%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP620+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:08:10 AM UTC 2025
% Result : Theorem 0.61s 0.81s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP620+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:30:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.61/0.81 % SZS status Theorem
% 0.61/0.81 % SZS output start Proof
% 0.61/0.81 tff(m2_relset_1_type, type, (
% 0.61/0.81 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(u1_struct_0_type, type, (
% 0.61/0.81 u1_struct_0: $i > $i)).
% 0.61/0.81 tff(tptp_fun_A_0_type, type, (
% 0.61/0.81 tptp_fun_A_0: $i)).
% 0.61/0.81 tff(g1_group_1_type, type, (
% 0.61/0.81 g1_group_1: ( $i * $i ) > $i)).
% 0.61/0.81 tff(u1_group_1_type, type, (
% 0.61/0.81 u1_group_1: $i > $i)).
% 0.61/0.81 tff(tptp_fun_B_1_type, type, (
% 0.61/0.81 tptp_fun_B_1: $i)).
% 0.61/0.81 tff(l1_group_1_type, type, (
% 0.61/0.81 l1_group_1: $i > $o)).
% 0.61/0.81 tff(v1_group_1_type, type, (
% 0.61/0.81 v1_group_1: $i > $o)).
% 0.61/0.81 tff(m2_fraenkel_type, type, (
% 0.61/0.81 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.61/0.81 tff(k1_autgroup_type, type, (
% 0.61/0.81 k1_autgroup: $i > $i)).
% 0.61/0.81 tff(k2_funct_1_type, type, (
% 0.61/0.81 k2_funct_1: $i > $i)).
% 0.61/0.81 tff(v4_group_1_type, type, (
% 0.61/0.81 v4_group_1: $i > $o)).
% 0.61/0.81 tff(v3_group_1_type, type, (
% 0.61/0.81 v3_group_1: $i > $o)).
% 0.61/0.81 tff(v3_struct_0_type, type, (
% 0.61/0.81 v3_struct_0: $i > $o)).
% 0.61/0.81 tff(v1_funct_2_type, type, (
% 0.61/0.81 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(v1_group_6_type, type, (
% 0.61/0.81 v1_group_6: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(v1_funct_1_type, type, (
% 0.61/0.81 v1_funct_1: $i > $o)).
% 0.61/0.81 tff(r2_hidden_type, type, (
% 0.61/0.81 r2_hidden: ( $i * $i ) > $o)).
% 0.61/0.81 tff(v3_group_6_type, type, (
% 0.61/0.81 v3_group_6: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(v2_funct_1_type, type, (
% 0.61/0.81 v2_funct_1: $i > $o)).
% 0.61/0.81 tff(tptp_fun_C_3_type, type, (
% 0.61/0.81 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.61/0.81 tff(tptp_fun_C_2_type, type, (
% 0.61/0.81 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.61/0.81 tff(m1_fraenkel_type, type, (
% 0.61/0.81 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(v4_group_6_type, type, (
% 0.61/0.81 v4_group_6: ( $i * $i * $i ) > $o)).
% 0.61/0.81 tff(m1_subset_1_type, type, (
% 0.61/0.81 m1_subset_1: ( $i * $i ) > $o)).
% 0.61/0.81 tff(v1_xboole_0_type, type, (
% 0.61/0.81 v1_xboole_0: $i > $o)).
% 0.61/0.81 tff(l1_struct_0_type, type, (
% 0.61/0.81 l1_struct_0: $i > $o)).
% 0.61/0.81 tff(v1_fraenkel_type, type, (
% 0.61/0.81 v1_fraenkel: $i > $o)).
% 0.61/0.81 tff(1,plain,
% 0.61/0.81 (^[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))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(2,plain,
% 0.61/0.81 (![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)))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.61/0.81 tff(3,plain,
% 0.61/0.81 (![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)))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(4,plain,
% 0.61/0.81 (^[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)))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(5,plain,
% 0.61/0.81 (![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)))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[4])).
% 0.61/0.81 tff(6,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')).
% 0.61/0.81 tff(7,plain,
% 0.61/0.81 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.61/0.81 tff(8,plain,
% 0.61/0.81 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.61/0.81 tff(9,plain,(
% 0.61/0.81 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.61/0.81 inference(skolemize,[status(sab)],[8])).
% 0.61/0.81 tff(10,plain,
% 0.61/0.81 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~v1_group_1(A)) | (~l1_group_1(A)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.61/0.81 tff(11,plain,
% 0.61/0.81 ((((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(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) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(12,plain,
% 0.61/0.81 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(13,plain,
% 0.61/0.81 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(14,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_autgroup')).
% 0.61/0.81 tff(15,plain,
% 0.61/0.81 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.61/0.81 tff(16,plain,
% 0.61/0.81 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.61/0.81 tff(17,plain,
% 0.61/0.81 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.61/0.81 tff(18,plain,
% 0.61/0.81 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.61/0.81 tff(19,plain,
% 0.61/0.81 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.61/0.81 tff(20,plain,
% 0.61/0.81 (l1_group_1(A!0)),
% 0.61/0.81 inference(and_elim,[status(thm)],[19])).
% 0.61/0.81 tff(21,plain,
% 0.61/0.81 (v1_group_1(A!0)),
% 0.61/0.81 inference(and_elim,[status(thm)],[19])).
% 0.61/0.81 tff(22,plain,
% 0.61/0.81 (((~![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))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(23,plain,
% 0.61/0.81 (((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))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(24,plain,
% 0.61/0.81 (((~![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)))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[23])).
% 0.61/0.81 tff(25,plain,
% 0.61/0.81 (((~![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))))),
% 0.61/0.81 inference(transitivity,[status(thm)],[24, 22])).
% 0.61/0.81 tff(26,plain,
% 0.61/0.81 ((~![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)))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(27,plain,
% 0.61/0.81 ((~![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)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.61/0.81 tff(28,plain,
% 0.61/0.81 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[27, 21, 20, 10])).
% 0.61/0.81 tff(29,plain,
% 0.61/0.81 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 0.61/0.81 inference(symmetry,[status(thm)],[28])).
% 0.61/0.81 tff(30,plain,
% 0.61/0.81 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[29])).
% 0.61/0.81 tff(31,plain,
% 0.61/0.81 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)) <=> m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.81 tff(32,plain,
% 0.61/0.81 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))),
% 0.61/0.81 inference(symmetry,[status(thm)],[31])).
% 0.61/0.81 tff(33,plain,
% 0.61/0.81 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))), ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(34,plain,
% 0.61/0.81 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[33])).
% 0.61/0.81 tff(35,plain,
% 0.61/0.81 (^[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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(36,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[35])).
% 0.61/0.82 tff(37,plain,
% 0.61/0.82 (^[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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(38,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[37])).
% 0.61/0.82 tff(39,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(transitivity,[status(thm)],[38, 36])).
% 0.61/0.82 tff(40,plain,
% 0.61/0.82 (^[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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(41,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[40])).
% 0.61/0.82 tff(42,plain,
% 0.61/0.82 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(43,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[42])).
% 0.61/0.82 tff(44,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(45,plain,
% 0.61/0.82 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) <=> ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), rewrite((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), (![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(46,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[45])).
% 0.61/0.82 tff(47,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_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_autgroup')).
% 0.61/0.82 tff(48,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.61/0.82 tff(49,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.61/0.82 tff(50,plain,(
% 0.61/0.82 ![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A))))))))))),
% 0.61/0.82 inference(skolemize,[status(sab)],[49])).
% 0.61/0.82 tff(51,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_2(B, A)) & v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_2(B, A), A, A) & m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_3(B, A), B) <=> (v2_funct_1(tptp_fun_C_3(B, A)) & v3_group_6(tptp_fun_C_3(B, A), A, A)))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.61/0.82 tff(52,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.61/0.82 tff(53,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B)))))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[52, 39])).
% 0.61/0.82 tff(54,plain,
% 0.61/0.82 (![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[53, 34])).
% 0.61/0.82 tff(55,plain,
% 0.61/0.82 (v4_group_1(A!0)),
% 0.61/0.82 inference(and_elim,[status(thm)],[19])).
% 0.61/0.82 tff(56,plain,
% 0.61/0.82 (v3_group_1(A!0)),
% 0.61/0.82 inference(and_elim,[status(thm)],[19])).
% 0.61/0.82 tff(57,plain,
% 0.61/0.82 (~v3_struct_0(A!0)),
% 0.61/0.82 inference(and_elim,[status(thm)],[19])).
% 0.61/0.82 tff(58,plain,
% 0.61/0.82 (((~![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(59,plain,
% 0.61/0.82 ((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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(60,plain,
% 0.61/0.83 (^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(61,plain,
% 0.61/0.83 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[60])).
% 0.61/0.83 tff(62,plain,
% 0.61/0.83 ((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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[61])).
% 0.61/0.83 tff(63,plain,
% 0.61/0.83 ((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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(transitivity,[status(thm)],[62, 59])).
% 0.61/0.83 tff(64,plain,
% 0.61/0.83 (((~![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[63])).
% 0.61/0.83 tff(65,plain,
% 0.61/0.83 (((~![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(transitivity,[status(thm)],[64, 58])).
% 0.61/0.83 tff(66,plain,
% 0.61/0.83 ((~![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A!0))) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B)))))))))))))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(67,plain,
% 0.61/0.83 ((~![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_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_2(B, A))) | (~v1_funct_2(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_2(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_2(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_3(B, A))) | (~v3_group_6(tptp_fun_C_3(B, A), A, A))) <=> r2_hidden(tptp_fun_C_3(B, A), B))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A, A))) <=> r2_hidden(C, 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_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.61/0.83 tff(68,plain,
% 0.61/0.83 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[67, 57, 21, 56, 55, 20, 54])).
% 0.61/0.83 tff(69,plain,
% 0.61/0.83 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(70,plain,
% 0.61/0.83 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[69])).
% 0.61/0.84 tff(71,plain,
% 0.61/0.84 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(72,plain,
% 0.61/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[71])).
% 0.61/0.84 tff(73,plain,
% 0.61/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(74,plain,
% 0.61/0.84 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(75,plain,
% 0.61/0.84 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[74])).
% 0.61/0.84 tff(76,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 0.61/0.84 tff(77,plain,
% 0.61/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.61/0.84 tff(78,plain,
% 0.61/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.61/0.84 tff(79,plain,(
% 0.61/0.84 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.61/0.84 inference(skolemize,[status(sab)],[78])).
% 0.61/0.84 tff(80,plain,
% 0.61/0.84 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.61/0.84 tff(81,plain,
% 0.61/0.84 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.61/0.84 tff(82,plain,
% 0.61/0.84 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(83,plain,
% 0.61/0.84 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(84,plain,
% 0.61/0.84 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[83])).
% 0.61/0.84 tff(85,plain,
% 0.61/0.84 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.61/0.84 inference(transitivity,[status(thm)],[84, 82])).
% 0.61/0.84 tff(86,plain,
% 0.61/0.84 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.61/0.84 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(87,plain,
% 0.61/0.84 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.61/0.84 tff(88,plain,
% 0.61/0.84 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[87, 57, 21, 56, 55, 20, 81])).
% 0.61/0.84 tff(89,plain,
% 0.61/0.84 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(90,plain,
% 0.61/0.84 (((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0))))))))))))) <=> ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(91,plain,
% 0.61/0.84 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))))))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[90])).
% 0.61/0.84 tff(92,plain,
% 0.61/0.84 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))))),
% 0.61/0.84 inference(transitivity,[status(thm)],[91, 89])).
% 0.61/0.84 tff(93,plain,
% 0.61/0.84 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~m2_relset_1(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))))))))))),
% 0.61/0.84 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(94,plain,
% 0.61/0.84 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_2(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_2(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_2(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_3(B, A!0))) | (~v3_group_6(tptp_fun_C_3(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_3(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, B))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.61/0.84 tff(95,plain,
% 0.61/0.84 (~((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[94, 88, 68])).
% 0.61/0.84 tff(96,plain,
% 0.61/0.84 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))) <=> r2_hidden(C, k1_autgroup(A!0)))))) | (~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0)))))))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(tautology,[status(thm)],[])).
% 0.61/0.85 tff(97,plain,
% 0.61/0.85 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.61/0.85 tff(98,plain,
% 0.61/0.85 (~((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.61/0.85 inference(and_elim,[status(thm)],[19])).
% 0.61/0.85 tff(99,plain,
% 0.61/0.85 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.61/0.85 inference(or_elim,[status(thm)],[98])).
% 0.61/0.85 tff(100,plain,
% 0.61/0.85 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(101,plain,
% 0.61/0.85 (((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(102,plain,
% 0.61/0.85 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[101])).
% 0.61/0.85 tff(103,plain,
% 0.61/0.85 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(transitivity,[status(thm)],[102, 100])).
% 0.61/0.85 tff(104,plain,
% 0.61/0.85 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(quant_inst,[status(thm)],[])).
% 0.61/0.85 tff(105,plain,
% 0.61/0.85 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.61/0.85 tff(106,plain,
% 0.61/0.85 (~((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[105, 99, 97])).
% 0.61/0.85 tff(107,plain,
% 0.61/0.85 (((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.85 inference(tautology,[status(thm)],[])).
% 0.61/0.85 tff(108,plain,
% 0.61/0.85 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.61/0.85 tff(109,plain,
% 0.61/0.85 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[108, 32])).
% 0.61/0.85 tff(110,plain,
% 0.61/0.85 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0) <=> v1_group_6(B!1, A!0, A!0)),
% 0.61/0.85 inference(monotonicity,[status(thm)],[29])).
% 0.61/0.85 tff(111,plain,
% 0.61/0.85 (v1_group_6(B!1, A!0, A!0) <=> v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)),
% 0.61/0.85 inference(symmetry,[status(thm)],[110])).
% 0.61/0.85 tff(112,plain,
% 0.61/0.85 (((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_group_6(B!1, A!0, A!0)),
% 0.61/0.85 inference(tautology,[status(thm)],[])).
% 0.61/0.85 tff(113,plain,
% 0.61/0.85 (v1_group_6(B!1, A!0, A!0)),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[112, 106])).
% 0.61/0.85 tff(114,plain,
% 0.61/0.85 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[113, 111])).
% 0.61/0.85 tff(115,plain,
% 0.61/0.85 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)) <=> v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.85 tff(116,plain,
% 0.61/0.85 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))),
% 0.61/0.85 inference(symmetry,[status(thm)],[115])).
% 0.61/0.85 tff(117,plain,
% 0.61/0.85 (((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.85 inference(tautology,[status(thm)],[])).
% 0.61/0.85 tff(118,plain,
% 0.61/0.85 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[117, 106])).
% 0.61/0.85 tff(119,plain,
% 0.61/0.85 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[118, 116])).
% 0.61/0.85 tff(120,plain,
% 0.61/0.85 (v4_group_6(B!1, A!0, A!0) <=> v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)),
% 0.61/0.85 inference(monotonicity,[status(thm)],[28])).
% 0.61/0.85 tff(121,plain,
% 0.61/0.85 (((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(B!1)),
% 0.61/0.85 inference(tautology,[status(thm)],[])).
% 0.61/0.85 tff(122,plain,
% 0.61/0.85 (v1_funct_1(B!1)),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[121, 106])).
% 0.61/0.85 tff(123,plain,
% 0.61/0.85 (^[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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))),
% 0.61/0.85 inference(bind,[status(th)],[])).
% 0.61/0.85 tff(124,plain,
% 0.61/0.85 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(quant_intro,[status(thm)],[123])).
% 0.61/0.85 tff(125,plain,
% 0.61/0.85 (^[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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))),
% 0.61/0.85 inference(bind,[status(th)],[])).
% 0.61/0.85 tff(126,plain,
% 0.61/0.85 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(quant_intro,[status(thm)],[125])).
% 0.61/0.85 tff(127,plain,
% 0.61/0.85 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(transitivity,[status(thm)],[126, 124])).
% 0.61/0.85 tff(128,plain,
% 0.61/0.85 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), (((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), (((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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))) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, 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))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))))),
% 0.61/0.85 inference(bind,[status(th)],[])).
% 0.61/0.85 tff(129,plain,
% 0.61/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, 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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(quant_intro,[status(thm)],[128])).
% 0.61/0.85 tff(130,plain,
% 0.61/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, 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] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(131,plain,
% 0.61/0.85 (^[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(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A))), ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> ((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))), ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), (((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))), (((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))))), (![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))))),
% 0.61/0.85 inference(bind,[status(th)],[])).
% 0.61/0.85 tff(132,plain,
% 0.61/0.85 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, 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] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 0.61/0.85 inference(quant_intro,[status(thm)],[131])).
% 0.61/0.85 tff(133,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_autgroup')).
% 0.61/0.85 tff(134,plain,
% 0.61/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.61/0.85 tff(135,plain,
% 0.61/0.85 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.61/0.85 tff(136,plain,(
% 0.61/0.85 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 0.61/0.85 inference(skolemize,[status(sab)],[135])).
% 0.61/0.85 tff(137,plain,
% 0.61/0.85 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.61/0.85 tff(138,plain,
% 0.61/0.85 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.61/0.85 tff(139,plain,
% 0.61/0.85 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(140,plain,
% 0.61/0.85 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(141,plain,
% 0.61/0.85 (^[B: $i] : rewrite(((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(bind,[status(th)],[])).
% 0.61/0.85 tff(142,plain,
% 0.61/0.85 (![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.85 inference(quant_intro,[status(thm)],[141])).
% 0.61/0.85 tff(143,plain,
% 0.61/0.85 ((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] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[142])).
% 0.61/0.85 tff(144,plain,
% 0.61/0.85 ((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] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(transitivity,[status(thm)],[143, 140])).
% 0.61/0.85 tff(145,plain,
% 0.61/0.85 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[144])).
% 0.61/0.85 tff(146,plain,
% 0.61/0.85 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(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] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(transitivity,[status(thm)],[145, 139])).
% 0.61/0.85 tff(147,plain,
% 0.61/0.85 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.61/0.85 inference(quant_inst,[status(thm)],[])).
% 0.61/0.85 tff(148,plain,
% 0.61/0.85 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(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)) | ![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.61/0.85 tff(149,plain,
% 0.61/0.85 (![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[148, 57, 21, 56, 55, 20, 138])).
% 0.61/0.85 tff(150,plain,
% 0.61/0.85 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(151,plain,
% 0.61/0.86 (((~v1_funct_1(B!1)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(152,plain,
% 0.61/0.86 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))))),
% 0.61/0.86 inference(monotonicity,[status(thm)],[151])).
% 0.61/0.86 tff(153,plain,
% 0.61/0.86 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 0.61/0.86 inference(transitivity,[status(thm)],[152, 150])).
% 0.61/0.86 tff(154,plain,
% 0.61/0.86 ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.61/0.86 inference(quant_inst,[status(thm)],[])).
% 0.61/0.86 tff(155,plain,
% 0.61/0.86 ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_group_6(B!1, A!0, A!0)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.61/0.86 tff(156,plain,
% 0.61/0.86 (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)),
% 0.61/0.86 inference(unit_resolution,[status(thm)],[155, 149, 122, 113, 118, 108])).
% 0.61/0.86 tff(157,plain,
% 0.61/0.86 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(158,plain,
% 0.61/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[157])).
% 0.61/0.86 tff(159,plain,
% 0.61/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(160,plain,
% 0.61/0.86 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(161,plain,
% 0.61/0.86 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[160])).
% 0.61/0.86 tff(162,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.61/0.86 tff(163,plain,
% 0.61/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.61/0.86 tff(164,plain,
% 0.61/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.61/0.86 tff(165,plain,(
% 0.61/0.86 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(skolemize,[status(sab)],[164])).
% 0.61/0.86 tff(166,plain,
% 0.61/0.86 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.61/0.86 tff(167,plain,
% 0.61/0.86 (((~![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)))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(168,plain,
% 0.61/0.86 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.61/0.86 inference(quant_inst,[status(thm)],[])).
% 0.61/0.86 tff(169,plain,
% 0.61/0.86 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.61/0.86 tff(170,plain,
% 0.61/0.86 (l1_struct_0(A!0)),
% 0.61/0.86 inference(unit_resolution,[status(thm)],[169, 20, 166])).
% 0.61/0.86 tff(171,plain,
% 0.61/0.86 (^[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))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(172,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[171])).
% 0.61/0.86 tff(173,plain,
% 0.61/0.86 (^[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)))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(174,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[173])).
% 0.61/0.86 tff(175,plain,
% 0.61/0.86 (![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))))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(176,plain,
% 0.61/0.86 (^[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)))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(177,plain,
% 0.61/0.86 (![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))))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[176])).
% 0.61/0.86 tff(178,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')).
% 0.61/0.86 tff(179,plain,
% 0.61/0.86 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.61/0.86 tff(180,plain,
% 0.61/0.86 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.61/0.86 tff(181,plain,(
% 0.61/0.86 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.86 inference(skolemize,[status(sab)],[180])).
% 0.61/0.86 tff(182,plain,
% 0.61/0.86 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.61/0.86 tff(183,plain,
% 0.61/0.86 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.61/0.86 tff(184,plain,
% 0.61/0.86 (((~![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))))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(185,plain,
% 0.61/0.86 ((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))))),
% 0.61/0.86 inference(rewrite,[status(thm)],[])).
% 0.61/0.86 tff(186,plain,
% 0.61/0.86 (((~![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)))))),
% 0.61/0.86 inference(monotonicity,[status(thm)],[185])).
% 0.61/0.86 tff(187,plain,
% 0.61/0.86 (((~![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))))),
% 0.61/0.86 inference(transitivity,[status(thm)],[186, 184])).
% 0.61/0.86 tff(188,plain,
% 0.61/0.86 ((~![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)))),
% 0.61/0.86 inference(quant_inst,[status(thm)],[])).
% 0.61/0.86 tff(189,plain,
% 0.61/0.86 ((~![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)))),
% 0.61/0.86 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.61/0.86 tff(190,plain,
% 0.61/0.86 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.61/0.86 inference(unit_resolution,[status(thm)],[189, 57, 183])).
% 0.61/0.86 tff(191,plain,
% 0.61/0.86 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.61/0.86 inference(unit_resolution,[status(thm)],[190, 170])).
% 0.61/0.86 tff(192,plain,
% 0.61/0.86 (^[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))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(193,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[192])).
% 0.61/0.86 tff(194,plain,
% 0.61/0.86 (^[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))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(195,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[194])).
% 0.61/0.86 tff(196,plain,
% 0.61/0.86 (^[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))))),
% 0.61/0.86 inference(bind,[status(th)],[])).
% 0.61/0.86 tff(197,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(quant_intro,[status(thm)],[196])).
% 0.61/0.86 tff(198,plain,
% 0.61/0.86 (![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)))),
% 0.61/0.86 inference(transitivity,[status(thm)],[197, 195])).
% 0.61/0.86 tff(199,plain,
% 0.61/0.86 (^[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)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(200,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[199])).
% 0.71/0.86 tff(201,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(202,plain,
% 0.71/0.86 (^[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))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(203,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[202])).
% 0.71/0.86 tff(204,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')).
% 0.71/0.86 tff(205,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.71/0.86 tff(206,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.71/0.86 tff(207,plain,(
% 0.71/0.86 ![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)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[206])).
% 0.71/0.86 tff(208,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.71/0.86 tff(209,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[208, 198])).
% 0.71/0.86 tff(210,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[209, 193])).
% 0.71/0.86 tff(211,plain,
% 0.71/0.86 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(212,plain,
% 0.71/0.86 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(213,plain,
% 0.71/0.86 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.71/0.86 tff(214,plain,
% 0.71/0.86 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[213, 210, 191, 88])).
% 0.71/0.86 tff(215,plain,
% 0.71/0.86 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(216,plain,
% 0.71/0.86 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.71/0.86 tff(217,plain,
% 0.71/0.86 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(218,plain,
% 0.71/0.86 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[217, 99])).
% 0.71/0.86 tff(219,plain,
% 0.71/0.86 (m1_subset_1(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[218, 216])).
% 0.71/0.86 tff(220,plain,
% 0.71/0.86 (^[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))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(221,plain,
% 0.71/0.86 (![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)))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[220])).
% 0.71/0.86 tff(222,plain,
% 0.71/0.86 (^[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))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(223,plain,
% 0.71/0.86 (![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)))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[222])).
% 0.71/0.86 tff(224,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(225,plain,
% 0.71/0.86 (^[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))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(226,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[225])).
% 0.71/0.86 tff(227,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')).
% 0.71/0.86 tff(228,plain,
% 0.71/0.86 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.71/0.86 tff(229,plain,
% 0.71/0.86 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.71/0.86 tff(230,plain,(
% 0.71/0.86 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[229])).
% 0.71/0.86 tff(231,plain,
% 0.71/0.86 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.71/0.86 tff(232,plain,
% 0.71/0.86 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[231, 221])).
% 0.71/0.86 tff(233,plain,
% 0.71/0.86 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(234,plain,
% 0.71/0.86 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(235,plain,
% 0.71/0.86 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.71/0.86 tff(236,plain,
% 0.71/0.86 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[235, 232, 88])).
% 0.71/0.86 tff(237,plain,
% 0.71/0.86 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(238,plain,
% 0.71/0.86 (~v1_xboole_0(k1_autgroup(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.71/0.86 tff(239,plain,
% 0.71/0.86 (^[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))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(240,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[239])).
% 0.71/0.86 tff(241,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(242,plain,
% 0.71/0.86 (^[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))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(243,plain,
% 0.71/0.86 (![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)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[242])).
% 0.71/0.86 tff(244,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')).
% 0.71/0.86 tff(245,plain,
% 0.71/0.86 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.71/0.86 tff(246,plain,
% 0.71/0.86 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.71/0.86 tff(247,plain,(
% 0.71/0.86 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[246])).
% 0.71/0.86 tff(248,plain,
% 0.71/0.86 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[247, 240])).
% 0.71/0.86 tff(249,plain,
% 0.71/0.86 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(250,plain,
% 0.71/0.86 ((r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(251,plain,
% 0.71/0.86 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[250])).
% 0.71/0.86 tff(252,plain,
% 0.71/0.86 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[251, 249])).
% 0.71/0.86 tff(253,plain,
% 0.71/0.86 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(254,plain,
% 0.71/0.86 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.71/0.86 tff(255,plain,
% 0.71/0.86 (r2_hidden(B!1, k1_autgroup(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[254, 248, 238, 219])).
% 0.71/0.86 tff(256,plain,
% 0.71/0.86 ((~(r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))) | (~r2_hidden(B!1, k1_autgroup(A!0))) | v4_group_6(B!1, A!0, A!0)),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(257,plain,
% 0.71/0.86 (v4_group_6(B!1, A!0, A!0)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[256, 255, 156])).
% 0.71/0.86 tff(258,plain,
% 0.71/0.86 (v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[257, 120])).
% 0.71/0.86 tff(259,plain,
% 0.71/0.86 (v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.86 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.86 tff(260,plain,
% 0.71/0.86 (v1_group_6(k2_funct_1(B!1), A!0, A!0) <=> v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.86 inference(symmetry,[status(thm)],[259])).
% 0.71/0.86 tff(261,plain,
% 0.71/0.86 (^[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] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(262,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[261])).
% 0.71/0.86 tff(263,plain,
% 0.71/0.86 (^[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] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(264,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[263])).
% 0.71/0.86 tff(265,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.86 inference(transitivity,[status(thm)],[264, 262])).
% 0.71/0.86 tff(266,plain,
% 0.71/0.86 (^[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(((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))), (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(267,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[266])).
% 0.71/0.86 tff(268,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(269,plain,
% 0.71/0.86 (^[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(trans(monotonicity(rewrite(((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) <=> (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A))), ((((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) <=> ((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))), ((((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))), ((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))), rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))), ((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), 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)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), 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)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(270,plain,
% 0.71/0.86 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), 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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[269])).
% 0.71/0.87 tff(271,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => (((v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) & v1_group_6(k2_funct_1(B), A, A)) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_autgroup')).
% 0.71/0.87 tff(272,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.71/0.87 tff(273,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.71/0.87 tff(274,plain,(
% 0.71/0.87 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (v1_funct_1(k2_funct_1(B)) & v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(k2_funct_1(B), A, A) & m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[273])).
% 0.71/0.87 tff(275,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.71/0.87 tff(276,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[275, 265])).
% 0.71/0.87 tff(277,plain,
% 0.71/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(278,plain,
% 0.71/0.87 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(279,plain,
% 0.71/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[278])).
% 0.71/0.87 tff(280,plain,
% 0.71/0.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[279, 277])).
% 0.71/0.87 tff(281,plain,
% 0.71/0.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(282,plain,
% 0.71/0.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(k2_funct_1(B), A, A)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A), u1_struct_0(A)))))))) | v3_struct_0(A!0) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v1_group_1(A!0))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.71/0.87 tff(283,plain,
% 0.71/0.87 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[282, 57, 21, 56, 55, 20, 276])).
% 0.71/0.87 tff(284,plain,
% 0.71/0.87 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(285,plain,
% 0.71/0.87 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(286,plain,
% 0.71/0.87 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B))) | (~v1_funct_2(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.71/0.87 tff(287,plain,
% 0.71/0.87 (~((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[286, 99, 283])).
% 0.71/0.87 tff(288,plain,
% 0.71/0.87 (((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(289,plain,
% 0.71/0.87 (v1_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.71/0.87 tff(290,plain,
% 0.71/0.87 (v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[289, 260])).
% 0.71/0.87 tff(291,plain,
% 0.71/0.87 (v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[30])).
% 0.71/0.87 tff(292,plain,
% 0.71/0.87 (v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(symmetry,[status(thm)],[291])).
% 0.71/0.87 tff(293,plain,
% 0.71/0.87 (((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(294,plain,
% 0.71/0.87 (v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[293, 287])).
% 0.71/0.87 tff(295,plain,
% 0.71/0.87 (v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[294, 292])).
% 0.71/0.87 tff(296,plain,
% 0.71/0.87 (m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[30])).
% 0.71/0.87 tff(297,plain,
% 0.71/0.87 (m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(symmetry,[status(thm)],[296])).
% 0.71/0.87 tff(298,plain,
% 0.71/0.87 (((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(299,plain,
% 0.71/0.87 (m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[298, 287])).
% 0.71/0.87 tff(300,plain,
% 0.71/0.87 (m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[299, 297])).
% 0.71/0.87 tff(301,plain,
% 0.71/0.87 (v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.87 tff(302,plain,
% 0.71/0.87 (v4_group_6(k2_funct_1(B!1), A!0, A!0) <=> v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[301])).
% 0.71/0.87 tff(303,plain,
% 0.71/0.87 ((~v4_group_6(k2_funct_1(B!1), A!0, A!0)) <=> (~v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[302])).
% 0.71/0.87 tff(304,plain,
% 0.71/0.87 (((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k2_funct_1(B!1))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(305,plain,
% 0.71/0.87 (v1_funct_1(k2_funct_1(B!1))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[304, 287])).
% 0.71/0.87 tff(306,plain,
% 0.71/0.87 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(307,plain,
% 0.71/0.87 (((~v1_funct_1(k2_funct_1(B!1))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(308,plain,
% 0.71/0.87 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k2_funct_1(B!1))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[307])).
% 0.71/0.87 tff(309,plain,
% 0.71/0.87 (((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k2_funct_1(B!1))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[308, 306])).
% 0.71/0.87 tff(310,plain,
% 0.71/0.87 ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k2_funct_1(B!1))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(311,plain,
% 0.71/0.87 ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k2_funct_1(B!1))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k2_funct_1(B!1), A!0, A!0)) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.71/0.87 tff(312,plain,
% 0.71/0.87 (r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[311, 149, 305, 294, 289, 299])).
% 0.71/0.87 tff(313,plain,
% 0.71/0.87 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(314,plain,
% 0.71/0.87 (m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[313, 214])).
% 0.71/0.87 tff(315,plain,
% 0.71/0.87 (~m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.71/0.87 inference(or_elim,[status(thm)],[98])).
% 0.71/0.87 tff(316,plain,
% 0.71/0.87 ((~(m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))) | m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) | (~m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(317,plain,
% 0.71/0.87 ((~(m2_fraenkel(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))) | (~m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[316, 315])).
% 0.71/0.87 tff(318,plain,
% 0.71/0.87 (~m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[317, 314])).
% 0.71/0.87 tff(319,plain,
% 0.71/0.87 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(320,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[319])).
% 0.71/0.87 tff(321,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(322,plain,
% 0.71/0.87 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(323,plain,
% 0.71/0.87 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[322])).
% 0.71/0.87 tff(324,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.71/0.87 tff(325,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.71/0.87 tff(326,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.71/0.87 tff(327,plain,(
% 0.71/0.87 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(skolemize,[status(sab)],[326])).
% 0.71/0.87 tff(328,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[327, 320])).
% 0.71/0.87 tff(329,plain,
% 0.71/0.87 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0))) | m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0))) | m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(330,plain,
% 0.71/0.87 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0))) | m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(331,plain,
% 0.71/0.87 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0))) | m1_subset_1(k2_funct_1(B!1), k1_autgroup(A!0))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.71/0.87 tff(332,plain,
% 0.71/0.87 (~r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[331, 328, 318])).
% 0.71/0.87 tff(333,plain,
% 0.71/0.87 ((~(r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) <=> v4_group_6(k2_funct_1(B!1), A!0, A!0))) | r2_hidden(k2_funct_1(B!1), k1_autgroup(A!0)) | (~v4_group_6(k2_funct_1(B!1), A!0, A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(334,plain,
% 0.71/0.87 (~v4_group_6(k2_funct_1(B!1), A!0, A!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[333, 332, 312])).
% 0.71/0.87 tff(335,plain,
% 0.71/0.87 (~v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[334, 303])).
% 0.71/0.87 tff(336,plain,
% 0.71/0.87 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.87 tff(337,plain,
% 0.71/0.87 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[336])).
% 0.71/0.87 tff(338,plain,
% 0.71/0.87 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[337])).
% 0.71/0.87 tff(339,plain,
% 0.71/0.87 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[57, 338])).
% 0.71/0.87 tff(340,plain,
% 0.71/0.87 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.87 tff(341,plain,
% 0.71/0.87 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[340])).
% 0.71/0.87 tff(342,plain,
% 0.71/0.87 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[55, 341])).
% 0.71/0.87 tff(343,plain,
% 0.71/0.87 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.87 tff(344,plain,
% 0.71/0.87 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[343])).
% 0.71/0.87 tff(345,plain,
% 0.71/0.87 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[56, 344])).
% 0.71/0.87 tff(346,plain,
% 0.71/0.87 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 0.71/0.87 inference(monotonicity,[status(thm)],[29])).
% 0.71/0.87 tff(347,plain,
% 0.71/0.87 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[346])).
% 0.71/0.87 tff(348,plain,
% 0.71/0.87 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[20, 347])).
% 0.71/0.87 tff(349,plain,
% 0.71/0.87 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(350,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[349])).
% 0.71/0.87 tff(351,plain,
% 0.71/0.87 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(352,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[351])).
% 0.71/0.87 tff(353,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.87 inference(transitivity,[status(thm)],[352, 350])).
% 0.71/0.87 tff(354,plain,
% 0.71/0.87 (^[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] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite(((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), (((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(355,plain,
% 0.71/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[354])).
% 0.71/0.88 tff(356,plain,
% 0.71/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(357,plain,
% 0.71/0.88 (^[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(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)) <=> ((~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | v4_group_6(D, A, B))), (((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | v4_group_6(D, A, B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | v4_group_6(D, A, B))) <=> (v4_group_6(D, A, B) | (~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | (~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), (((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))) <=> (v4_group_6(D, A, B) | (~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | (~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))), (![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))) <=> ![D: $i] : (v4_group_6(D, A, B) | (~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | (~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))))), trans(der(![D: $i] : (v4_group_6(D, A, B) | (~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | (~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))) <=> ![D: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)))), elim_unused(![D: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)))), (![D: $i] : (v4_group_6(D, A, B) | (~(v4_group_6(C, B, A) & (D = k2_funct_1(C)))) | (~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A))))), (![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))) <=> ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))) <=> ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), (![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(358,plain,
% 0.71/0.88 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[357])).
% 0.71/0.88 tff(359,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v1_group_6(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((v4_group_6(C, B, A) & (D = k2_funct_1(C))) => v4_group_6(D, A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t73_group_6')).
% 0.71/0.88 tff(360,plain,
% 0.71/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.71/0.88 tff(361,plain,
% 0.71/0.88 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.71/0.88 tff(362,plain,(
% 0.71/0.88 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_group_6(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 0.71/0.88 inference(skolemize,[status(sab)],[361])).
% 0.71/0.88 tff(363,plain,
% 0.71/0.88 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[362, 355])).
% 0.71/0.88 tff(364,plain,
% 0.71/0.88 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[363, 353])).
% 0.71/0.88 tff(365,plain,
% 0.71/0.88 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(366,plain,
% 0.71/0.88 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(367,plain,
% 0.71/0.88 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[366])).
% 0.71/0.88 tff(368,plain,
% 0.71/0.88 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[367, 365])).
% 0.71/0.88 tff(369,plain,
% 0.71/0.88 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(370,plain,
% 0.71/0.88 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A, B) | (~v1_funct_1(k2_funct_1(C))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A, B)) | (~v4_group_6(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~v1_group_6(C, B, A)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.71/0.88 tff(371,plain,
% 0.71/0.88 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[370, 57, 56, 55, 20, 364])).
% 0.71/0.88 tff(372,plain,
% 0.71/0.88 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))) | (v3_struct_0(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)))) | (~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)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))) | v3_struct_0(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)))) | (~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)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(373,plain,
% 0.71/0.88 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))) | (v3_struct_0(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)))) | (~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)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(374,plain,
% 0.71/0.88 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | v4_group_6(k2_funct_1(C), A!0, B) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(k2_funct_1(C), A!0, B)) | (~v4_group_6(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_group_6(C, B, A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0)))))) | v3_struct_0(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)))) | (~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)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.71/0.88 tff(375,plain,
% 0.71/0.88 (v3_struct_0(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)))) | (~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)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[374, 371])).
% 0.71/0.89 tff(376,plain,
% 0.71/0.89 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[375, 348, 345, 342, 339])).
% 0.71/0.89 tff(377,plain,
% 0.71/0.89 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(k2_funct_1(B!1))) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(k2_funct_1(B!1))) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(378,plain,
% 0.71/0.89 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(k2_funct_1(B!1))) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(379,plain,
% 0.71/0.89 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(k2_funct_1(C))) | (~m2_relset_1(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(C), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(C), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(C, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(C, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(k2_funct_1(B!1))) | (~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.71/0.89 tff(380,plain,
% 0.71/0.89 ((~m2_relset_1(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | v4_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(k2_funct_1(B!1), u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k2_funct_1(B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), A!0)) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(A!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[379, 122, 305, 376])).
% 0.71/0.89 tff(381,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[380, 335, 300, 295, 290, 258, 119, 114, 109])).
% 0.71/0.89 % SZS output end Proof
% 0.74/0.89 % E exiting
%------------------------------------------------------------------------------