.30/90.52 tff(416,plain,
% 90.30/90.52 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.30/90.52 inference(quant_inst,[status(thm)],[])).
% 90.30/90.52 tff(417,plain,
% 90.30/90.52 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)))) | (~v1_funct_2(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[416, 415])).
% 90.30/90.53 tff(418,plain,
% 90.30/90.53 ((~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.30/90.53 inference(unit_resolution,[status(thm)],[417, 411, 79, 275, 273, 398])).
% 90.30/90.53 tff(419,plain,
% 90.30/90.53 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.30/90.53 inference(unit_resolution,[status(thm)],[418, 393])).
% 90.30/90.53 tff(420,plain,
% 90.30/90.53 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.30/90.53 inference(monotonicity,[status(thm)],[390])).
% 90.30/90.53 tff(421,plain,
% 90.30/90.53 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k2_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.30/90.53 inference(symmetry,[status(thm)],[420])).
% 90.30/90.53 tff(422,plain,
% 90.30/90.53 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))))),
% 90.30/90.53 inference(bind,[status(th)],[])).
% 90.30/90.53 tff(423,plain,
% 90.30/90.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(quant_intro,[status(thm)],[422])).
% 90.30/90.53 tff(424,plain,
% 90.30/90.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))))),
% 90.30/90.53 inference(bind,[status(th)],[])).
% 90.30/90.53 tff(425,plain,
% 90.30/90.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(quant_intro,[status(thm)],[424])).
% 90.30/90.53 tff(426,plain,
% 90.30/90.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(transitivity,[status(thm)],[425, 423])).
% 90.30/90.53 tff(427,plain,
% 90.30/90.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))))),
% 90.30/90.53 inference(bind,[status(th)],[])).
% 90.30/90.53 tff(428,plain,
% 90.30/90.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(quant_intro,[status(thm)],[427])).
% 90.30/90.53 tff(429,plain,
% 90.30/90.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))),
% 90.30/90.53 inference(rewrite,[status(thm)],[])).
% 90.30/90.53 tff(430,plain,
% 90.30/90.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(bind,[status(th)],[])).
% 90.30/90.53 tff(431,plain,
% 90.30/90.53 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))),
% 90.30/90.53 inference(quant_intro,[status(thm)],[430])).
% 90.30/90.53 tff(432,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_group_3')).
% 90.30/90.53 tff(433,plain,
% 90.30/90.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[432, 431])).
% 90.30/90.53 tff(434,plain,
% 90.30/90.53 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[433, 429])).
% 90.30/90.53 tff(435,plain,(
% 90.30/90.53 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B) & (k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))),
% 90.30/90.53 inference(skolemize,[status(sab)],[434])).
% 90.30/90.53 tff(436,plain,
% 90.30/90.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[435, 428])).
% 90.30/90.53 tff(437,plain,
% 90.30/90.53 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[436, 426])).
% 90.30/90.53 tff(438,plain,
% 90.30/90.53 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B)))))))),
% 90.30/90.53 inference(rewrite,[status(thm)],[])).
% 90.30/90.53 tff(439,plain,
% 90.30/90.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B)))))))),
% 90.30/90.53 inference(quant_inst,[status(thm)],[])).
% 90.30/90.53 tff(440,plain,
% 90.30/90.53 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(k2_group_3(A, k2_group_3(A, B, C), k3_group_1(A, C)) = B)) | (~(k2_group_3(A, k2_group_3(A, B, k3_group_1(A, C)), C) = B)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[439, 438])).
% 90.30/90.53 tff(441,plain,
% 90.30/90.53 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))),
% 90.30/90.53 inference(unit_resolution,[status(thm)],[440, 37, 35, 34, 33, 437])).
% 90.30/90.53 tff(442,plain,
% 90.30/90.53 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.30/90.53 inference(rewrite,[status(thm)],[])).
% 90.30/90.53 tff(443,plain,
% 90.30/90.53 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))))),
% 90.30/90.53 inference(quant_inst,[status(thm)],[])).
% 90.30/90.53 tff(444,plain,
% 90.30/90.53 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, B, C), k3_group_1(A!0, C)) = B)) | (~(k2_group_3(A!0, k2_group_3(A!0, B, k3_group_1(A!0, C)), C) = B))))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.30/90.53 inference(modus_ponens,[status(thm)],[443, 442])).
% 90.30/90.53 tff(445,plain,
% 90.30/90.53 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.30/90.53 inference(unit_resolution,[status(thm)],[444, 441, 312])).
% 90.30/90.53 tff(446,plain,
% 90.30/90.53 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.30/90.53 inference(rewrite,[status(thm)],[])).
% 90.30/90.53 tff(447,plain,
% 90.30/90.53 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))),
% 90.30/90.53 inference(quant_inst,[status(thm)],[])).
% 90.30/90.53 tff(448,plain,
% 90.30/90.53 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), C), k3_group_1(A!0, C)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, C)), C) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))))),
% 90.30/90.54 inference(modus_ponens,[status(thm)],[447, 446])).
% 90.30/90.54 tff(449,plain,
% 90.30/90.54 (~((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))),
% 90.30/90.54 inference(unit_resolution,[status(thm)],[448, 114, 445])).
% 90.30/90.54 tff(450,plain,
% 90.30/90.54 (((~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), B!1), k3_group_1(A!0, B!1)) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) | (~(k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))) | (k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.30/90.54 inference(tautology,[status(thm)],[])).
% 90.30/90.54 tff(451,plain,
% 90.30/90.54 (k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1) = tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.30/90.54 inference(unit_resolution,[status(thm)],[450, 449])).
% 90.30/90.54 tff(452,plain,
% 90.30/90.54 (^[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))))),
% 90.30/90.54 inference(bind,[status(th)],[])).
% 90.30/90.54 tff(453,plain,
% 90.30/90.54 (![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)))),
% 90.30/90.54 inference(quant_intro,[status(thm)],[452])).
% 90.30/90.54 tff(454,plain,
% 90.30/90.54 (![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)))),
% 90.30/90.54 inference(rewrite,[status(thm)],[])).
% 90.30/90.54 tff(455,plain,
% 90.30/90.54 (^[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)))))),
% 90.30/90.54 inference(bind,[status(th)],[])).
% 90.30/90.54 tff(456,plain,
% 90.30/90.54 (![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)))),
% 90.30/90.54 inference(quant_intro,[status(thm)],[455])).
% 90.30/90.54 tff(457,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/sandbox/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 90.30/90.54 tff(458,plain,
% 90.30/90.54 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 90.30/90.54 inference(modus_ponens,[status(thm)],[457, 456])).
% 90.30/90.54 tff(459,plain,
% 90.30/90.54 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 90.30/90.54 inference(modus_ponens,[status(thm)],[458, 454])).
% 90.30/90.54 tff(460,plain,(
% 90.30/90.54 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 90.30/90.54 inference(skolemize,[status(sab)],[459])).
% 90.30/90.54 tff(461,plain,
% 90.30/90.54 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 90.30/90.54 inference(modus_ponens,[status(thm)],[460, 453])).
% 90.30/90.54 tff(462,plain,
% 90.30/90.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(rewrite,[status(thm)],[])).
% 90.32/90.54 tff(463,plain,
% 90.32/90.54 (((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0))) <=> ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(rewrite,[status(thm)],[])).
% 90.32/90.54 tff(464,plain,
% 90.32/90.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[463])).
% 90.32/90.54 tff(465,plain,
% 90.32/90.54 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(transitivity,[status(thm)],[464, 462])).
% 90.32/90.54 tff(466,plain,
% 90.32/90.54 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)))),
% 90.32/90.54 inference(quant_inst,[status(thm)],[])).
% 90.32/90.54 tff(467,plain,
% 90.32/90.54 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[466, 465])).
% 90.32/90.54 tff(468,plain,
% 90.32/90.54 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 90.32/90.54 inference(unit_resolution,[status(thm)],[467, 36, 33, 461])).
% 90.32/90.54 tff(469,plain,
% 90.32/90.54 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 90.32/90.54 inference(symmetry,[status(thm)],[468])).
% 90.32/90.54 tff(470,plain,
% 90.32/90.54 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469])).
% 90.32/90.54 tff(471,plain,
% 90.32/90.54 (u1_struct_0(A!0) = u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(symmetry,[status(thm)],[470])).
% 90.32/90.54 tff(472,plain,
% 90.32/90.54 (k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469, 390])).
% 90.32/90.54 tff(473,plain,
% 90.32/90.54 (k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)) = k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1))),
% 90.32/90.54 inference(symmetry,[status(thm)],[472])).
% 90.32/90.54 tff(474,plain,
% 90.32/90.54 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0)) <=> m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[473, 471])).
% 90.32/90.54 tff(475,plain,
% 90.32/90.54 (m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))),
% 90.32/90.54 inference(symmetry,[status(thm)],[474])).
% 90.32/90.54 tff(476,plain,
% 90.32/90.54 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[390, 470])).
% 90.32/90.54 tff(477,plain,
% 90.32/90.54 (m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(symmetry,[status(thm)],[476])).
% 90.32/90.54 tff(478,plain,
% 90.32/90.54 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[312, 477])).
% 90.32/90.54 tff(479,plain,
% 90.32/90.54 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469])).
% 90.32/90.54 tff(480,plain,
% 90.32/90.54 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(symmetry,[status(thm)],[479])).
% 90.32/90.54 tff(481,plain,
% 90.32/90.54 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[33, 480])).
% 90.32/90.54 tff(482,plain,
% 90.32/90.54 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469])).
% 90.32/90.54 tff(483,plain,
% 90.32/90.54 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(symmetry,[status(thm)],[482])).
% 90.32/90.54 tff(484,plain,
% 90.32/90.54 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[34, 483])).
% 90.32/90.54 tff(485,plain,
% 90.32/90.54 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469])).
% 90.32/90.54 tff(486,plain,
% 90.32/90.54 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(symmetry,[status(thm)],[485])).
% 90.32/90.54 tff(487,plain,
% 90.32/90.54 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[35, 486])).
% 90.32/90.54 tff(488,plain,
% 90.32/90.54 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[470])).
% 90.32/90.54 tff(489,plain,
% 90.32/90.54 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0)) <=> m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(symmetry,[status(thm)],[488])).
% 90.32/90.54 tff(490,plain,
% 90.32/90.54 (m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[150, 489])).
% 90.32/90.54 tff(491,plain,
% 90.32/90.54 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 90.32/90.54 inference(monotonicity,[status(thm)],[469])).
% 90.32/90.54 tff(492,plain,
% 90.32/90.54 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(symmetry,[status(thm)],[491])).
% 90.32/90.54 tff(493,plain,
% 90.32/90.54 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[492])).
% 90.32/90.54 tff(494,plain,
% 90.32/90.54 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[37, 493])).
% 90.32/90.54 tff(495,plain,
% 90.32/90.54 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 90.32/90.54 inference(bind,[status(th)],[])).
% 90.32/90.54 tff(496,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 90.32/90.54 inference(quant_intro,[status(thm)],[495])).
% 90.32/90.54 tff(497,plain,
% 90.32/90.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 90.32/90.54 inference(bind,[status(th)],[])).
% 90.32/90.54 tff(498,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 90.32/90.54 inference(quant_intro,[status(thm)],[497])).
% 90.32/90.54 tff(499,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))),
% 90.32/90.54 inference(rewrite,[status(thm)],[])).
% 90.32/90.54 tff(500,plain,
% 90.32/90.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))))),
% 90.32/90.54 inference(bind,[status(th)],[])).
% 90.32/90.54 tff(501,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))),
% 90.32/90.54 inference(quant_intro,[status(thm)],[500])).
% 90.32/90.54 tff(502,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_group_3')).
% 90.32/90.54 tff(503,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[502, 501])).
% 90.32/90.54 tff(504,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[503, 499])).
% 90.32/90.54 tff(505,plain,(
% 90.32/90.54 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)))),
% 90.32/90.54 inference(skolemize,[status(sab)],[504])).
% 90.32/90.54 tff(506,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[505, 498])).
% 90.32/90.54 tff(507,plain,
% 90.32/90.54 (![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 90.32/90.54 inference(modus_ponens,[status(thm)],[506, 496])).
% 90.32/90.54 tff(508,plain,
% 90.32/90.54 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 90.32/90.54 inference(rewrite,[status(thm)],[])).
% 90.32/90.54 tff(509,plain,
% 90.32/90.54 ((m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 90.32/90.54 inference(rewrite,[status(thm)],[])).
% 90.32/90.54 tff(510,plain,
% 90.32/90.54 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 90.32/90.54 inference(monotonicity,[status(thm)],[509])).
% 90.32/90.54 tff(511,plain,
% 90.32/90.54 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 90.32/90.54 inference(transitivity,[status(thm)],[510, 508])).
% 90.32/90.54 tff(512,plain,
% 90.32/90.54 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 90.32/90.55 inference(quant_inst,[status(thm)],[])).
% 90.32/90.55 tff(513,plain,
% 90.32/90.55 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.55 inference(modus_ponens,[status(thm)],[512, 511])).
% 90.32/90.55 tff(514,plain,
% 90.32/90.55 ((~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.55 inference(unit_resolution,[status(thm)],[513, 507, 494, 490, 487, 484, 481])).
% 90.32/90.55 tff(515,plain,
% 90.32/90.55 (m1_subset_1(k2_group_3(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 90.32/90.55 inference(unit_resolution,[status(thm)],[514, 478])).
% 90.32/90.55 tff(516,plain,
% 90.32/90.55 (m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))),
% 90.32/90.55 inference(modus_ponens,[status(thm)],[515, 475])).
% 90.32/90.55 tff(517,plain,
% 90.32/90.55 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1))))))))),
% 90.32/90.55 inference(rewrite,[status(thm)],[])).
% 90.32/90.55 tff(518,plain,
% 90.32/90.55 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1))))))))),
% 90.32/90.55 inference(quant_inst,[status(thm)],[])).
% 90.32/90.55 tff(519,plain,
% 90.32/90.55 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))),
% 90.32/90.55 inference(modus_ponens,[status(thm)],[518, 517])).
% 90.32/90.55 tff(520,plain,
% 90.32/90.55 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))),
% 90.32/90.55 inference(unit_resolution,[status(thm)],[519, 114, 339])).
% 90.32/90.55 tff(521,plain,
% 90.32/90.55 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))),
% 90.32/90.55 inference(rewrite,[status(thm)],[])).
% 90.32/90.55 tff(522,plain,
% 90.32/90.55 (((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), B!1)))) | (k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1))))))) <=> ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))),
% 90.32/90.55 inference(rewrite,[status(thm)],[])).
% 90.32/90.55 tff(523,plain,
% 90.32/90.55 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), B!1)))) | (k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1)))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))))),
% 90.32/90.55 inference(monotonicity,[status(thm)],[522])).
% 90.32/90.55 tff(524,plain,
% 90.32/90.55 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), B!1)))) | (k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1)))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))),
% 90.32/90.55 inference(transitivity,[status(thm)],[523, 521])).
% 90.32/90.55 tff(525,plain,
% 90.32/90.55 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | ((~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, B!1), B!1, A!0), B!1)))) | (k6_autgroup(A!0, B!1) = k6_autgroup(A!0, B!1)))))))),
% 90.32/90.55 inference(quant_inst,[status(thm)],[])).
% 90.32/90.55 tff(526,plain,
% 90.32/90.55 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B!1))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B!1, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B!1, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B!1, A!0), B!1)))) | (C = k6_autgroup(A!0, B!1)))))))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))),
% 90.32/90.55 inference(modus_ponens,[status(thm)],[525, 524])).
% 90.32/90.55 tff(527,plain,
% 90.32/90.55 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))),
% 90.32/90.55 inference(unit_resolution,[status(thm)],[526, 121, 520])).
% 90.32/90.55 tff(528,plain,
% 90.32/90.55 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))) | ((~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1)))),
% 90.32/90.55 inference(rewrite,[status(thm)],[])).
% 90.32/90.55 tff(529,plain,
% 90.32/90.55 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))) | ((~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1)))),
% 90.32/90.55 inference(quant_inst,[status(thm)],[])).
% 90.32/90.55 tff(530,plain,
% 90.32/90.55 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), D) = k2_group_3(A!0, D, B!1)))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1))),
% 90.32/90.55 inference(modus_ponens,[status(thm)],[529, 528])).
% 90.32/90.55 tff(531,plain,
% 90.32/90.55 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k2_group_3(A!0, k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), B!1)),
% 90.32/90.55 inference(unit_resolution,[status(thm)],[530, 527, 516])).
% 90.32/90.55 tff(532,plain,
% 90.32/90.55 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))))),
% 90.32/90.55 inference(rewrite,[status(thm)],[])).
% 90.32/90.55 tff(533,plain,
% 90.32/90.55 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))))),
% 90.32/90.56 inference(rewrite,[status(thm)],[])).
% 90.32/90.56 tff(534,plain,
% 90.32/90.56 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))))))),
% 90.32/90.56 inference(monotonicity,[status(thm)],[533])).
% 90.32/90.56 tff(535,plain,
% 90.32/90.56 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))))),
% 90.32/90.56 inference(transitivity,[status(thm)],[534, 532])).
% 90.32/90.56 tff(536,plain,
% 90.32/90.56 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))))),
% 90.32/90.56 inference(quant_inst,[status(thm)],[])).
% 90.32/90.56 tff(537,plain,
% 90.32/90.56 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_funct_2(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))))),
% 90.32/90.56 inference(modus_ponens,[status(thm)],[536, 535])).
% 90.32/90.56 tff(538,plain,
% 90.32/90.56 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))),
% 90.32/90.56 inference(unit_resolution,[status(thm)],[537, 411, 79, 167, 165, 130, 516])).
% 90.32/90.56 tff(539,plain,
% 90.32/90.56 (k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))),
% 90.32/90.56 inference(symmetry,[status(thm)],[538])).
% 90.32/90.56 tff(540,plain,
% 90.32/90.56 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))))))))),
% 90.32/90.56 inference(rewrite,[status(thm)],[])).
% 90.32/90.56 tff(541,plain,
% 90.32/90.56 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | ((~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))))))))),
% 90.32/90.56 inference(quant_inst,[status(thm)],[])).
% 90.32/90.56 tff(542,plain,
% 90.32/90.56 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, B))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, B))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, B, A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, B, A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, B, A!0), B)))) | (C = k6_autgroup(A!0, B))))))))) | (~m1_subset_1(k3_group_1(A!0, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))),
% 90.32/90.56 inference(modus_ponens,[status(thm)],[541, 540])).
% 90.32/90.56 tff(543,plain,
% 90.32/90.56 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))),
% 90.32/90.56 inference(unit_resolution,[status(thm)],[542, 339, 150])).
% 90.32/90.56 tff(544,plain,
% 90.32/90.56 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))),
% 90.32/90.56 inference(rewrite,[status(thm)],[])).
% 90.32/90.56 tff(545,plain,
% 90.32/90.56 (((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1)))))))) <=> ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))),
% 90.32/90.56 inference(rewrite,[status(thm)],[])).
% 90.32/90.56 tff(546,plain,
% 90.32/90.56 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))))),
% 90.32/90.56 inference(monotonicity,[status(thm)],[545])).
% 90.32/90.56 tff(547,plain,
% 90.32/90.56 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))),
% 90.32/90.57 inference(transitivity,[status(thm)],[546, 544])).
% 90.32/90.57 tff(548,plain,
% 90.32/90.57 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | ((~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (k6_autgroup(A!0, k3_group_1(A!0, B!1)) = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))),
% 90.32/90.57 inference(quant_inst,[status(thm)],[])).
% 90.32/90.57 tff(549,plain,
% 90.32/90.57 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~((~(C = k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), C, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0)) = k2_group_3(A!0, tptp_fun_D_2(C, k3_group_1(A!0, B!1), A!0), k3_group_1(A!0, B!1))))) | (C = k6_autgroup(A!0, k3_group_1(A!0, B!1))))))))) | (~m2_fraenkel(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))),
% 90.32/90.57 inference(modus_ponens,[status(thm)],[548, 547])).
% 90.32/90.57 tff(550,plain,
% 90.32/90.57 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))),
% 90.32/90.57 inference(unit_resolution,[status(thm)],[549, 157, 543])).
% 90.32/90.57 tff(551,plain,
% 90.32/90.57 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))))),
% 90.32/90.57 inference(rewrite,[status(thm)],[])).
% 90.32/90.57 tff(552,plain,
% 90.32/90.57 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))) | ((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))))),
% 90.32/90.57 inference(quant_inst,[status(thm)],[])).
% 90.32/90.57 tff(553,plain,
% 90.32/90.57 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), D) = k2_group_3(A!0, D, k3_group_1(A!0, B!1))))) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))),
% 90.32/90.57 inference(modus_ponens,[status(thm)],[552, 551])).
% 90.32/90.57 tff(554,plain,
% 90.32/90.57 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))),
% 90.32/90.57 inference(unit_resolution,[status(thm)],[553, 550, 312])).
% 90.32/90.57 tff(555,plain,
% 90.32/90.57 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.32/90.57 inference(monotonicity,[status(thm)],[390])).
% 90.32/90.57 tff(556,plain,
% 90.32/90.57 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.57 inference(rewrite,[status(thm)],[])).
% 90.32/90.57 tff(557,plain,
% 90.32/90.57 ((v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.57 inference(rewrite,[status(thm)],[])).
% 90.32/90.57 tff(558,plain,
% 90.32/90.57 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.57 inference(monotonicity,[status(thm)],[557])).
% 90.32/90.57 tff(559,plain,
% 90.32/90.57 (((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.57 inference(transitivity,[status(thm)],[558, 556])).
% 90.32/90.57 tff(560,plain,
% 90.32/90.57 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.32/90.57 inference(quant_inst,[status(thm)],[])).
% 90.32/90.57 tff(561,plain,
% 90.32/90.57 ((~![A: $i, B: $i, C: $i, D: $i] : (v1_xboole_0(A) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.32/90.57 inference(modus_ponens,[status(thm)],[560, 559])).
% 90.32/90.57 tff(562,plain,
% 90.32/90.57 ((~m1_subset_1(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))),
% 90.32/90.57 inference(unit_resolution,[status(thm)],[561, 411, 79, 163, 169, 176])).
% 90.32/90.57 tff(563,plain,
% 90.32/90.57 (k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.32/90.57 inference(unit_resolution,[status(thm)],[562, 393])).
% 90.32/90.57 tff(564,plain,
% 90.32/90.57 (k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k8_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))),
% 90.32/90.57 inference(symmetry,[status(thm)],[563])).
% 90.32/90.57 tff(565,plain,
% 90.32/90.57 (k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1))),
% 90.32/90.57 inference(transitivity,[status(thm)],[564, 555, 554])).
% 90.32/90.57 tff(566,plain,
% 90.32/90.57 (k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) = k1_funct_1(k6_autgroup(A!0, B!1), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k3_group_1(A!0, B!1)))),
% 90.32/90.57 inference(monotonicity,[status(thm)],[565])).
% 90.32/90.57 tff(567,plain,
% 90.32/90.57 (k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.32/90.58 inference(transitivity,[status(thm)],[566, 539, 531, 451, 385, 421, 419, 388])).
% 90.32/90.58 tff(568,plain,
% 90.32/90.58 (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))),
% 90.32/90.58 inference(monotonicity,[status(thm)],[390])).
% 90.32/90.58 tff(569,plain,
% 90.32/90.58 ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) <=> (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.32/90.58 inference(monotonicity,[status(thm)],[568, 567])).
% 90.32/90.58 tff(570,plain,
% 90.32/90.58 ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) <=> (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.32/90.58 inference(transitivity,[status(thm)],[569, 1])).
% 90.32/90.58 tff(571,plain,
% 90.32/90.58 ((k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))) <=> (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.58 inference(symmetry,[status(thm)],[570])).
% 90.32/90.58 tff(572,plain,
% 90.32/90.58 ((~(k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))) <=> (~(k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.58 inference(monotonicity,[status(thm)],[571])).
% 90.32/90.58 tff(573,plain,
% 90.32/90.58 (((~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))) | (~(k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)))))),
% 90.32/90.58 inference(tautology,[status(thm)],[])).
% 90.32/90.58 tff(574,plain,
% 90.32/90.58 (~(k1_funct_1(k6_autgroup(A!0, k2_group_1(A!0)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))) = k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0))))),
% 90.32/90.58 inference(unit_resolution,[status(thm)],[573, 310])).
% 90.32/90.58 tff(575,plain,
% 90.32/90.58 (~(k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.58 inference(modus_ponens,[status(thm)],[574, 572])).
% 90.32/90.58 tff(576,plain,
% 90.32/90.58 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))))),
% 90.32/90.58 inference(bind,[status(th)],[])).
% 90.32/90.58 tff(577,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(quant_intro,[status(thm)],[576])).
% 90.32/90.58 tff(578,plain,
% 90.32/90.58 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))))),
% 90.32/90.58 inference(bind,[status(th)],[])).
% 90.32/90.58 tff(579,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(quant_intro,[status(thm)],[578])).
% 90.32/90.58 tff(580,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(transitivity,[status(thm)],[579, 577])).
% 90.32/90.58 tff(581,plain,
% 90.32/90.58 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))), ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(E) & v1_funct_1(E)) <=> (~((~v1_relat_1(E)) | (~v1_funct_1(E))))), ((~(v1_relat_1(E) & v1_funct_1(E))) <=> (~(~((~v1_relat_1(E)) | (~v1_funct_1(E))))))), rewrite((~(~((~v1_relat_1(E)) | (~v1_funct_1(E))))) <=> ((~v1_relat_1(E)) | (~v1_funct_1(E)))), ((~(v1_relat_1(E) & v1_funct_1(E))) <=> ((~v1_relat_1(E)) | (~v1_funct_1(E))))), (((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | ((~v1_relat_1(E)) | (~v1_funct_1(E)))))), rewrite(((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | ((~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))), (((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))))), (![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))) <=> ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))), (((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))), (((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))))),
% 90.32/90.58 inference(bind,[status(th)],[])).
% 90.32/90.58 tff(582,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(quant_intro,[status(thm)],[581])).
% 90.32/90.58 tff(583,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))),
% 90.32/90.58 inference(rewrite,[status(thm)],[])).
% 90.32/90.58 tff(584,plain,
% 90.32/90.58 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)))), (((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C)))))) <=> ((v1_relat_1(E) & v1_funct_1(E)) => ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)))))), rewrite(((v1_relat_1(E) & v1_funct_1(E)) => ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))), (((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C)))))) <=> ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))))), (![E: $i] : ((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C)))))) <=> ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))), ((((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => ![E: $i] : ((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))))))) <=> ((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) => ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)) => ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))), ((((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => ![E: $i] : ((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))))),
% 90.32/90.58 inference(bind,[status(th)],[])).
% 90.32/90.58 tff(585,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => ![E: $i] : ((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))),
% 90.32/90.58 inference(quant_intro,[status(thm)],[584])).
% 90.32/90.58 tff(586,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) => ![E: $i] : ((v1_relat_1(E) & v1_funct_1(E)) => (r2_hidden(C, A) => ((B = k1_xboole_0) | (k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_funct_2')).
% 90.32/90.58 tff(587,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))),
% 90.32/90.58 inference(modus_ponens,[status(thm)],[586, 585])).
% 90.32/90.58 tff(588,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))),
% 90.32/90.58 inference(modus_ponens,[status(thm)],[587, 583])).
% 90.32/90.58 tff(589,plain,(
% 90.32/90.58 ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~(v1_relat_1(E) & v1_funct_1(E)))))),
% 90.32/90.58 inference(skolemize,[status(sab)],[588])).
% 90.32/90.58 tff(590,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(modus_ponens,[status(thm)],[589, 582])).
% 90.32/90.58 tff(591,plain,
% 90.32/90.58 (![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.58 inference(modus_ponens,[status(thm)],[590, 580])).
% 90.32/90.58 tff(592,plain,
% 90.32/90.58 (((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.58 inference(rewrite,[status(thm)],[])).
% 90.32/90.58 tff(593,plain,
% 90.32/90.58 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) <=> ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.58 inference(rewrite,[status(thm)],[])).
% 90.32/90.58 tff(594,plain,
% 90.32/90.58 (^[E: $i] : rewrite(((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E))) <=> ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.58 inference(bind,[status(th)],[])).
% 90.32/90.58 tff(595,plain,
% 90.32/90.58 (![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E))) <=> ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[594])).
% 90.32/90.59 tff(596,plain,
% 90.32/90.59 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.59 inference(monotonicity,[status(thm)],[595])).
% 90.32/90.59 tff(597,plain,
% 90.32/90.59 (((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E)))) <=> ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.59 inference(transitivity,[status(thm)],[596, 593])).
% 90.32/90.59 tff(598,plain,
% 90.32/90.59 (((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))))),
% 90.32/90.59 inference(monotonicity,[status(thm)],[597])).
% 90.32/90.59 tff(599,plain,
% 90.32/90.59 (((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.59 inference(transitivity,[status(thm)],[598, 592])).
% 90.32/90.59 tff(600,plain,
% 90.32/90.59 ((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | ((~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(E)) | (~v1_funct_1(E))))),
% 90.32/90.59 inference(quant_inst,[status(thm)],[])).
% 90.32/90.59 tff(601,plain,
% 90.32/90.59 ((~![A: $i, B: $i, C: $i, D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)) | ![E: $i] : ((k1_funct_1(k5_relat_1(D, E), C) = k1_funct_1(E, k1_funct_1(D, C))) | (B = k1_xboole_0) | (~r2_hidden(C, A)) | (~v1_relat_1(E)) | (~v1_funct_1(E))))) | (~v1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)))) | (~v1_funct_2(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), u1_struct_0(A!0), u1_struct_0(A!0))) | ![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[600, 599])).
% 90.32/90.59 tff(602,plain,
% 90.32/90.59 (![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[601, 591, 163, 169, 173])).
% 90.32/90.59 tff(603,plain,
% 90.32/90.59 (r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0)) <=> r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.32/90.59 inference(monotonicity,[status(thm)],[390])).
% 90.32/90.59 tff(604,plain,
% 90.32/90.59 (r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.32/90.59 inference(symmetry,[status(thm)],[603])).
% 90.32/90.59 tff(605,plain,
% 90.32/90.59 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(606,plain,
% 90.32/90.59 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[605])).
% 90.32/90.59 tff(607,plain,
% 90.32/90.59 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(608,plain,
% 90.32/90.59 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(609,plain,
% 90.32/90.59 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[608])).
% 90.32/90.59 tff(610,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 90.32/90.59 tff(611,plain,
% 90.32/90.59 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[610, 609])).
% 90.32/90.59 tff(612,plain,
% 90.32/90.59 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[611, 607])).
% 90.32/90.59 tff(613,plain,(
% 90.32/90.59 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(skolemize,[status(sab)],[612])).
% 90.32/90.59 tff(614,plain,
% 90.32/90.59 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[613, 606])).
% 90.32/90.59 tff(615,plain,
% 90.32/90.59 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(616,plain,
% 90.32/90.59 ((r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(617,plain,
% 90.32/90.59 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 90.32/90.59 inference(monotonicity,[status(thm)],[616])).
% 90.32/90.59 tff(618,plain,
% 90.32/90.59 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 90.32/90.59 inference(transitivity,[status(thm)],[617, 615])).
% 90.32/90.59 tff(619,plain,
% 90.32/90.59 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 90.32/90.59 inference(quant_inst,[status(thm)],[])).
% 90.32/90.59 tff(620,plain,
% 90.32/90.59 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[619, 618])).
% 90.32/90.59 tff(621,plain,
% 90.32/90.59 (r2_hidden(tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[620, 614, 79, 312])).
% 90.32/90.59 tff(622,plain,
% 90.32/90.59 (r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[621, 604])).
% 90.32/90.59 tff(623,plain,
% 90.32/90.59 (^[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))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(624,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[623])).
% 90.32/90.59 tff(625,plain,
% 90.32/90.59 (^[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))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(626,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[625])).
% 90.32/90.59 tff(627,plain,
% 90.32/90.59 (^[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))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(628,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[627])).
% 90.32/90.59 tff(629,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(transitivity,[status(thm)],[628, 626])).
% 90.32/90.59 tff(630,plain,
% 90.32/90.59 (^[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)))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(631,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[630])).
% 90.32/90.59 tff(632,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(633,plain,
% 90.32/90.59 (^[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))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(634,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[633])).
% 90.32/90.59 tff(635,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/sandbox/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 90.32/90.59 tff(636,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[635, 634])).
% 90.32/90.59 tff(637,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[636, 632])).
% 90.32/90.59 tff(638,plain,(
% 90.32/90.59 ![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)))),
% 90.32/90.59 inference(skolemize,[status(sab)],[637])).
% 90.32/90.59 tff(639,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[638, 631])).
% 90.32/90.59 tff(640,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[639, 629])).
% 90.32/90.59 tff(641,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[640, 624])).
% 90.32/90.59 tff(642,plain,
% 90.32/90.59 (((~![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(k4_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), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_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(k4_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), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(643,plain,
% 90.32/90.59 ((~![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(k4_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), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 90.32/90.59 inference(quant_inst,[status(thm)],[])).
% 90.32/90.59 tff(644,plain,
% 90.32/90.59 ((~![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(k4_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), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 90.32/90.59 inference(modus_ponens,[status(thm)],[643, 642])).
% 90.32/90.59 tff(645,plain,
% 90.32/90.59 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[644, 641, 79, 44])).
% 90.32/90.59 tff(646,plain,
% 90.32/90.59 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))) | (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0)))),
% 90.32/90.59 inference(quant_inst,[status(thm)],[])).
% 90.32/90.59 tff(647,plain,
% 90.32/90.59 (m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[646, 645])).
% 90.32/90.59 tff(648,plain,
% 90.32/90.59 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0)))) | (~m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))),
% 90.32/90.59 inference(tautology,[status(thm)],[])).
% 90.32/90.59 tff(649,plain,
% 90.32/90.59 ((~(m2_fraenkel(k6_autgroup(A!0, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0)))) | m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[648, 121])).
% 90.32/90.59 tff(650,plain,
% 90.32/90.59 (m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))),
% 90.32/90.59 inference(unit_resolution,[status(thm)],[649, 647])).
% 90.32/90.59 tff(651,plain,
% 90.32/90.59 (^[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))))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(652,plain,
% 90.32/90.59 (![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)))))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[651])).
% 90.32/90.59 tff(653,plain,
% 90.32/90.59 (^[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))))))),
% 90.32/90.59 inference(bind,[status(th)],[])).
% 90.32/90.59 tff(654,plain,
% 90.32/90.59 (![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)))))),
% 90.32/90.59 inference(quant_intro,[status(thm)],[653])).
% 90.32/90.59 tff(655,plain,
% 90.32/90.59 (![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)))),
% 90.32/90.59 inference(rewrite,[status(thm)],[])).
% 90.32/90.59 tff(656,plain,
% 90.32/90.59 (^[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))))),
% 90.32/90.60 inference(bind,[status(th)],[])).
% 90.32/90.60 tff(657,plain,
% 90.32/90.60 (![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)))),
% 90.32/90.60 inference(quant_intro,[status(thm)],[656])).
% 90.32/90.60 tff(658,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 90.32/90.60 tff(659,plain,
% 90.32/90.60 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[658, 657])).
% 90.32/90.60 tff(660,plain,
% 90.32/90.60 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[659, 655])).
% 90.32/90.60 tff(661,plain,(
% 90.32/90.60 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 90.32/90.60 inference(skolemize,[status(sab)],[660])).
% 90.32/90.60 tff(662,plain,
% 90.32/90.60 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[661, 654])).
% 90.32/90.60 tff(663,plain,
% 90.32/90.60 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[662, 652])).
% 90.32/90.60 tff(664,plain,
% 90.32/90.60 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(665,plain,
% 90.32/90.60 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0))))))),
% 90.32/90.60 inference(quant_inst,[status(thm)],[])).
% 90.32/90.60 tff(666,plain,
% 90.32/90.60 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[665, 664])).
% 90.32/90.60 tff(667,plain,
% 90.32/90.60 (~(v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0))))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[666, 663, 44])).
% 90.32/90.60 tff(668,plain,
% 90.32/90.60 ((v1_xboole_0(k4_autgroup(A!0)) | (~v1_fraenkel(k4_autgroup(A!0)))) | v1_fraenkel(k4_autgroup(A!0))),
% 90.32/90.60 inference(tautology,[status(thm)],[])).
% 90.32/90.60 tff(669,plain,
% 90.32/90.60 (v1_fraenkel(k4_autgroup(A!0))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[668, 667])).
% 90.32/90.60 tff(670,plain,
% 90.32/90.60 (^[A: $i] : refl(((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) <=> ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))))),
% 90.32/90.60 inference(bind,[status(th)],[])).
% 90.32/90.60 tff(671,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(quant_intro,[status(thm)],[670])).
% 90.32/90.60 tff(672,plain,
% 90.32/90.60 (^[A: $i] : rewrite(((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) <=> ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))))),
% 90.32/90.60 inference(bind,[status(th)],[])).
% 90.32/90.60 tff(673,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(quant_intro,[status(thm)],[672])).
% 90.32/90.60 tff(674,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(transitivity,[status(thm)],[673, 671])).
% 90.32/90.60 tff(675,plain,
% 90.32/90.60 (^[A: $i] : rewrite(((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))) <=> ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))))),
% 90.32/90.60 inference(bind,[status(th)],[])).
% 90.32/90.60 tff(676,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(quant_intro,[status(thm)],[675])).
% 90.32/90.60 tff(677,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(678,plain,
% 90.32/90.60 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B))) <=> ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))), (![B: $i] : (m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B))) <=> ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))), ((v1_fraenkel(A) => ![B: $i] : (m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B)))) <=> (v1_fraenkel(A) => ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))))), rewrite((v1_fraenkel(A) => ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))) <=> ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))), ((v1_fraenkel(A) => ![B: $i] : (m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B)))) <=> ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))))),
% 90.32/90.60 inference(bind,[status(th)],[])).
% 90.32/90.60 tff(679,plain,
% 90.32/90.60 (![A: $i] : (v1_fraenkel(A) => ![B: $i] : (m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B)))) <=> ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 90.32/90.60 inference(quant_intro,[status(thm)],[678])).
% 90.32/90.60 tff(680,axiom,(![A: $i] : (v1_fraenkel(A) => ![B: $i] : (m1_subset_1(B, A) => (v1_relat_1(B) & v1_funct_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_fraenkel')).
% 90.32/90.60 tff(681,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[680, 679])).
% 90.32/90.60 tff(682,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[681, 677])).
% 90.32/90.60 tff(683,plain,(
% 90.32/90.60 ![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 90.32/90.60 inference(skolemize,[status(sab)],[682])).
% 90.32/90.60 tff(684,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[683, 676])).
% 90.32/90.60 tff(685,plain,
% 90.32/90.60 (![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[684, 674])).
% 90.32/90.60 tff(686,plain,
% 90.32/90.60 (((~![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))) | ((~v1_fraenkel(k4_autgroup(A!0))) | ![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))) <=> ((~![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))) | (~v1_fraenkel(k4_autgroup(A!0))) | ![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(687,plain,
% 90.32/90.60 ((~![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))) | ((~v1_fraenkel(k4_autgroup(A!0))) | ![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 90.32/90.60 inference(quant_inst,[status(thm)],[])).
% 90.32/90.60 tff(688,plain,
% 90.32/90.60 ((~![A: $i] : ((~v1_fraenkel(A)) | ![B: $i] : ((~m1_subset_1(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))) | (~v1_fraenkel(k4_autgroup(A!0))) | ![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[687, 686])).
% 90.32/90.60 tff(689,plain,
% 90.32/90.60 (![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[688, 685, 669])).
% 90.32/90.60 tff(690,plain,
% 90.32/90.60 (((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(691,plain,
% 90.32/90.60 (((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1)))))) <=> ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(692,plain,
% 90.32/90.60 (((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1)))))))),
% 90.32/90.60 inference(monotonicity,[status(thm)],[691])).
% 90.32/90.60 tff(693,plain,
% 90.32/90.60 (((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))))))),
% 90.32/90.60 inference(transitivity,[status(thm)],[692, 690])).
% 90.32/90.60 tff(694,plain,
% 90.32/90.60 ((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))))))),
% 90.32/90.60 inference(quant_inst,[status(thm)],[])).
% 90.32/90.60 tff(695,plain,
% 90.32/90.60 ((~![B: $i] : ((~m1_subset_1(B, k4_autgroup(A!0))) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_subset_1(k6_autgroup(A!0, B!1), k4_autgroup(A!0))) | (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[694, 693])).
% 90.32/90.60 tff(696,plain,
% 90.32/90.60 (~((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[695, 689, 650])).
% 90.32/90.60 tff(697,plain,
% 90.32/90.60 (((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1)))) | v1_relat_1(k6_autgroup(A!0, B!1))),
% 90.32/90.60 inference(tautology,[status(thm)],[])).
% 90.32/90.60 tff(698,plain,
% 90.32/90.60 (v1_relat_1(k6_autgroup(A!0, B!1))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[697, 696])).
% 90.32/90.60 tff(699,plain,
% 90.32/90.60 (((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) <=> ((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(700,plain,
% 90.32/90.60 (((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))) <=> ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(701,plain,
% 90.32/90.60 (((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | ((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) <=> ((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | ((~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))))),
% 90.32/90.60 inference(monotonicity,[status(thm)],[700])).
% 90.32/90.60 tff(702,plain,
% 90.32/90.60 (((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | ((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) <=> ((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.60 inference(transitivity,[status(thm)],[701, 699])).
% 90.32/90.60 tff(703,plain,
% 90.32/90.60 ((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | ((~v1_relat_1(k6_autgroup(A!0, B!1))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))),
% 90.32/90.60 inference(quant_inst,[status(thm)],[])).
% 90.32/90.60 tff(704,plain,
% 90.32/90.60 ((~![E: $i] : ((~v1_relat_1(E)) | (~v1_funct_1(E)) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), E), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(E, k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))))))) | (~v1_funct_1(k6_autgroup(A!0, B!1))) | (~v1_relat_1(k6_autgroup(A!0, B!1))) | (u1_struct_0(A!0) = k1_xboole_0) | (~r2_hidden(k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)), u1_struct_0(A!0))) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.60 inference(modus_ponens,[status(thm)],[703, 702])).
% 90.32/90.60 tff(705,plain,
% 90.32/90.60 ((u1_struct_0(A!0) = k1_xboole_0) | (k1_funct_1(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0))) = k1_funct_1(k6_autgroup(A!0, B!1), k1_funct_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k2_group_3(A!0, tptp_fun_E_24(k5_relat_1(k6_autgroup(A!0, k3_group_1(A!0, B!1)), k6_autgroup(A!0, B!1)), k6_autgroup(A!0, k2_group_1(A!0)), u1_struct_0(A!0)), k2_group_1(A!0)))))),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[704, 167, 698, 622, 602])).
% 90.32/90.60 tff(706,plain,
% 90.32/90.60 (u1_struct_0(A!0) = k1_xboole_0),
% 90.32/90.60 inference(unit_resolution,[status(thm)],[705, 575])).
% 90.32/90.60 tff(707,plain,
% 90.32/90.60 (v1_xboole_0(u1_struct_0(A!0)) <=> v1_xboole_0(k1_xboole_0)),
% 90.32/90.60 inference(monotonicity,[status(thm)],[706])).
% 90.32/90.60 tff(708,plain,
% 90.32/90.60 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(u1_struct_0(A!0))),
% 90.32/90.60 inference(symmetry,[status(thm)],[707])).
% 90.32/90.60 tff(709,plain,
% 90.32/90.60 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 90.32/90.60 inference(rewrite,[status(thm)],[])).
% 90.32/90.60 tff(710,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 90.32/90.60 tff(711,plain,
% 90.32/90.60 (v1_xboole_0(k1_xboole_0)),
% 90.47/90.73 inference(modus_ponens,[status(thm)],[710, 709])).
% 90.47/90.73 tff(712,plain,
% 90.47/90.73 (v1_xboole_0(u1_struct_0(A!0))),
% 90.47/90.73 inference(modus_ponens,[status(thm)],[711, 708])).
% 90.47/90.73 tff(713,plain,
% 90.47/90.73 ($false),
% 90.47/90.73 inference(unit_resolution,[status(thm)],[79, 712])).
% 90.47/90.73 % SZS output end Proof
% 90.77/91.01 % E exiting
%------------------------------------------------------------------------------