%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP621+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:08:11 AM UTC 2025
% Result : Theorem 0.93s 1.13s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP621+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:25:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.93/1.13 % SZS status Theorem
% 0.93/1.13 % SZS output start Proof
% 0.93/1.13 tff(r2_hidden_type, type, (
% 0.93/1.13 r2_hidden: ( $i * $i ) > $o)).
% 0.93/1.13 tff(k1_autgroup_type, type, (
% 0.93/1.13 k1_autgroup: $i > $i)).
% 0.93/1.13 tff(tptp_fun_A_0_type, type, (
% 0.93/1.13 tptp_fun_A_0: $i)).
% 0.93/1.13 tff(k5_relat_1_type, type, (
% 0.93/1.13 k5_relat_1: ( $i * $i ) > $i)).
% 0.93/1.13 tff(tptp_fun_B_1_type, type, (
% 0.93/1.13 tptp_fun_B_1: $i)).
% 0.93/1.13 tff(tptp_fun_C_2_type, type, (
% 0.93/1.13 tptp_fun_C_2: $i)).
% 0.93/1.13 tff(k7_funct_2_type, type, (
% 0.93/1.13 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.93/1.13 tff(u1_struct_0_type, type, (
% 0.93/1.13 u1_struct_0: $i > $i)).
% 0.93/1.13 tff(m1_relset_1_type, type, (
% 0.93/1.13 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(m2_relset_1_type, type, (
% 0.93/1.13 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v1_group_6_type, type, (
% 0.93/1.13 v1_group_6: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v1_funct_2_type, type, (
% 0.93/1.13 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v1_funct_1_type, type, (
% 0.93/1.13 v1_funct_1: $i > $o)).
% 0.93/1.13 tff(m2_fraenkel_type, type, (
% 0.93/1.13 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v3_group_6_type, type, (
% 0.93/1.13 v3_group_6: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v2_funct_1_type, type, (
% 0.93/1.13 v2_funct_1: $i > $o)).
% 0.93/1.13 tff(tptp_fun_C_4_type, type, (
% 0.93/1.13 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.93/1.13 tff(tptp_fun_C_3_type, type, (
% 0.93/1.13 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.93/1.13 tff(m1_fraenkel_type, type, (
% 0.93/1.13 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(v4_group_1_type, type, (
% 0.93/1.13 v4_group_1: $i > $o)).
% 0.93/1.13 tff(v3_group_1_type, type, (
% 0.93/1.13 v3_group_1: $i > $o)).
% 0.93/1.13 tff(v1_group_1_type, type, (
% 0.93/1.13 v1_group_1: $i > $o)).
% 0.93/1.13 tff(l1_group_1_type, type, (
% 0.93/1.13 l1_group_1: $i > $o)).
% 0.93/1.13 tff(v3_struct_0_type, type, (
% 0.93/1.13 v3_struct_0: $i > $o)).
% 0.93/1.13 tff(v1_xboole_0_type, type, (
% 0.93/1.13 v1_xboole_0: $i > $o)).
% 0.93/1.13 tff(l1_struct_0_type, type, (
% 0.93/1.13 l1_struct_0: $i > $o)).
% 0.93/1.13 tff(m1_subset_1_type, type, (
% 0.93/1.13 m1_subset_1: ( $i * $i ) > $o)).
% 0.93/1.13 tff(v4_group_6_type, type, (
% 0.93/1.13 v4_group_6: ( $i * $i * $i ) > $o)).
% 0.93/1.13 tff(g1_group_1_type, type, (
% 0.93/1.13 g1_group_1: ( $i * $i ) > $i)).
% 0.93/1.13 tff(u1_group_1_type, type, (
% 0.93/1.13 u1_group_1: $i > $i)).
% 0.93/1.13 tff(k8_group_6_type, type, (
% 0.93/1.13 k8_group_6: ( $i * $i * $i * $i * $i ) > $i)).
% 0.93/1.13 tff(v1_fraenkel_type, type, (
% 0.93/1.13 v1_fraenkel: $i > $o)).
% 0.93/1.13 tff(1,plain,
% 0.93/1.13 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(2,plain,
% 0.93/1.13 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1])).
% 0.93/1.13 tff(3,plain,
% 0.93/1.13 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.93/1.13 tff(5,plain,
% 0.93/1.13 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.93/1.13 tff(6,plain,(
% 0.93/1.13 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.93/1.13 inference(skolemize,[status(sab)],[5])).
% 0.93/1.13 tff(7,plain,
% 0.93/1.13 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.93/1.13 tff(8,plain,
% 0.93/1.13 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(9,plain,
% 0.93/1.13 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.93/1.13 tff(10,plain,
% 0.93/1.13 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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))))))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(11,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[10])).
% 0.93/1.13 tff(12,plain,
% 0.93/1.13 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(13,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[12])).
% 0.93/1.13 tff(14,plain,
% 0.93/1.13 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(15,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[14])).
% 0.93/1.13 tff(16,plain,
% 0.93/1.13 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.13 inference(transitivity,[status(thm)],[15, 13])).
% 0.93/1.13 tff(17,plain,
% 0.93/1.13 (^[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) | (~l1_group_1(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) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(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) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(18,plain,
% 0.93/1.14 (![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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[17])).
% 0.93/1.14 tff(19,plain,
% 0.93/1.14 (^[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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(20,plain,
% 0.93/1.14 (![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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[19])).
% 0.93/1.14 tff(21,plain,
% 0.93/1.14 (![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))))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(22,plain,
% 0.93/1.14 (^[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))))))))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(23,plain,
% 0.93/1.14 (![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))))))))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[22])).
% 0.93/1.14 tff(24,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')).
% 0.93/1.14 tff(25,plain,
% 0.93/1.14 (![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))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.93/1.14 tff(26,plain,
% 0.93/1.14 (![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))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.93/1.14 tff(27,plain,(
% 0.93/1.14 ![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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))),
% 0.93/1.14 inference(skolemize,[status(sab)],[26])).
% 0.93/1.14 tff(28,plain,
% 0.93/1.14 (![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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (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))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.93/1.14 tff(29,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.93/1.14 tff(30,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(B, A), B)))))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.93/1.14 tff(31,plain,
% 0.93/1.14 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.93/1.14 tff(32,plain,
% 0.93/1.14 ((((~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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, 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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(33,plain,
% 0.93/1.14 ((~![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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, 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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(34,plain,
% 0.93/1.14 ((~![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)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, 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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(35,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)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_autgroup')).
% 0.93/1.14 tff(36,plain,
% 0.93/1.14 (~![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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.93/1.14 tff(37,plain,
% 0.93/1.14 (~![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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.93/1.14 tff(38,plain,
% 0.93/1.14 (~![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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.93/1.14 tff(39,plain,
% 0.93/1.14 (~![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))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.93/1.14 tff(40,plain,
% 0.93/1.14 ((~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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.93/1.14 tff(41,plain,
% 0.93/1.14 (l1_group_1(A!0)),
% 0.93/1.14 inference(and_elim,[status(thm)],[40])).
% 0.93/1.14 tff(42,plain,
% 0.93/1.14 (v4_group_1(A!0)),
% 0.93/1.14 inference(and_elim,[status(thm)],[40])).
% 0.93/1.14 tff(43,plain,
% 0.93/1.14 (v3_group_1(A!0)),
% 0.93/1.14 inference(and_elim,[status(thm)],[40])).
% 0.93/1.14 tff(44,plain,
% 0.93/1.14 (v1_group_1(A!0)),
% 0.93/1.14 inference(and_elim,[status(thm)],[40])).
% 0.93/1.14 tff(45,plain,
% 0.93/1.14 (~v3_struct_0(A!0)),
% 0.93/1.14 inference(and_elim,[status(thm)],[40])).
% 0.93/1.14 tff(46,plain,
% 0.93/1.14 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(47,plain,
% 0.93/1.14 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, 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)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(48,plain,
% 0.93/1.14 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, 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)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[47])).
% 0.93/1.14 tff(49,plain,
% 0.93/1.14 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, 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)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.15 inference(transitivity,[status(thm)],[48, 46])).
% 0.93/1.15 tff(50,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, 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)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(51,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~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))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~(((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))) <=> r2_hidden(tptp_fun_C_4(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) | (~l1_group_1(A!0)) | (~v1_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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.93/1.15 tff(52,plain,
% 0.93/1.15 (![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))))),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[51, 45, 44, 43, 42, 41, 31])).
% 0.93/1.15 tff(53,plain,
% 0.93/1.15 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(54,plain,
% 0.93/1.15 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[53])).
% 0.93/1.15 tff(55,plain,
% 0.93/1.15 (^[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) | (~l1_group_1(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) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(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) | (~l1_group_1(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))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(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))) | 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)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(56,plain,
% 0.93/1.15 (![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)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[55])).
% 0.93/1.15 tff(57,plain,
% 0.93/1.15 (![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)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(58,plain,
% 0.93/1.15 (^[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)))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(59,plain,
% 0.93/1.15 (![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)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[58])).
% 0.93/1.15 tff(60,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')).
% 0.93/1.15 tff(61,plain,
% 0.93/1.15 (![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)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.93/1.15 tff(62,plain,
% 0.93/1.15 (![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)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.93/1.15 tff(63,plain,(
% 0.93/1.15 ![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)))),
% 0.93/1.15 inference(skolemize,[status(sab)],[62])).
% 0.93/1.15 tff(64,plain,
% 0.93/1.15 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.93/1.15 tff(65,plain,
% 0.93/1.15 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.93/1.15 tff(66,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A)) | (~v1_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)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(67,plain,
% 0.93/1.15 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)) | (~v1_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)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(68,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A!0)) | (~v1_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)) | (~l1_group_1(A)) | (~v1_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))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[67])).
% 0.93/1.15 tff(69,plain,
% 0.93/1.15 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A!0)) | (~v1_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)) | (~l1_group_1(A)) | (~v1_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)))),
% 0.93/1.15 inference(transitivity,[status(thm)],[68, 66])).
% 0.93/1.15 tff(70,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(71,plain,
% 0.93/1.15 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_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))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.93/1.15 tff(72,plain,
% 0.93/1.15 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[71, 45, 44, 43, 42, 41, 65])).
% 0.93/1.15 tff(73,plain,
% 0.93/1.15 (((~![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(74,plain,
% 0.93/1.15 (((~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_3(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_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_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(75,plain,
% 0.93/1.15 (((~![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(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_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_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[74])).
% 0.93/1.15 tff(76,plain,
% 0.93/1.15 (((~![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(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_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_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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))))))))))),
% 0.93/1.16 inference(transitivity,[status(thm)],[75, 73])).
% 0.93/1.16 tff(77,plain,
% 0.93/1.16 ((~![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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_3(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_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_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))))))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(78,plain,
% 0.93/1.16 ((~![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_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~m2_relset_1(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_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_3(B, A!0))))))) | (~((~(((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))) <=> r2_hidden(tptp_fun_C_4(B, A!0), B))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_1(tptp_fun_C_4(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)))))))))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.93/1.16 tff(79,plain,
% 0.93/1.16 (~((~![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))))))))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[78, 72, 52])).
% 0.93/1.16 tff(80,plain,
% 0.93/1.16 (((~![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))))))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(81,plain,
% 0.93/1.16 (![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))))))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.93/1.16 tff(82,plain,
% 0.93/1.16 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.93/1.16 inference(and_elim,[status(thm)],[40])).
% 0.93/1.16 tff(83,plain,
% 0.93/1.16 (((~![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))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!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_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)))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(84,plain,
% 0.93/1.16 (((~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_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)))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(85,plain,
% 0.93/1.16 (((~![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_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))))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[84])).
% 0.93/1.16 tff(86,plain,
% 0.93/1.16 (((~![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_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)))))),
% 0.93/1.16 inference(transitivity,[status(thm)],[85, 83])).
% 0.93/1.16 tff(87,plain,
% 0.93/1.16 ((~![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))))))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(88,plain,
% 0.93/1.16 ((~![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))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.93/1.16 tff(89,plain,
% 0.93/1.16 (~((~v1_funct_1(B!1)) | (~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)))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[88, 82, 81])).
% 0.93/1.16 tff(90,plain,
% 0.93/1.16 (((~v1_funct_1(B!1)) | (~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))) | m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(91,plain,
% 0.93/1.16 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.93/1.16 tff(92,plain,
% 0.93/1.16 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_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))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(93,plain,
% 0.93/1.16 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.93/1.16 tff(94,plain,
% 0.93/1.16 (m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[93, 9])).
% 0.93/1.16 tff(95,plain,
% 0.93/1.16 (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.93/1.16 inference(and_elim,[status(thm)],[40])).
% 0.93/1.16 tff(96,plain,
% 0.93/1.16 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.93/1.16 inference(or_elim,[status(thm)],[95])).
% 0.93/1.16 tff(97,plain,
% 0.93/1.16 (((~![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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(98,plain,
% 0.93/1.16 (((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(99,plain,
% 0.93/1.16 (((~![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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, 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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[98])).
% 0.93/1.16 tff(100,plain,
% 0.93/1.16 (((~![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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, 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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 0.93/1.16 inference(transitivity,[status(thm)],[99, 97])).
% 0.93/1.16 tff(101,plain,
% 0.93/1.16 ((~![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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(102,plain,
% 0.93/1.16 ((~![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(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.93/1.16 tff(103,plain,
% 0.93/1.16 (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[102, 96, 81])).
% 0.93/1.16 tff(104,plain,
% 0.93/1.16 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_funct_1(C!2)),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(105,plain,
% 0.93/1.16 (v1_funct_1(C!2)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.93/1.16 tff(106,plain,
% 0.93/1.16 (((~v1_funct_1(B!1)) | (~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))) | v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(107,plain,
% 0.93/1.16 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[106, 89])).
% 0.93/1.16 tff(108,plain,
% 0.93/1.16 (((~v1_funct_1(B!1)) | (~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))) | v1_funct_1(B!1)),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(109,plain,
% 0.93/1.16 (v1_funct_1(B!1)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[108, 89])).
% 0.93/1.16 tff(110,plain,
% 0.93/1.16 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(111,plain,
% 0.93/1.16 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[110, 103])).
% 0.93/1.16 tff(112,plain,
% 0.93/1.16 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(113,plain,
% 0.93/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[112])).
% 0.93/1.16 tff(114,plain,
% 0.93/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(115,plain,
% 0.93/1.16 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(116,plain,
% 0.93/1.16 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[115])).
% 0.93/1.16 tff(117,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.93/1.16 tff(118,plain,
% 0.93/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.93/1.16 tff(119,plain,
% 0.93/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.93/1.16 tff(120,plain,(
% 0.93/1.16 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(skolemize,[status(sab)],[119])).
% 0.93/1.16 tff(121,plain,
% 0.93/1.16 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.93/1.16 tff(122,plain,
% 0.93/1.16 (((~![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)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(123,plain,
% 0.93/1.16 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(124,plain,
% 0.93/1.16 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.93/1.16 tff(125,plain,
% 0.93/1.16 (l1_struct_0(A!0)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[124, 41, 121])).
% 0.93/1.16 tff(126,plain,
% 0.93/1.16 (^[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))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(127,plain,
% 0.93/1.16 (![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)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[126])).
% 0.93/1.16 tff(128,plain,
% 0.93/1.16 (^[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)))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(129,plain,
% 0.93/1.16 (![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)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[128])).
% 0.93/1.16 tff(130,plain,
% 0.93/1.16 (![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))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(131,plain,
% 0.93/1.16 (^[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)))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(132,plain,
% 0.93/1.16 (![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))))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[131])).
% 0.93/1.16 tff(133,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')).
% 0.93/1.16 tff(134,plain,
% 0.93/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.93/1.16 tff(135,plain,
% 0.93/1.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.93/1.16 tff(136,plain,(
% 0.93/1.16 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.93/1.16 inference(skolemize,[status(sab)],[135])).
% 0.93/1.16 tff(137,plain,
% 0.93/1.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.93/1.16 tff(138,plain,
% 0.93/1.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.93/1.16 tff(139,plain,
% 0.93/1.16 (((~![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))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(140,plain,
% 0.93/1.16 ((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))))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(141,plain,
% 0.93/1.16 (((~![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)))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[140])).
% 0.93/1.16 tff(142,plain,
% 0.93/1.16 (((~![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))))),
% 0.93/1.16 inference(transitivity,[status(thm)],[141, 139])).
% 0.93/1.16 tff(143,plain,
% 0.93/1.16 ((~![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)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(144,plain,
% 0.93/1.16 ((~![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)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.93/1.16 tff(145,plain,
% 0.93/1.16 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[144, 45, 138])).
% 0.93/1.16 tff(146,plain,
% 0.93/1.16 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[145, 125])).
% 0.93/1.16 tff(147,plain,
% 0.93/1.16 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(148,plain,
% 0.93/1.16 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[147, 7])).
% 0.93/1.16 tff(149,plain,
% 0.93/1.16 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(150,plain,
% 0.93/1.16 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[149, 103])).
% 0.93/1.16 tff(151,plain,
% 0.93/1.16 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(tautology,[status(thm)],[])).
% 0.93/1.16 tff(152,plain,
% 0.93/1.16 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.93/1.16 tff(153,plain,
% 0.93/1.16 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[152, 148])).
% 0.93/1.16 tff(154,plain,
% 0.93/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(155,plain,
% 0.93/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[154])).
% 0.93/1.16 tff(156,plain,
% 0.93/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(157,plain,
% 0.93/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[156])).
% 0.93/1.16 tff(158,plain,
% 0.93/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(159,plain,
% 0.93/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(160,plain,
% 0.93/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[159])).
% 0.93/1.17 tff(161,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 0.93/1.17 tff(162,plain,
% 0.93/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.93/1.17 tff(163,plain,
% 0.93/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.93/1.17 tff(164,plain,(
% 0.93/1.17 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.93/1.17 inference(skolemize,[status(sab)],[163])).
% 0.93/1.17 tff(165,plain,
% 0.93/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.93/1.17 tff(166,plain,
% 0.93/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.93/1.17 tff(167,plain,
% 0.93/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(168,plain,
% 0.93/1.17 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(169,plain,
% 0.93/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[168])).
% 0.93/1.17 tff(170,plain,
% 0.93/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[169, 167])).
% 0.93/1.17 tff(171,plain,
% 0.93/1.17 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(172,plain,
% 0.93/1.17 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.93/1.17 tff(173,plain,
% 0.93/1.17 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[172, 166])).
% 0.93/1.17 tff(174,plain,
% 0.93/1.17 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[173, 153, 146, 111, 109, 107, 105, 94])).
% 0.93/1.17 tff(175,plain,
% 0.93/1.17 (k5_relat_1(C!2, B!1) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 0.93/1.17 inference(symmetry,[status(thm)],[174])).
% 0.93/1.17 tff(176,plain,
% 0.93/1.17 (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[175])).
% 0.93/1.17 tff(177,plain,
% 0.93/1.17 (r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)) <=> r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(symmetry,[status(thm)],[176])).
% 0.93/1.17 tff(178,plain,
% 0.93/1.17 ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) <=> (~r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[177])).
% 0.93/1.17 tff(179,plain,
% 0.93/1.17 (^[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))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(180,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[179])).
% 0.93/1.17 tff(181,plain,
% 0.93/1.17 (^[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))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(182,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[181])).
% 0.93/1.17 tff(183,plain,
% 0.93/1.17 (^[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))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(184,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[183])).
% 0.93/1.17 tff(185,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[184, 182])).
% 0.93/1.17 tff(186,plain,
% 0.93/1.17 (^[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)))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(187,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[186])).
% 0.93/1.17 tff(188,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(189,plain,
% 0.93/1.17 (^[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))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(190,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[189])).
% 0.93/1.17 tff(191,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')).
% 0.93/1.17 tff(192,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.93/1.17 tff(193,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.93/1.17 tff(194,plain,(
% 0.93/1.17 ![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)))),
% 0.93/1.17 inference(skolemize,[status(sab)],[193])).
% 0.93/1.17 tff(195,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.93/1.17 tff(196,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[195, 185])).
% 0.93/1.17 tff(197,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[196, 180])).
% 0.93/1.17 tff(198,plain,
% 0.93/1.17 (((~![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))))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(199,plain,
% 0.93/1.17 ((~![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))))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(200,plain,
% 0.93/1.17 ((~![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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.93/1.17 tff(201,plain,
% 0.93/1.17 (![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)))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[200, 197, 146, 72])).
% 0.93/1.17 tff(202,plain,
% 0.93/1.17 ((~![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(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(203,plain,
% 0.93/1.17 (m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.93/1.17 tff(204,plain,
% 0.93/1.17 (~m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.93/1.17 inference(or_elim,[status(thm)],[95])).
% 0.93/1.17 tff(205,plain,
% 0.93/1.17 ((~(m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) | (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(tautology,[status(thm)],[])).
% 0.93/1.17 tff(206,plain,
% 0.93/1.17 ((~(m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) | (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.93/1.17 tff(207,plain,
% 0.93/1.17 (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[206, 203])).
% 0.93/1.17 tff(208,plain,
% 0.93/1.17 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(209,plain,
% 0.93/1.17 (![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))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[208])).
% 0.93/1.17 tff(210,plain,
% 0.93/1.17 (![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))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(211,plain,
% 0.93/1.17 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(212,plain,
% 0.93/1.17 (![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))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[211])).
% 0.93/1.17 tff(213,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.93/1.17 tff(214,plain,
% 0.93/1.17 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.93/1.17 tff(215,plain,
% 0.93/1.17 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.93/1.17 tff(216,plain,(
% 0.93/1.17 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.93/1.17 inference(skolemize,[status(sab)],[215])).
% 0.93/1.17 tff(217,plain,
% 0.93/1.17 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.93/1.17 tff(218,plain,
% 0.93/1.17 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(219,plain,
% 0.93/1.17 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(220,plain,
% 0.93/1.17 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.93/1.17 tff(221,plain,
% 0.93/1.17 (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[220, 217, 207])).
% 0.93/1.17 tff(222,plain,
% 0.93/1.17 (~r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[221, 178])).
% 0.93/1.17 tff(223,plain,
% 0.93/1.17 (^[A: $i] : refl(((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))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(224,plain,
% 0.93/1.17 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[223])).
% 0.93/1.17 tff(225,plain,
% 0.93/1.17 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(226,plain,
% 0.93/1.17 (^[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))) | (~l1_group_1(A)) | (~v1_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))) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(227,plain,
% 0.93/1.17 (![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))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[226])).
% 0.93/1.17 tff(228,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')).
% 0.93/1.17 tff(229,plain,
% 0.93/1.17 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.93/1.17 tff(230,plain,
% 0.93/1.17 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.93/1.17 tff(231,plain,(
% 0.93/1.17 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(skolemize,[status(sab)],[230])).
% 0.93/1.17 tff(232,plain,
% 0.93/1.17 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.93/1.17 tff(233,plain,
% 0.93/1.17 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_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))) | (~l1_group_1(A)) | (~v1_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))))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(234,plain,
% 0.93/1.17 (((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_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))))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(235,plain,
% 0.93/1.17 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_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)))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[234])).
% 0.93/1.17 tff(236,plain,
% 0.93/1.17 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_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))))),
% 0.93/1.17 inference(transitivity,[status(thm)],[235, 233])).
% 0.93/1.17 tff(237,plain,
% 0.93/1.17 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(238,plain,
% 0.93/1.17 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_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)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.93/1.17 tff(239,plain,
% 0.93/1.17 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[238, 44, 41, 232])).
% 0.93/1.17 tff(240,plain,
% 0.93/1.17 (k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 0.93/1.17 inference(monotonicity,[status(thm)],[239])).
% 0.93/1.17 tff(241,plain,
% 0.93/1.17 (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 0.93/1.17 inference(symmetry,[status(thm)],[240])).
% 0.93/1.17 tff(242,plain,
% 0.93/1.17 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 0.93/1.17 inference(symmetry,[status(thm)],[239])).
% 0.93/1.17 tff(243,plain,
% 0.93/1.17 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 0.93/1.17 inference(monotonicity,[status(thm)],[242])).
% 0.93/1.17 tff(244,plain,
% 0.93/1.17 (m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[243, 243])).
% 0.93/1.17 tff(245,plain,
% 0.93/1.17 (m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.17 inference(symmetry,[status(thm)],[244])).
% 0.93/1.17 tff(246,plain,
% 0.93/1.17 (m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[94, 245])).
% 0.93/1.17 tff(247,plain,
% 0.93/1.17 (m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[243, 243])).
% 0.93/1.17 tff(248,plain,
% 0.93/1.17 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.17 inference(symmetry,[status(thm)],[247])).
% 0.93/1.17 tff(249,plain,
% 0.93/1.17 (m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[153, 248])).
% 0.93/1.17 tff(250,plain,
% 0.93/1.17 (v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(C!2, A!0, A!0)),
% 0.93/1.17 inference(monotonicity,[status(thm)],[242, 242])).
% 0.93/1.17 tff(251,plain,
% 0.93/1.17 (v1_group_6(C!2, A!0, A!0) <=> v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.17 inference(symmetry,[status(thm)],[250])).
% 0.93/1.17 tff(252,plain,
% 0.93/1.17 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_group_6(C!2, A!0, A!0)),
% 0.93/1.17 inference(tautology,[status(thm)],[])).
% 0.93/1.17 tff(253,plain,
% 0.93/1.17 (v1_group_6(C!2, A!0, A!0)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[252, 103])).
% 0.93/1.17 tff(254,plain,
% 0.93/1.17 (v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[253, 251])).
% 0.93/1.18 tff(255,plain,
% 0.93/1.18 (v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[243, 243])).
% 0.93/1.18 tff(256,plain,
% 0.93/1.18 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.18 inference(symmetry,[status(thm)],[255])).
% 0.93/1.18 tff(257,plain,
% 0.93/1.18 (v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[111, 256])).
% 0.93/1.18 tff(258,plain,
% 0.93/1.18 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(B!1, A!0, A!0)),
% 0.93/1.18 inference(monotonicity,[status(thm)],[242, 242])).
% 0.93/1.18 tff(259,plain,
% 0.93/1.18 (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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(symmetry,[status(thm)],[258])).
% 0.93/1.18 tff(260,plain,
% 0.93/1.18 (((~v1_funct_1(B!1)) | (~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))) | v1_group_6(B!1, A!0, A!0)),
% 0.93/1.18 inference(tautology,[status(thm)],[])).
% 0.93/1.18 tff(261,plain,
% 0.93/1.18 (v1_group_6(B!1, A!0, A!0)),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[260, 89])).
% 0.93/1.18 tff(262,plain,
% 0.93/1.18 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[261, 259])).
% 0.93/1.18 tff(263,plain,
% 0.93/1.18 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[243, 243])).
% 0.93/1.18 tff(264,plain,
% 0.93/1.18 (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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.18 inference(symmetry,[status(thm)],[263])).
% 0.93/1.18 tff(265,plain,
% 0.93/1.18 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[107, 264])).
% 0.93/1.18 tff(266,plain,
% 0.93/1.18 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 0.93/1.18 inference(monotonicity,[status(thm)],[242])).
% 0.93/1.18 tff(267,plain,
% 0.93/1.18 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(symmetry,[status(thm)],[266])).
% 0.93/1.18 tff(268,plain,
% 0.93/1.18 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[42, 267])).
% 0.93/1.18 tff(269,plain,
% 0.93/1.18 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 0.93/1.18 inference(monotonicity,[status(thm)],[242])).
% 0.93/1.18 tff(270,plain,
% 0.93/1.18 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(symmetry,[status(thm)],[269])).
% 0.93/1.18 tff(271,plain,
% 0.93/1.18 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[43, 270])).
% 0.93/1.18 tff(272,plain,
% 0.93/1.18 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 0.93/1.18 inference(monotonicity,[status(thm)],[242])).
% 0.93/1.18 tff(273,plain,
% 0.93/1.18 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(symmetry,[status(thm)],[272])).
% 0.93/1.18 tff(274,plain,
% 0.93/1.18 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[41, 273])).
% 0.93/1.18 tff(275,plain,
% 0.93/1.18 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 0.93/1.18 inference(monotonicity,[status(thm)],[242])).
% 0.93/1.18 tff(276,plain,
% 0.93/1.18 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(symmetry,[status(thm)],[275])).
% 0.93/1.18 tff(277,plain,
% 0.93/1.18 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[276])).
% 0.93/1.18 tff(278,plain,
% 0.93/1.18 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[45, 277])).
% 0.93/1.18 tff(279,plain,
% 0.93/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))),
% 0.93/1.18 inference(bind,[status(th)],[])).
% 0.93/1.18 tff(280,plain,
% 0.93/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 0.93/1.18 inference(quant_intro,[status(thm)],[279])).
% 0.93/1.18 tff(281,plain,
% 0.93/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $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(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))),
% 0.93/1.18 inference(bind,[status(th)],[])).
% 0.93/1.18 tff(282,plain,
% 0.93/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 0.93/1.18 inference(quant_intro,[status(thm)],[281])).
% 0.93/1.18 tff(283,plain,
% 0.93/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(284,plain,
% 1.02/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 1.02/1.18 inference(bind,[status(th)],[])).
% 1.02/1.18 tff(285,plain,
% 1.02/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.02/1.18 inference(quant_intro,[status(thm)],[284])).
% 1.02/1.18 tff(286,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_group_6')).
% 1.02/1.18 tff(287,plain,
% 1.02/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.02/1.18 tff(288,plain,
% 1.02/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[287, 283])).
% 1.02/1.18 tff(289,plain,(
% 1.02/1.18 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.02/1.18 inference(skolemize,[status(sab)],[288])).
% 1.02/1.18 tff(290,plain,
% 1.02/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[289, 282])).
% 1.02/1.18 tff(291,plain,
% 1.02/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[290, 280])).
% 1.02/1.18 tff(292,plain,
% 1.02/1.18 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(293,plain,
% 1.02/1.18 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(294,plain,
% 1.02/1.19 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[293])).
% 1.02/1.19 tff(295,plain,
% 1.02/1.19 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[294, 292])).
% 1.02/1.19 tff(296,plain,
% 1.02/1.19 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(297,plain,
% 1.02/1.19 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.02/1.19 tff(298,plain,
% 1.02/1.19 ((~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[297, 291, 109, 105, 278, 274, 271, 268, 265, 262, 257, 254])).
% 1.02/1.19 tff(299,plain,
% 1.02/1.19 (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[298, 249, 246])).
% 1.02/1.19 tff(300,plain,
% 1.02/1.19 (k5_relat_1(C!2, B!1) = k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.02/1.19 inference(symmetry,[status(thm)],[299])).
% 1.02/1.19 tff(301,plain,
% 1.02/1.19 (k5_relat_1(C!2, B!1) = k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.02/1.19 inference(transitivity,[status(thm)],[300, 241])).
% 1.02/1.19 tff(302,plain,
% 1.02/1.19 (v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0) <=> v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[301, 239])).
% 1.02/1.19 tff(303,plain,
% 1.02/1.19 (v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.02/1.19 inference(symmetry,[status(thm)],[302])).
% 1.02/1.19 tff(304,plain,
% 1.02/1.19 (v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(C!2, A!0, A!0)),
% 1.02/1.19 inference(monotonicity,[status(thm)],[242])).
% 1.02/1.19 tff(305,plain,
% 1.02/1.19 (v4_group_6(C!2, A!0, A!0) <=> v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.02/1.19 inference(symmetry,[status(thm)],[304])).
% 1.02/1.19 tff(306,plain,
% 1.02/1.19 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(307,plain,
% 1.02/1.19 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[306])).
% 1.02/1.19 tff(308,plain,
% 1.02/1.19 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(309,plain,
% 1.02/1.19 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[308])).
% 1.02/1.19 tff(310,plain,
% 1.02/1.19 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.02/1.19 inference(transitivity,[status(thm)],[309, 307])).
% 1.02/1.19 tff(311,plain,
% 1.02/1.19 (^[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) | (~l1_group_1(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) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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)))))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(312,plain,
% 1.03/1.19 (![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) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[311])).
% 1.03/1.19 tff(313,plain,
% 1.03/1.19 (![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))))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(314,plain,
% 1.03/1.19 (^[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))))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(315,plain,
% 1.03/1.19 (![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))))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[314])).
% 1.03/1.19 tff(316,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')).
% 1.03/1.19 tff(317,plain,
% 1.03/1.19 (![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))))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.03/1.19 tff(318,plain,
% 1.03/1.19 (![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))))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.03/1.19 tff(319,plain,(
% 1.03/1.19 ![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))))),
% 1.03/1.19 inference(skolemize,[status(sab)],[318])).
% 1.03/1.19 tff(320,plain,
% 1.03/1.19 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[319, 312])).
% 1.03/1.19 tff(321,plain,
% 1.03/1.19 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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)))))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[320, 310])).
% 1.03/1.19 tff(322,plain,
% 1.03/1.19 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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)))))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(323,plain,
% 1.03/1.19 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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)))))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(324,plain,
% 1.03/1.19 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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))))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[323])).
% 1.03/1.19 tff(325,plain,
% 1.03/1.19 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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)))))),
% 1.03/1.19 inference(transitivity,[status(thm)],[324, 322])).
% 1.03/1.19 tff(326,plain,
% 1.03/1.19 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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)))))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(327,plain,
% 1.03/1.19 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_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) | (~l1_group_1(A!0)) | (~v1_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))))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.03/1.19 tff(328,plain,
% 1.03/1.19 (![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))))),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[327, 45, 44, 43, 42, 41, 321])).
% 1.03/1.19 tff(329,plain,
% 1.03/1.19 (((~![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(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, 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(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(330,plain,
% 1.03/1.19 (((~v1_funct_1(C!2)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(331,plain,
% 1.03/1.19 (((~![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(C!2)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, 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(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[330])).
% 1.03/1.20 tff(332,plain,
% 1.03/1.20 (((~![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(C!2)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, 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(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[331, 329])).
% 1.03/1.20 tff(333,plain,
% 1.03/1.20 ((~![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(C!2)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(334,plain,
% 1.03/1.20 ((~![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(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.03/1.20 tff(335,plain,
% 1.03/1.20 (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[334, 328, 105, 111, 150, 253])).
% 1.03/1.20 tff(336,plain,
% 1.03/1.20 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(337,plain,
% 1.03/1.20 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[336, 201])).
% 1.03/1.20 tff(338,plain,
% 1.03/1.20 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(339,plain,
% 1.03/1.20 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[338, 96])).
% 1.03/1.20 tff(340,plain,
% 1.03/1.20 (m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[339, 337])).
% 1.03/1.20 tff(341,plain,
% 1.03/1.20 (^[A: $i, B: $i, C: $i] : refl(((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(342,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[341])).
% 1.03/1.20 tff(343,plain,
% 1.03/1.20 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(344,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[343])).
% 1.03/1.20 tff(345,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(346,plain,
% 1.03/1.20 (^[A: $i, B: $i, C: $i] : rewrite((m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(347,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[346])).
% 1.03/1.20 tff(348,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')).
% 1.03/1.20 tff(349,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.03/1.20 tff(350,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[349, 345])).
% 1.03/1.20 tff(351,plain,(
% 1.03/1.20 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.03/1.20 inference(skolemize,[status(sab)],[350])).
% 1.03/1.20 tff(352,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[351, 344])).
% 1.03/1.20 tff(353,plain,
% 1.03/1.20 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[352, 342])).
% 1.03/1.20 tff(354,plain,
% 1.03/1.20 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(355,plain,
% 1.03/1.20 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(356,plain,
% 1.03/1.20 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.03/1.20 tff(357,plain,
% 1.03/1.20 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[356, 353, 72])).
% 1.03/1.20 tff(358,plain,
% 1.03/1.20 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(359,plain,
% 1.03/1.20 (~v1_xboole_0(k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[358, 357])).
% 1.03/1.20 tff(360,plain,
% 1.03/1.20 (^[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))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(361,plain,
% 1.03/1.20 (![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)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[360])).
% 1.03/1.20 tff(362,plain,
% 1.03/1.20 (![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)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(363,plain,
% 1.03/1.20 (^[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))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(364,plain,
% 1.03/1.20 (![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)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[363])).
% 1.03/1.20 tff(365,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')).
% 1.03/1.20 tff(366,plain,
% 1.03/1.20 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.03/1.20 tff(367,plain,
% 1.03/1.20 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[366, 362])).
% 1.03/1.20 tff(368,plain,(
% 1.03/1.20 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.03/1.20 inference(skolemize,[status(sab)],[367])).
% 1.03/1.20 tff(369,plain,
% 1.03/1.20 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[368, 361])).
% 1.03/1.20 tff(370,plain,
% 1.03/1.20 (((~![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(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, 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(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(371,plain,
% 1.03/1.20 ((r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(372,plain,
% 1.03/1.20 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, 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(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[371])).
% 1.03/1.20 tff(373,plain,
% 1.03/1.20 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, 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(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[372, 370])).
% 1.03/1.20 tff(374,plain,
% 1.03/1.20 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(375,plain,
% 1.03/1.20 ((~![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(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.03/1.20 tff(376,plain,
% 1.03/1.20 (r2_hidden(C!2, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[375, 369, 359, 340])).
% 1.03/1.20 tff(377,plain,
% 1.03/1.20 ((~(r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))) | (~r2_hidden(C!2, k1_autgroup(A!0))) | v4_group_6(C!2, A!0, A!0)),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(378,plain,
% 1.03/1.20 ((~(r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))) | v4_group_6(C!2, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[377, 376])).
% 1.03/1.20 tff(379,plain,
% 1.03/1.20 (v4_group_6(C!2, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[378, 335])).
% 1.03/1.20 tff(380,plain,
% 1.03/1.20 (v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[379, 305])).
% 1.03/1.20 tff(381,plain,
% 1.03/1.20 (v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(B!1, A!0, A!0)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[242, 242])).
% 1.03/1.20 tff(382,plain,
% 1.03/1.20 (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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.03/1.20 inference(symmetry,[status(thm)],[381])).
% 1.03/1.20 tff(383,plain,
% 1.03/1.20 (((~![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_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)) | (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_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)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(384,plain,
% 1.03/1.20 (((~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_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)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(385,plain,
% 1.03/1.20 (((~![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_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)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[384])).
% 1.03/1.20 tff(386,plain,
% 1.03/1.20 (((~![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_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)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[385, 383])).
% 1.03/1.20 tff(387,plain,
% 1.03/1.20 ((~![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))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(388,plain,
% 1.03/1.20 ((~![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_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)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.03/1.20 tff(389,plain,
% 1.03/1.20 (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[388, 328, 109, 107, 91, 261])).
% 1.03/1.20 tff(390,plain,
% 1.03/1.20 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(391,plain,
% 1.03/1.20 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[390, 201])).
% 1.03/1.20 tff(392,plain,
% 1.03/1.20 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(393,plain,
% 1.03/1.20 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[392, 82])).
% 1.03/1.20 tff(394,plain,
% 1.03/1.20 (m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[393, 391])).
% 1.03/1.20 tff(395,plain,
% 1.03/1.20 (((~![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)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(396,plain,
% 1.03/1.20 ((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)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(397,plain,
% 1.03/1.20 (((~![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))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[396])).
% 1.03/1.20 tff(398,plain,
% 1.03/1.20 (((~![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)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[397, 395])).
% 1.03/1.20 tff(399,plain,
% 1.03/1.20 ((~![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))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(400,plain,
% 1.03/1.20 ((~![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))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.03/1.20 tff(401,plain,
% 1.03/1.20 (r2_hidden(B!1, k1_autgroup(A!0))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[400, 369, 359, 394])).
% 1.03/1.20 tff(402,plain,
% 1.03/1.20 ((~(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)),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(403,plain,
% 1.03/1.20 ((~(r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))) | v4_group_6(B!1, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[402, 401])).
% 1.03/1.20 tff(404,plain,
% 1.03/1.20 (v4_group_6(B!1, A!0, A!0)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[403, 389])).
% 1.03/1.20 tff(405,plain,
% 1.03/1.20 (v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[404, 382])).
% 1.03/1.20 tff(406,plain,
% 1.03/1.20 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[243, 243])).
% 1.03/1.20 tff(407,plain,
% 1.03/1.20 (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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(symmetry,[status(thm)],[406])).
% 1.03/1.20 tff(408,plain,
% 1.03/1.20 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[91, 407])).
% 1.03/1.20 tff(409,plain,
% 1.03/1.20 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[243])).
% 1.03/1.20 tff(410,plain,
% 1.03/1.20 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(symmetry,[status(thm)],[409])).
% 1.03/1.20 tff(411,plain,
% 1.03/1.20 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[150, 410])).
% 1.03/1.20 tff(412,plain,
% 1.03/1.20 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[243])).
% 1.03/1.20 tff(413,plain,
% 1.03/1.20 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(symmetry,[status(thm)],[412])).
% 1.03/1.20 tff(414,plain,
% 1.03/1.20 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[111, 413])).
% 1.03/1.20 tff(415,plain,
% 1.03/1.20 (v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(C!2, A!0, A!0)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[242])).
% 1.03/1.20 tff(416,plain,
% 1.03/1.20 (v1_group_6(C!2, A!0, A!0) <=> v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.03/1.20 inference(symmetry,[status(thm)],[415])).
% 1.03/1.20 tff(417,plain,
% 1.03/1.20 (v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[253, 416])).
% 1.03/1.20 tff(418,plain,
% 1.03/1.20 (^[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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(419,plain,
% 1.03/1.20 (![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[418])).
% 1.03/1.20 tff(420,plain,
% 1.03/1.20 (^[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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(421,plain,
% 1.03/1.20 (![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[420])).
% 1.03/1.20 tff(422,plain,
% 1.03/1.20 (![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[421, 419])).
% 1.03/1.20 tff(423,plain,
% 1.03/1.20 (^[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(((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) <=> (~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))), ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) <=> (~(~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))))), rewrite((~(~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)))), ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))), 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) & 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((~(~((~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)))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((v4_group_6(D, A, B) & v4_group_6(E, B, C)) <=> (~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) <=> (~(~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), rewrite((~(~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))) <=> ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))), ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) <=> ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), trans(monotonicity(rewrite((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))) | ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))), rewrite((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))) | ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))), ((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, 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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), 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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, 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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, 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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ((v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), rewrite(((v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (((~((~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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ((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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))), 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (((~((~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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(424,plain,
% 1.03/1.21 (![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[423])).
% 1.03/1.21 tff(425,plain,
% 1.03/1.21 (![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(426,plain,
% 1.03/1.21 (^[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((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), 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))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite(((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)) <=> ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))), (((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> ((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), (((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), (![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, 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))) => ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), 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))) => ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, 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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), (![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))) <=> ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> (((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) => ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), rewrite((((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) => ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), (![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))))), (![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), ((((((~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] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> (((~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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))))), 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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ((~((~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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), ((((((~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] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> ((~((~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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(427,plain,
% 1.03/1.21 (![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] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> ![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[426])).
% 1.03/1.21 tff(428,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] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![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))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t74_group_6')).
% 1.03/1.21 tff(429,plain,
% 1.03/1.21 (![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.03/1.21 tff(430,plain,
% 1.03/1.21 (![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[429, 425])).
% 1.03/1.21 tff(431,plain,(
% 1.03/1.21 ![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] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![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)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.03/1.21 inference(skolemize,[status(sab)],[430])).
% 1.03/1.21 tff(432,plain,
% 1.03/1.21 (![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[431, 424])).
% 1.03/1.21 tff(433,plain,
% 1.03/1.21 (![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[432, 422])).
% 1.03/1.21 tff(434,plain,
% 1.03/1.21 (((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))) <=> ((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(435,plain,
% 1.03/1.21 ((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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C))))))) <=> (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(436,plain,
% 1.03/1.21 (((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))) <=> ((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[435])).
% 1.03/1.21 tff(437,plain,
% 1.03/1.21 (((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))) <=> ((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[436, 434])).
% 1.03/1.21 tff(438,plain,
% 1.03/1.21 ((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(439,plain,
% 1.03/1.21 ((~![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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![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))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.03/1.21 tff(440,plain,
% 1.03/1.21 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[439, 45, 43, 42, 41, 433])).
% 1.03/1.21 tff(441,plain,
% 1.03/1.21 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(442,plain,
% 1.03/1.21 ((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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(443,plain,
% 1.03/1.22 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[442])).
% 1.03/1.22 tff(444,plain,
% 1.03/1.22 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[443, 441])).
% 1.03/1.22 tff(445,plain,
% 1.03/1.22 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(446,plain,
% 1.03/1.22 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | 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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[445, 444])).
% 1.03/1.22 tff(447,plain,
% 1.03/1.22 (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] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[446, 440])).
% 1.03/1.22 tff(448,plain,
% 1.03/1.22 (![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[447, 274, 271, 268, 278])).
% 1.03/1.22 tff(449,plain,
% 1.03/1.22 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(450,plain,
% 1.03/1.22 ((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)))) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(451,plain,
% 1.03/1.22 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[450])).
% 1.03/1.22 tff(452,plain,
% 1.03/1.22 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[451, 449])).
% 1.03/1.22 tff(453,plain,
% 1.03/1.22 ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(454,plain,
% 1.03/1.23 ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~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)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.03/1.23 tff(455,plain,
% 1.03/1.23 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[454, 278, 274, 271, 268, 448])).
% 1.07/1.23 tff(456,plain,
% 1.07/1.23 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(457,plain,
% 1.07/1.23 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(458,plain,
% 1.07/1.23 (^[E: $i] : rewrite(((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(459,plain,
% 1.07/1.23 (![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[458])).
% 1.07/1.23 tff(460,plain,
% 1.07/1.23 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[459])).
% 1.07/1.23 tff(461,plain,
% 1.07/1.23 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[460, 457])).
% 1.07/1.23 tff(462,plain,
% 1.07/1.23 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[461])).
% 1.07/1.23 tff(463,plain,
% 1.07/1.23 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[462, 456])).
% 1.07/1.23 tff(464,plain,
% 1.07/1.23 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(465,plain,
% 1.07/1.24 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.07/1.24 tff(466,plain,
% 1.07/1.24 ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[465, 105, 455])).
% 1.07/1.24 tff(467,plain,
% 1.07/1.24 (![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[466, 417, 414, 411])).
% 1.07/1.24 tff(468,plain,
% 1.07/1.24 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(469,plain,
% 1.07/1.24 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(470,plain,
% 1.07/1.24 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[469])).
% 1.07/1.24 tff(471,plain,
% 1.07/1.24 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[470, 468])).
% 1.07/1.24 tff(472,plain,
% 1.07/1.24 ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(473,plain,
% 1.07/1.24 ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.07/1.24 tff(474,plain,
% 1.07/1.24 ((~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(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(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)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[473, 109, 467])).
% 1.07/1.24 tff(475,plain,
% 1.07/1.24 (v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[474, 265, 262, 408, 405, 380])).
% 1.07/1.24 tff(476,plain,
% 1.07/1.24 (v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[475, 303])).
% 1.07/1.24 tff(477,plain,
% 1.07/1.24 (m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[175])).
% 1.07/1.24 tff(478,plain,
% 1.07/1.24 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.24 inference(symmetry,[status(thm)],[477])).
% 1.07/1.24 tff(479,plain,
% 1.07/1.24 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(480,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[479])).
% 1.07/1.24 tff(481,plain,
% 1.07/1.24 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), rewrite((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(482,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[481])).
% 1.07/1.24 tff(483,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(484,plain,
% 1.07/1.24 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), rewrite(((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(485,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[484])).
% 1.07/1.24 tff(486,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_funct_2')).
% 1.07/1.24 tff(487,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.07/1.24 tff(488,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[487, 483])).
% 1.07/1.24 tff(489,plain,(
% 1.07/1.24 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[488])).
% 1.07/1.24 tff(490,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[489, 482])).
% 1.07/1.24 tff(491,plain,
% 1.07/1.24 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[490, 480])).
% 1.07/1.24 tff(492,plain,
% 1.07/1.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(493,plain,
% 1.07/1.24 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(494,plain,
% 1.07/1.24 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.07/1.25 tff(495,plain,
% 1.07/1.25 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, 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))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[494, 491])).
% 1.07/1.25 tff(496,plain,
% 1.07/1.25 (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[495, 153, 146, 111, 109, 107, 105, 94])).
% 1.07/1.25 tff(497,plain,
% 1.07/1.25 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.25 inference(tautology,[status(thm)],[])).
% 1.07/1.25 tff(498,plain,
% 1.07/1.25 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[497, 496])).
% 1.07/1.25 tff(499,plain,
% 1.07/1.25 (m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[498, 478])).
% 1.07/1.25 tff(500,plain,
% 1.07/1.25 (v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0) <=> v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[301, 239, 239])).
% 1.07/1.25 tff(501,plain,
% 1.07/1.25 (v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.07/1.25 inference(symmetry,[status(thm)],[500])).
% 1.07/1.25 tff(502,plain,
% 1.07/1.25 (v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[241])).
% 1.07/1.25 tff(503,plain,
% 1.07/1.25 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(504,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[503])).
% 1.07/1.25 tff(505,plain,
% 1.07/1.25 (^[A: $i, B: $i, C: $i, D: $i, E: $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(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), rewrite((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))))), rewrite(((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(506,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[505])).
% 1.07/1.25 tff(507,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(508,plain,
% 1.07/1.25 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), trans(monotonicity(rewrite(((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C))), ((((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> ((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), rewrite(((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))), ((((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(509,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[508])).
% 1.07/1.25 tff(510,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_group_6')).
% 1.07/1.25 tff(511,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.07/1.25 tff(512,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[511, 507])).
% 1.07/1.25 tff(513,plain,(
% 1.07/1.25 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.07/1.25 inference(skolemize,[status(sab)],[512])).
% 1.07/1.25 tff(514,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[513, 506])).
% 1.07/1.25 tff(515,plain,
% 1.07/1.25 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[514, 504])).
% 1.07/1.25 tff(516,plain,
% 1.07/1.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(517,plain,
% 1.07/1.26 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(518,plain,
% 1.07/1.26 ((~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(519,plain,
% 1.07/1.26 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[518])).
% 1.07/1.26 tff(520,plain,
% 1.07/1.26 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.26 inference(transitivity,[status(thm)],[519, 517])).
% 1.07/1.26 tff(521,plain,
% 1.07/1.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | ((~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[520])).
% 1.07/1.26 tff(522,plain,
% 1.07/1.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[521, 516])).
% 1.07/1.27 tff(523,plain,
% 1.07/1.27 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(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(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(524,plain,
% 1.07/1.27 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v4_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)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[523, 522])).
% 1.07/1.27 tff(525,plain,
% 1.07/1.27 ((~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[524, 515, 109, 105, 278, 274, 271, 268, 265, 262, 257, 254])).
% 1.07/1.27 tff(526,plain,
% 1.07/1.27 (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[525, 249, 246])).
% 1.07/1.27 tff(527,plain,
% 1.07/1.27 (((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.27 inference(tautology,[status(thm)],[])).
% 1.07/1.27 tff(528,plain,
% 1.07/1.27 (v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[527, 526])).
% 1.07/1.27 tff(529,plain,
% 1.07/1.27 (v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[528, 502])).
% 1.07/1.27 tff(530,plain,
% 1.07/1.27 (v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[529, 501])).
% 1.07/1.27 tff(531,plain,
% 1.07/1.27 (v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[175])).
% 1.07/1.27 tff(532,plain,
% 1.07/1.27 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.27 inference(symmetry,[status(thm)],[531])).
% 1.07/1.27 tff(533,plain,
% 1.07/1.27 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.27 inference(tautology,[status(thm)],[])).
% 1.07/1.27 tff(534,plain,
% 1.07/1.27 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[533, 496])).
% 1.07/1.27 tff(535,plain,
% 1.07/1.27 (v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[534, 532])).
% 1.07/1.27 tff(536,plain,
% 1.07/1.27 (v1_funct_1(k5_relat_1(C!2, B!1)) <=> v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[175])).
% 1.07/1.27 tff(537,plain,
% 1.07/1.27 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)) <=> v1_funct_1(k5_relat_1(C!2, B!1))),
% 1.07/1.27 inference(symmetry,[status(thm)],[536])).
% 1.07/1.27 tff(538,plain,
% 1.07/1.27 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.07/1.27 inference(tautology,[status(thm)],[])).
% 1.07/1.27 tff(539,plain,
% 1.07/1.27 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[538, 496])).
% 1.07/1.27 tff(540,plain,
% 1.07/1.27 (v1_funct_1(k5_relat_1(C!2, B!1))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[539, 537])).
% 1.07/1.27 tff(541,plain,
% 1.07/1.27 (((~![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(k5_relat_1(C!2, B!1))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, 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(k5_relat_1(C!2, B!1))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(542,plain,
% 1.07/1.27 ((~![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(k5_relat_1(C!2, B!1))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(543,plain,
% 1.07/1.27 ((~![B: $i] : ((~v1_funct_1(B)) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k5_relat_1(C!2, B!1))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.07/1.28 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.07/1.28 tff(544,plain,
% 1.07/1.28 (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[543, 328, 540, 535, 530, 499])).
% 1.07/1.28 tff(545,plain,
% 1.07/1.28 ((~(r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0))) | r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) | (~v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0))),
% 1.07/1.28 inference(tautology,[status(thm)],[])).
% 1.07/1.28 tff(546,plain,
% 1.07/1.28 ($false),
% 1.07/1.28 inference(unit_resolution,[status(thm)],[545, 544, 476, 222])).
% 1.07/1.28 % SZS output end Proof
% 1.07/1.28 % E exiting
%------------------------------------------------------------------------------