%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT353+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 05:14:29 AM UTC 2025
% Result : Theorem 2.56s 2.73s
% Output : Proof 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT353+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:34:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.56/2.73 % SZS status Theorem
% 2.56/2.73 % SZS output start Proof
% 2.56/2.73 tff(r4_waybel_1_type, type, (
% 2.56/2.73 r4_waybel_1: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(k10_relat_1_type, type, (
% 2.56/2.73 k10_relat_1: ( $i * $i ) > $i)).
% 2.56/2.73 tff(k6_waybel_0_type, type, (
% 2.56/2.73 k6_waybel_0: ( $i * $i ) > $i)).
% 2.56/2.73 tff(tptp_fun_D_3_type, type, (
% 2.56/2.73 tptp_fun_D_3: $i)).
% 2.56/2.73 tff(tptp_fun_A_0_type, type, (
% 2.56/2.73 tptp_fun_A_0: $i)).
% 2.56/2.73 tff(tptp_fun_C_2_type, type, (
% 2.56/2.73 tptp_fun_C_2: $i)).
% 2.56/2.73 tff(k1_funct_1_type, type, (
% 2.56/2.73 k1_funct_1: ( $i * $i ) > $i)).
% 2.56/2.73 tff(k2_waybel34_type, type, (
% 2.56/2.73 k2_waybel34: ( $i * $i * $i ) > $i)).
% 2.56/2.73 tff(tptp_fun_B_1_type, type, (
% 2.56/2.73 tptp_fun_B_1: $i)).
% 2.56/2.73 tff(k1_yellow_0_type, type, (
% 2.56/2.73 k1_yellow_0: ( $i * $i ) > $i)).
% 2.56/2.73 tff(r2_hidden_type, type, (
% 2.56/2.73 r2_hidden: ( $i * $i ) > $o)).
% 2.56/2.73 tff(r1_yellow_0_type, type, (
% 2.56/2.73 r1_yellow_0: ( $i * $i ) > $o)).
% 2.56/2.73 tff(m1_subset_1_type, type, (
% 2.56/2.73 m1_subset_1: ( $i * $i ) > $o)).
% 2.56/2.73 tff(u1_struct_0_type, type, (
% 2.56/2.73 u1_struct_0: $i > $i)).
% 2.56/2.73 tff(k7_yellow_2_type, type, (
% 2.56/2.73 k7_yellow_2: ( $i * $i * $i * $i ) > $i)).
% 2.56/2.73 tff(v1_funct_2_type, type, (
% 2.56/2.73 v1_funct_2: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(m2_relset_1_type, type, (
% 2.56/2.73 m2_relset_1: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(v1_funct_1_type, type, (
% 2.56/2.73 v1_funct_1: $i > $o)).
% 2.56/2.73 tff(m1_relset_1_type, type, (
% 2.56/2.73 m1_relset_1: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(k5_pre_topc_type, type, (
% 2.56/2.73 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 2.56/2.73 tff(v18_waybel_0_type, type, (
% 2.56/2.73 v18_waybel_0: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(l1_orders_2_type, type, (
% 2.56/2.73 l1_orders_2: $i > $o)).
% 2.56/2.73 tff(v3_lattice3_type, type, (
% 2.56/2.73 v3_lattice3: $i > $o)).
% 2.56/2.73 tff(v2_lattice3_type, type, (
% 2.56/2.73 v2_lattice3: $i > $o)).
% 2.56/2.73 tff(v1_lattice3_type, type, (
% 2.56/2.73 v1_lattice3: $i > $o)).
% 2.56/2.73 tff(v4_orders_2_type, type, (
% 2.56/2.73 v4_orders_2: $i > $o)).
% 2.56/2.73 tff(v3_orders_2_type, type, (
% 2.56/2.73 v3_orders_2: $i > $o)).
% 2.56/2.73 tff(v2_orders_2_type, type, (
% 2.56/2.73 v2_orders_2: $i > $o)).
% 2.56/2.73 tff(v1_xboole_0_type, type, (
% 2.56/2.73 v1_xboole_0: $i > $o)).
% 2.56/2.73 tff(l1_struct_0_type, type, (
% 2.56/2.73 l1_struct_0: $i > $o)).
% 2.56/2.73 tff(v3_struct_0_type, type, (
% 2.56/2.73 v3_struct_0: $i > $o)).
% 2.56/2.73 tff(v5_orders_3_type, type, (
% 2.56/2.73 v5_orders_3: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(v3_waybel_1_type, type, (
% 2.56/2.73 v3_waybel_1: ( $i * $i * $i ) > $o)).
% 2.56/2.73 tff(k1_waybel_1_type, type, (
% 2.56/2.73 k1_waybel_1: ( $i * $i * $i * $i ) > $i)).
% 2.56/2.73 tff(tptp_fun_E_27_type, type, (
% 2.56/2.73 tptp_fun_E_27: ( $i * $i * $i * $i ) > $i)).
% 2.56/2.73 tff(1,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(2,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[1])).
% 2.56/2.73 tff(3,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 2.56/2.73 tff(5,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.56/2.73 tff(6,plain,(
% 2.56/2.73 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.56/2.73 inference(skolemize,[status(sab)],[5])).
% 2.56/2.73 tff(7,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.56/2.73 tff(8,plain,
% 2.56/2.73 ((~![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(B!1), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)))),
% 2.56/2.73 inference(quant_inst,[status(thm)],[])).
% 2.56/2.73 tff(9,plain,
% 2.56/2.73 (m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[8, 7])).
% 2.56/2.73 tff(10,plain,
% 2.56/2.73 (((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0)) & (v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(11,plain,
% 2.56/2.73 (((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))) <=> (v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(12,plain,
% 2.56/2.73 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(13,plain,
% 2.56/2.73 (((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))) <=> ((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[12])).
% 2.56/2.73 tff(14,plain,
% 2.56/2.73 (((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))) <=> (v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))),
% 2.56/2.73 inference(transitivity,[status(thm)],[13, 11])).
% 2.56/2.73 tff(15,plain,
% 2.56/2.73 (((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0)) & ((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))))) <=> ((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0)) & (v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))))),
% 2.56/2.73 inference(monotonicity,[status(thm)],[14])).
% 2.56/2.73 tff(16,plain,
% 2.56/2.73 (((v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0)) & ((v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))))) <=> (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))))),
% 2.56/2.73 inference(transitivity,[status(thm)],[15, 10])).
% 2.56/2.73 tff(17,plain,
% 2.56/2.73 ((~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D)))))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(18,plain,
% 2.56/2.73 ((~![A: $i] : (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & v3_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & v3_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v18_waybel_0(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D)))))))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(19,axiom,(~![A: $i] : (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & v3_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & v3_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & v18_waybel_0(C, B, A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_waybel34')).
% 2.56/2.73 tff(20,plain,
% 2.56/2.73 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.56/2.73 tff(21,plain,
% 2.56/2.73 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[20, 17])).
% 2.56/2.73 tff(22,plain,
% 2.56/2.73 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.56/2.73 tff(23,plain,
% 2.56/2.73 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v18_waybel_0(C, B, A) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (k7_yellow_2(u1_struct_0(A), B, k2_waybel34(A, B, C), D) = k1_yellow_0(B, k5_pre_topc(B, A, C, k6_waybel_0(A, D))))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[22, 17])).
% 2.56/2.73 tff(24,plain,
% 2.56/2.73 (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0) & v2_orders_2(B!1) & v3_orders_2(B!1) & v4_orders_2(B!1) & v1_lattice3(B!1) & v2_lattice3(B!1) & v3_lattice3(B!1) & l1_orders_2(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & v18_waybel_0(C!2, B!1, A!0) & m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) & (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))))),
% 2.56/2.73 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.56/2.73 tff(25,plain,
% 2.56/2.73 (m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.73 inference(and_elim,[status(thm)],[24])).
% 2.56/2.73 tff(26,plain,
% 2.56/2.73 ((~(m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.73 inference(tautology,[status(thm)],[])).
% 2.56/2.73 tff(27,plain,
% 2.56/2.73 ((~(m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0)))) | m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[26, 25])).
% 2.56/2.73 tff(28,plain,
% 2.56/2.73 (m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.73 inference(unit_resolution,[status(thm)],[27, 9])).
% 2.56/2.73 tff(29,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : refl(((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(30,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[29])).
% 2.56/2.73 tff(31,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (~((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), rewrite((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> (((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))))), rewrite((((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(32,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[31])).
% 2.56/2.73 tff(33,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))),
% 2.56/2.73 inference(rewrite,[status(thm)],[])).
% 2.56/2.73 tff(34,plain,
% 2.56/2.73 (^[A: $i, B: $i, C: $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(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) & v2_orders_2(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) & v2_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B)))), ((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B)) & v3_orders_2(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B)) & v3_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B))), ((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B)))), (((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B))), (((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)))), ((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B))), ((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)))), (((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B))), (((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)))), ((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))), ((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)))), (((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) & v1_funct_1(C)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) & v1_funct_1(C)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C))), (((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C)))), ((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)))), ((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))))), (((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))), (((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), rewrite(((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))), ((((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))),
% 2.56/2.73 inference(bind,[status(th)],[])).
% 2.56/2.73 tff(35,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : (((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)))) <=> ![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))),
% 2.56/2.73 inference(quant_intro,[status(thm)],[34])).
% 2.56/2.73 tff(36,axiom,(![A: $i, B: $i, C: $i] : (((((((((((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_waybel34')).
% 2.56/2.73 tff(37,plain,
% 2.56/2.73 (![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.56/2.74 tff(38,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[37, 33])).
% 2.56/2.74 tff(39,plain,(
% 2.56/2.74 ![A: $i, B: $i, C: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m1_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) | (v1_funct_1(k2_waybel34(A, B, C)) & v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))),
% 2.56/2.74 inference(skolemize,[status(sab)],[38])).
% 2.56/2.74 tff(40,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[39, 32])).
% 2.56/2.74 tff(41,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[40, 30])).
% 2.56/2.74 tff(42,plain,
% 2.56/2.74 (v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(43,plain,
% 2.56/2.74 (v1_funct_1(C!2)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(44,plain,
% 2.56/2.74 (l1_orders_2(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(45,plain,
% 2.56/2.74 (v2_lattice3(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(46,plain,
% 2.56/2.74 (v1_lattice3(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(47,plain,
% 2.56/2.74 (v4_orders_2(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(48,plain,
% 2.56/2.74 (v3_orders_2(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(49,plain,
% 2.56/2.74 (v2_orders_2(B!1)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(50,plain,
% 2.56/2.74 (l1_orders_2(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(51,plain,
% 2.56/2.74 (v2_lattice3(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(52,plain,
% 2.56/2.74 (v1_lattice3(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(53,plain,
% 2.56/2.74 (v4_orders_2(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(54,plain,
% 2.56/2.74 (v3_orders_2(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(55,plain,
% 2.56/2.74 (v2_orders_2(A!0)),
% 2.56/2.74 inference(and_elim,[status(thm)],[24])).
% 2.56/2.74 tff(56,plain,
% 2.56/2.74 (((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(57,plain,
% 2.56/2.74 (((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(58,plain,
% 2.56/2.74 ((~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(59,plain,
% 2.56/2.74 (((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[58])).
% 2.56/2.74 tff(60,plain,
% 2.56/2.74 (((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[59, 57])).
% 2.56/2.74 tff(61,plain,
% 2.56/2.74 (((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[60])).
% 2.56/2.74 tff(62,plain,
% 2.56/2.74 (((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[61, 56])).
% 2.56/2.74 tff(63,plain,
% 2.56/2.74 ((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v1_funct_1(C!2)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v1_lattice3(B!1)) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(64,plain,
% 2.56/2.74 ((~![A: $i, B: $i, C: $i] : ((~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v4_orders_2(B)) | (~v1_funct_1(C)) | (~v3_orders_2(B)) | (~v2_lattice3(B)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v1_lattice3(B)) | (~m1_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | (~((~v1_funct_1(k2_waybel34(A, B, C))) | (~v1_funct_2(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(k2_waybel34(A, B, C), u1_struct_0(A), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~l1_orders_2(B!1)) | (~v4_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(B!1)) | (~v4_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v1_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.56/2.74 tff(65,plain,
% 2.56/2.74 ((~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[64, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41])).
% 2.56/2.74 tff(66,plain,
% 2.56/2.74 (~((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[65, 28])).
% 2.56/2.74 tff(67,plain,
% 2.56/2.74 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(68,plain,
% 2.56/2.74 (v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[67, 66])).
% 2.56/2.74 tff(69,plain,
% 2.56/2.74 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))) | v1_funct_1(k2_waybel34(A!0, B!1, C!2))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(70,plain,
% 2.56/2.74 (v1_funct_1(k2_waybel34(A!0, B!1, C!2))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[69, 66])).
% 2.56/2.74 tff(71,plain,
% 2.56/2.74 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(72,plain,
% 2.56/2.74 (m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[71, 7])).
% 2.56/2.74 tff(73,plain,
% 2.56/2.74 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))) | m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(74,plain,
% 2.56/2.74 (m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[73, 66])).
% 2.56/2.74 tff(75,plain,
% 2.56/2.74 ((~(m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(tautology,[status(thm)],[])).
% 2.56/2.74 tff(76,plain,
% 2.56/2.74 ((~(m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[75, 74])).
% 2.56/2.74 tff(77,plain,
% 2.56/2.74 (m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[76, 72])).
% 2.56/2.74 tff(78,plain,
% 2.56/2.74 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(79,plain,
% 2.56/2.74 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[78])).
% 2.56/2.74 tff(80,plain,
% 2.56/2.74 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(81,plain,
% 2.56/2.74 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(82,plain,
% 2.56/2.74 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[81])).
% 2.56/2.74 tff(83,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 2.56/2.74 tff(84,plain,
% 2.56/2.74 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.56/2.74 tff(85,plain,
% 2.56/2.74 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.56/2.74 tff(86,plain,(
% 2.56/2.74 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(skolemize,[status(sab)],[85])).
% 2.56/2.74 tff(87,plain,
% 2.56/2.74 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[86, 79])).
% 2.56/2.74 tff(88,plain,
% 2.56/2.74 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(89,plain,
% 2.56/2.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(90,plain,
% 2.56/2.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[89, 88])).
% 2.56/2.74 tff(91,plain,
% 2.56/2.74 (l1_struct_0(A!0)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[90, 50, 87])).
% 2.56/2.74 tff(92,plain,
% 2.56/2.74 (^[A: $i] : refl(((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(93,plain,
% 2.56/2.74 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[92])).
% 2.56/2.74 tff(94,plain,
% 2.56/2.74 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(95,plain,
% 2.56/2.74 (^[A: $i] : trans(monotonicity(rewrite((v2_lattice3(A) => (~v3_struct_0(A))) <=> ((~v2_lattice3(A)) | (~v3_struct_0(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> (l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))))), rewrite((l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(96,plain,
% 2.56/2.74 (![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[95])).
% 2.56/2.74 tff(97,axiom,(![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_lattice3')).
% 2.56/2.74 tff(98,plain,
% 2.56/2.74 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.56/2.74 tff(99,plain,
% 2.56/2.74 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[98, 94])).
% 2.56/2.74 tff(100,plain,(
% 2.56/2.74 ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(skolemize,[status(sab)],[99])).
% 2.56/2.74 tff(101,plain,
% 2.56/2.74 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[100, 93])).
% 2.56/2.74 tff(102,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(103,plain,
% 2.56/2.74 (((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(104,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[103])).
% 2.56/2.74 tff(105,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 2.56/2.74 inference(transitivity,[status(thm)],[104, 102])).
% 2.56/2.74 tff(106,plain,
% 2.56/2.74 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(107,plain,
% 2.56/2.74 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.56/2.74 tff(108,plain,
% 2.56/2.74 (~v3_struct_0(A!0)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[107, 51, 50, 101])).
% 2.56/2.74 tff(109,plain,
% 2.56/2.74 (^[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))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(110,plain,
% 2.56/2.74 (![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)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[109])).
% 2.56/2.74 tff(111,plain,
% 2.56/2.74 (^[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)))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(112,plain,
% 2.56/2.74 (![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)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[111])).
% 2.56/2.74 tff(113,plain,
% 2.56/2.74 (![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))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(114,plain,
% 2.56/2.74 (^[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)))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(115,plain,
% 2.56/2.74 (![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))))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[114])).
% 2.56/2.74 tff(116,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 2.56/2.74 tff(117,plain,
% 2.56/2.74 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.56/2.74 tff(118,plain,
% 2.56/2.74 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[117, 113])).
% 2.56/2.74 tff(119,plain,(
% 2.56/2.74 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 2.56/2.74 inference(skolemize,[status(sab)],[118])).
% 2.56/2.74 tff(120,plain,
% 2.56/2.74 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[119, 112])).
% 2.56/2.74 tff(121,plain,
% 2.56/2.74 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[120, 110])).
% 2.56/2.74 tff(122,plain,
% 2.56/2.74 (((~![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))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(123,plain,
% 2.56/2.74 ((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))))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(124,plain,
% 2.56/2.74 (((~![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)))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[123])).
% 2.56/2.74 tff(125,plain,
% 2.56/2.74 (((~![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))))),
% 2.56/2.74 inference(transitivity,[status(thm)],[124, 122])).
% 2.56/2.74 tff(126,plain,
% 2.56/2.74 ((~![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)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(127,plain,
% 2.56/2.74 ((~![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)))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[126, 125])).
% 2.56/2.74 tff(128,plain,
% 2.56/2.74 (~v1_xboole_0(u1_struct_0(A!0))),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[127, 121, 108, 91])).
% 2.56/2.74 tff(129,plain,
% 2.56/2.74 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(B!1) | (~l1_orders_2(B!1)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(B!1) | (~l1_orders_2(B!1)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(130,plain,
% 2.56/2.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(B!1) | (~l1_orders_2(B!1)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(131,plain,
% 2.56/2.74 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(B!1) | (~l1_orders_2(B!1))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[130, 129])).
% 2.56/2.74 tff(132,plain,
% 2.56/2.74 (l1_struct_0(B!1)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[131, 44, 87])).
% 2.56/2.74 tff(133,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(134,plain,
% 2.56/2.74 (((~v3_struct_0(B!1)) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1))) <=> ((~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(135,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(B!1)) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1))))),
% 2.56/2.74 inference(monotonicity,[status(thm)],[134])).
% 2.56/2.74 tff(136,plain,
% 2.56/2.74 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(B!1)) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1)))),
% 2.56/2.74 inference(transitivity,[status(thm)],[135, 133])).
% 2.56/2.74 tff(137,plain,
% 2.56/2.74 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(B!1)) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)))),
% 2.56/2.74 inference(quant_inst,[status(thm)],[])).
% 2.56/2.74 tff(138,plain,
% 2.56/2.74 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(B!1)) | (~v2_lattice3(B!1)) | (~v3_struct_0(B!1))),
% 2.56/2.74 inference(modus_ponens,[status(thm)],[137, 136])).
% 2.56/2.74 tff(139,plain,
% 2.56/2.74 (~v3_struct_0(B!1)),
% 2.56/2.74 inference(unit_resolution,[status(thm)],[138, 45, 44, 101])).
% 2.56/2.74 tff(140,plain,
% 2.56/2.74 (^[A: $i, B: $i, C: $i, D: $i] : refl((v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(141,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[140])).
% 2.56/2.74 tff(142,plain,
% 2.56/2.74 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) <=> (~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) <=> (~(~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))))), rewrite((~(~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))))),
% 2.56/2.74 inference(bind,[status(th)],[])).
% 2.56/2.74 tff(143,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.74 inference(quant_intro,[status(thm)],[142])).
% 2.56/2.74 tff(144,plain,
% 2.56/2.74 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.56/2.74 inference(rewrite,[status(thm)],[])).
% 2.56/2.74 tff(145,plain,
% 2.56/2.74 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B))), (((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B)) & v1_funct_1(C)))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B)) & v1_funct_1(C)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C))), (((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)))), ((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)))), ((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))))), (((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)))), (((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))))), ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))), ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)))), (((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(146,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[145])).
% 2.56/2.75 tff(147,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_yellow_2')).
% 2.56/2.75 tff(148,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[147, 146])).
% 2.56/2.75 tff(149,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[148, 144])).
% 2.56/2.75 tff(150,plain,(
% 2.56/2.75 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)))),
% 2.56/2.75 inference(skolemize,[status(sab)],[149])).
% 2.56/2.75 tff(151,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[150, 143])).
% 2.56/2.75 tff(152,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[151, 141])).
% 2.56/2.75 tff(153,plain,
% 2.56/2.75 (~((~m1_subset_1(D!3, u1_struct_0(A!0))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))))),
% 2.56/2.75 inference(and_elim,[status(thm)],[24])).
% 2.56/2.75 tff(154,plain,
% 2.56/2.75 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 2.56/2.75 inference(or_elim,[status(thm)],[153])).
% 2.56/2.75 tff(155,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)))),
% 2.56/2.75 inference(rewrite,[status(thm)],[])).
% 2.56/2.75 tff(156,plain,
% 2.56/2.75 ((v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)))),
% 2.56/2.75 inference(rewrite,[status(thm)],[])).
% 2.56/2.75 tff(157,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3))))),
% 2.56/2.75 inference(monotonicity,[status(thm)],[156])).
% 2.56/2.75 tff(158,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)))),
% 2.56/2.75 inference(transitivity,[status(thm)],[157, 155])).
% 2.56/2.75 tff(159,plain,
% 2.56/2.75 ((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))),
% 2.56/2.75 inference(quant_inst,[status(thm)],[])).
% 2.56/2.75 tff(160,plain,
% 2.56/2.75 ((~![A: $i, B: $i, C: $i, D: $i] : (v3_struct_0(B) | v1_xboole_0(A) | (k7_yellow_2(A, B, C, D) = k1_funct_1(C, D)) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[159, 158])).
% 2.56/2.75 tff(161,plain,
% 2.56/2.75 ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3))),
% 2.56/2.75 inference(unit_resolution,[status(thm)],[160, 154, 152, 139, 132, 128])).
% 2.56/2.75 tff(162,plain,
% 2.56/2.75 (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3)),
% 2.56/2.75 inference(unit_resolution,[status(thm)],[161, 77, 70, 68])).
% 2.56/2.75 tff(163,plain,
% 2.56/2.75 (k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3)),
% 2.56/2.75 inference(symmetry,[status(thm)],[162])).
% 2.56/2.75 tff(164,plain,
% 2.56/2.75 (m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) <=> m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))),
% 2.56/2.75 inference(monotonicity,[status(thm)],[163])).
% 2.56/2.75 tff(165,plain,
% 2.56/2.75 (m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) <=> m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))),
% 2.56/2.75 inference(symmetry,[status(thm)],[164])).
% 2.56/2.75 tff(166,plain,
% 2.56/2.75 (^[A: $i, B: $i, C: $i, D: $i] : refl((m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) <=> (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(167,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[166])).
% 2.56/2.75 tff(168,plain,
% 2.56/2.75 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) <=> (~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) <=> (~(~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))))), rewrite((~(~(v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) <=> (v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ((v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))))), rewrite(((v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(169,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[168])).
% 2.56/2.75 tff(170,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))),
% 2.56/2.75 inference(rewrite,[status(thm)],[])).
% 2.56/2.75 tff(171,plain,
% 2.56/2.75 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B))), (((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B)) & v1_funct_1(C)))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B)) & v1_funct_1(C)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C))), (((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)))), ((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)))), ((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))))), (((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)))), (((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))))), ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))), ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)))), (((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> (((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))))), rewrite((((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))), (((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(172,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[171])).
% 2.56/2.75 tff(173,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((((~v1_xboole_0(A)) & (~v3_struct_0(B))) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, A, u1_struct_0(B))) & m1_relset_1(C, A, u1_struct_0(B))) & m1_subset_1(D, A)) => m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_yellow_2')).
% 2.56/2.75 tff(174,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[173, 172])).
% 2.56/2.75 tff(175,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[174, 170])).
% 2.56/2.75 tff(176,plain,(
% 2.56/2.75 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & (~v3_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, A, u1_struct_0(B)) & m1_relset_1(C, A, u1_struct_0(B)) & m1_subset_1(D, A))) | m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)))),
% 2.56/2.75 inference(skolemize,[status(sab)],[175])).
% 2.56/2.75 tff(177,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[176, 169])).
% 2.56/2.75 tff(178,plain,
% 2.56/2.75 (![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[177, 167])).
% 2.56/2.75 tff(179,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.56/2.75 inference(rewrite,[status(thm)],[])).
% 2.56/2.75 tff(180,plain,
% 2.56/2.75 ((m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0)))) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.56/2.75 inference(rewrite,[status(thm)],[])).
% 2.56/2.75 tff(181,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 2.56/2.75 inference(monotonicity,[status(thm)],[180])).
% 2.56/2.75 tff(182,plain,
% 2.56/2.75 (((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))))),
% 2.56/2.75 inference(transitivity,[status(thm)],[181, 179])).
% 2.56/2.75 tff(183,plain,
% 2.56/2.75 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~l1_struct_0(B!1)) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_subset_1(D!3, u1_struct_0(A!0))))),
% 2.56/2.75 inference(quant_inst,[status(thm)],[])).
% 2.56/2.75 tff(184,plain,
% 2.56/2.75 ((~![A: $i, B: $i, C: $i, D: $i] : (m1_subset_1(k7_yellow_2(A, B, C, D), u1_struct_0(B)) | v3_struct_0(B) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~l1_struct_0(B)) | (~v1_funct_2(C, A, u1_struct_0(B))) | (~m1_relset_1(C, A, u1_struct_0(B))) | (~m1_subset_1(D, A)))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(B!1) | v1_xboole_0(u1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.56/2.75 tff(185,plain,
% 2.56/2.75 ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1)) | (~m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1)))),
% 2.56/2.75 inference(unit_resolution,[status(thm)],[184, 154, 178, 139, 132, 128])).
% 2.56/2.75 tff(186,plain,
% 2.56/2.75 (m1_subset_1(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))),
% 2.56/2.75 inference(unit_resolution,[status(thm)],[185, 77, 70, 68])).
% 2.56/2.75 tff(187,plain,
% 2.56/2.75 (m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))),
% 2.56/2.75 inference(modus_ponens,[status(thm)],[186, 165])).
% 2.56/2.75 tff(188,plain,
% 2.56/2.75 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(189,plain,
% 2.56/2.75 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[188])).
% 2.56/2.75 tff(190,plain,
% 2.56/2.75 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.75 tff(191,plain,
% 2.56/2.75 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.75 inference(quant_intro,[status(thm)],[190])).
% 2.56/2.75 tff(192,plain,
% 2.56/2.75 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.75 inference(transitivity,[status(thm)],[191, 189])).
% 2.56/2.75 tff(193,plain,
% 2.56/2.75 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A))))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))))),
% 2.56/2.75 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(194,plain,
% 2.56/2.76 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[193])).
% 2.56/2.76 tff(195,plain,
% 2.56/2.76 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(196,plain,
% 2.56/2.76 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C))) <=> (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))), (![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C))) <=> ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(197,plain,
% 2.56/2.76 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[196])).
% 2.56/2.76 tff(198,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r4_waybel_1(A, B, C) <=> ((r1_yellow_0(A, C) & (B = k1_yellow_0(A, C))) & r2_hidden(k1_yellow_0(A, C), C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_waybel_1')).
% 2.56/2.76 tff(199,plain,
% 2.56/2.76 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.56/2.76 tff(200,plain,
% 2.56/2.76 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[199, 195])).
% 2.56/2.76 tff(201,plain,(
% 2.56/2.76 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r4_waybel_1(A, B, C) <=> (r1_yellow_0(A, C) & (B = k1_yellow_0(A, C)) & r2_hidden(k1_yellow_0(A, C), C)))))),
% 2.56/2.76 inference(skolemize,[status(sab)],[200])).
% 2.56/2.76 tff(202,plain,
% 2.56/2.76 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[201, 194])).
% 2.56/2.76 tff(203,plain,
% 2.56/2.76 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[202, 192])).
% 2.56/2.76 tff(204,plain,
% 2.56/2.76 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C)))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(205,plain,
% 2.56/2.76 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C)))))),
% 2.56/2.76 inference(quant_inst,[status(thm)],[])).
% 2.56/2.76 tff(206,plain,
% 2.56/2.76 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (~(((~r1_yellow_0(A, C)) | (~(B = k1_yellow_0(A, C))) | (~r2_hidden(k1_yellow_0(A, C), C))) <=> r4_waybel_1(A, B, C)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.56/2.76 tff(207,plain,
% 2.56/2.76 (v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[206, 44, 203])).
% 2.56/2.76 tff(208,plain,
% 2.56/2.76 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[207, 139])).
% 2.56/2.76 tff(209,plain,
% 2.56/2.76 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(210,plain,
% 2.56/2.76 (((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))) <=> ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(211,plain,
% 2.56/2.76 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))))),
% 2.56/2.76 inference(monotonicity,[status(thm)],[210])).
% 2.56/2.76 tff(212,plain,
% 2.56/2.76 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))),
% 2.56/2.76 inference(transitivity,[status(thm)],[211, 209])).
% 2.56/2.76 tff(213,plain,
% 2.56/2.76 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C))))),
% 2.56/2.76 inference(quant_inst,[status(thm)],[])).
% 2.56/2.76 tff(214,plain,
% 2.56/2.76 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))) <=> r4_waybel_1(B!1, B, C))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.56/2.76 tff(215,plain,
% 2.56/2.76 ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[214, 208])).
% 2.56/2.76 tff(216,plain,
% 2.56/2.76 (![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[215, 187])).
% 2.56/2.76 tff(217,plain,
% 2.56/2.76 ((~![C: $i] : (~(((~r1_yellow_0(B!1, C)) | (~r2_hidden(k1_yellow_0(B!1, C), C)) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, C)))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C)))) | (~(((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))),
% 2.56/2.76 inference(quant_inst,[status(thm)],[])).
% 2.56/2.76 tff(218,plain,
% 2.56/2.76 (~(((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[217, 216])).
% 2.56/2.76 tff(219,plain,
% 2.56/2.76 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(220,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[219])).
% 2.56/2.76 tff(221,plain,
% 2.56/2.76 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))), ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))), (((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(222,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[221])).
% 2.56/2.76 tff(223,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(224,plain,
% 2.56/2.76 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))), ((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))))), rewrite(((l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), ((((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(225,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[224])).
% 2.56/2.76 tff(226,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((((l1_struct_0(A) & l1_struct_0(B)) & v1_funct_1(C)) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k5_pre_topc')).
% 2.56/2.76 tff(227,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[226, 225])).
% 2.56/2.76 tff(228,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[227, 223])).
% 2.56/2.76 tff(229,plain,(
% 2.56/2.76 ![A: $i, B: $i, C: $i, D: $i] : ((~(l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | (k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)))),
% 2.56/2.76 inference(skolemize,[status(sab)],[228])).
% 2.56/2.76 tff(230,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[229, 222])).
% 2.56/2.76 tff(231,plain,
% 2.56/2.76 (![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[230, 220])).
% 2.56/2.76 tff(232,plain,
% 2.56/2.76 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | ((~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | (~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(233,plain,
% 2.56/2.76 (((k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_struct_0(B!1)) | (~l1_struct_0(A!0))) <=> ((~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.56/2.76 inference(rewrite,[status(thm)],[])).
% 2.56/2.76 tff(234,plain,
% 2.56/2.76 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | ((k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_struct_0(B!1)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | ((~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))),
% 2.56/2.76 inference(monotonicity,[status(thm)],[233])).
% 2.56/2.76 tff(235,plain,
% 2.56/2.76 (((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | ((k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_struct_0(B!1)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | (~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.56/2.76 inference(transitivity,[status(thm)],[234, 232])).
% 2.56/2.76 tff(236,plain,
% 2.56/2.76 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | ((k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~l1_struct_0(B!1)) | (~l1_struct_0(A!0)))),
% 2.56/2.76 inference(quant_inst,[status(thm)],[])).
% 2.56/2.76 tff(237,plain,
% 2.56/2.76 ((~![A: $i, B: $i, C: $i, D: $i] : ((k5_pre_topc(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m1_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | (~l1_struct_0(A)) | (~l1_struct_0(B)))) | (~v1_funct_1(C!2)) | (~l1_struct_0(A!0)) | (~l1_struct_0(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))),
% 2.56/2.76 inference(modus_ponens,[status(thm)],[236, 235])).
% 2.56/2.76 tff(238,plain,
% 2.56/2.76 ((~m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[237, 43, 42, 231, 91, 132])).
% 2.56/2.76 tff(239,plain,
% 2.56/2.76 (k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)) = k10_relat_1(C!2, k6_waybel_0(A!0, D!3))),
% 2.56/2.76 inference(unit_resolution,[status(thm)],[238, 28])).
% 2.56/2.76 tff(240,plain,
% 2.56/2.76 (k10_relat_1(C!2, k6_waybel_0(A!0, D!3)) = k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))),
% 2.56/2.76 inference(symmetry,[status(thm)],[239])).
% 2.56/2.76 tff(241,plain,
% 2.56/2.76 (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) <=> r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))),
% 2.56/2.76 inference(monotonicity,[status(thm)],[163, 240])).
% 2.56/2.76 tff(242,plain,
% 2.56/2.76 (r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))),
% 2.56/2.76 inference(symmetry,[status(thm)],[241])).
% 2.56/2.76 tff(243,plain,
% 2.56/2.76 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))))))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(244,plain,
% 2.56/2.76 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))),
% 2.56/2.76 inference(quant_intro,[status(thm)],[243])).
% 2.56/2.76 tff(245,plain,
% 2.56/2.76 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))))),
% 2.56/2.76 inference(bind,[status(th)],[])).
% 2.56/2.76 tff(246,plain,
% 2.56/2.76 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(quant_intro,[status(thm)],[245])).
% 2.56/2.77 tff(247,plain,
% 2.56/2.77 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))))),
% 2.56/2.77 inference(bind,[status(th)],[])).
% 2.56/2.77 tff(248,plain,
% 2.56/2.77 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(quant_intro,[status(thm)],[247])).
% 2.56/2.77 tff(249,plain,
% 2.56/2.77 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(transitivity,[status(thm)],[248, 246])).
% 2.56/2.77 tff(250,plain,
% 2.56/2.77 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)))), ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))), trans(monotonicity(rewrite(((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) <=> ((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))), rewrite((v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))) <=> (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))), ((((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) <=> (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))), rewrite((((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) <=> (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))), ((((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) <=> (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))), (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))), (((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))), (((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))) <=> ((v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))), rewrite(((v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))), (((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))))),
% 2.56/2.77 inference(bind,[status(th)],[])).
% 2.56/2.77 tff(251,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(quant_intro,[status(thm)],[250])).
% 2.56/2.77 tff(252,plain,
% 2.56/2.77 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | ((~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))),
% 2.56/2.77 inference(bind,[status(th)],[])).
% 2.56/2.77 tff(253,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | ((~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))),
% 2.56/2.77 inference(quant_intro,[status(thm)],[252])).
% 2.56/2.77 tff(254,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))),
% 2.56/2.77 inference(rewrite,[status(thm)],[])).
% 2.56/2.77 tff(255,plain,
% 2.56/2.77 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))), ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) <=> ((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B))), (((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) <=> (((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)))), rewrite((((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) <=> ((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B))), (((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) <=> ((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)))), ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) <=> (((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & l1_orders_2(B)))), rewrite((((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & l1_orders_2(B)) <=> ((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))), ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) <=> ((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))), rewrite((v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) <=> (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))), (((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) <=> (((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))), rewrite((((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) <=> ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))), (((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) <=> ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))), (![B: $i] : ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))), (((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))), (((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))))),
% 2.56/2.77 inference(bind,[status(th)],[])).
% 2.56/2.77 tff(256,plain,
% 2.56/2.77 (![A: $i] : ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))),
% 2.56/2.77 inference(quant_intro,[status(thm)],[255])).
% 2.56/2.77 tff(257,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v2_orders_2(A)) & v3_orders_2(A)) & v4_orders_2(A)) & l1_orders_2(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v2_orders_2(B)) & v3_orders_2(B)) & v4_orders_2(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_waybel_1')).
% 2.56/2.77 tff(258,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))),
% 2.56/2.77 inference(modus_ponens,[status(thm)],[257, 256])).
% 2.56/2.77 tff(259,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) <=> (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))))),
% 2.56/2.77 inference(modus_ponens,[status(thm)],[258, 254])).
% 2.56/2.77 tff(260,plain,(
% 2.56/2.77 ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | ((~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))))))))),
% 2.56/2.77 inference(skolemize,[status(sab)],[259])).
% 2.56/2.77 tff(261,plain,
% 2.56/2.77 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (v5_orders_3(D, B, A) & ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))) & (v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))),
% 2.56/2.77 inference(modus_ponens,[status(thm)],[260, 253])).
% 2.56/2.77 tff(262,plain,
% 2.56/2.77 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(modus_ponens,[status(thm)],[261, 251])).
% 2.56/2.77 tff(263,plain,
% 2.56/2.77 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E))))))))) | (~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A))))))))))))))),
% 2.56/2.77 inference(modus_ponens,[status(thm)],[262, 249])).
% 2.56/2.77 tff(264,plain,
% 2.56/2.77 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))),
% 2.56/2.78 inference(modus_ponens,[status(thm)],[263, 244])).
% 2.56/2.78 tff(265,plain,
% 2.56/2.78 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))),
% 2.56/2.78 inference(rewrite,[status(thm)],[])).
% 2.56/2.78 tff(266,plain,
% 2.56/2.78 ((v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~(v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~v5_orders_3(D, B, A!0)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))) <=> (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))),
% 2.56/2.78 inference(rewrite,[status(thm)],[])).
% 2.56/2.78 tff(267,plain,
% 2.56/2.78 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~(v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~v5_orders_3(D, B, A!0)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))))),
% 2.56/2.78 inference(monotonicity,[status(thm)],[266])).
% 2.56/2.78 tff(268,plain,
% 2.56/2.78 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~(v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~v5_orders_3(D, B, A!0)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))),
% 2.56/2.78 inference(transitivity,[status(thm)],[267, 265])).
% 2.56/2.78 tff(269,plain,
% 2.56/2.78 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~(v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~v5_orders_3(D, B, A!0)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E)))))))))))))))),
% 2.56/2.78 inference(quant_inst,[status(thm)],[])).
% 2.56/2.78 tff(270,plain,
% 2.56/2.78 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) | (~((~(v3_waybel_1(k1_waybel_1(A, B, C, D), A, B) | (~v5_orders_3(D, B, A)) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A), u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, tptp_fun_E_27(D, C, B, A)), k5_pre_topc(B, A, D, k6_waybel_0(A, tptp_fun_E_27(D, C, B, A)))))))) | (~((~v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~((~v5_orders_3(D, B, A)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A), B, C, E), k5_pre_topc(B, A, D, k6_waybel_0(A, E)))))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))),
% 2.56/2.78 inference(modus_ponens,[status(thm)],[269, 268])).
% 2.56/2.78 tff(271,plain,
% 2.56/2.78 (v3_struct_0(A!0) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))),
% 2.56/2.78 inference(unit_resolution,[status(thm)],[270, 55, 54, 53, 50, 264])).
% 2.56/2.78 tff(272,plain,
% 2.56/2.78 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))),
% 2.56/2.78 inference(unit_resolution,[status(thm)],[271, 108])).
% 2.56/2.78 tff(273,plain,
% 2.56/2.78 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))))),
% 2.56/2.78 inference(rewrite,[status(thm)],[])).
% 2.56/2.78 tff(274,plain,
% 2.56/2.78 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))))),
% 2.56/2.78 inference(quant_inst,[status(thm)],[])).
% 2.56/2.78 tff(275,plain,
% 2.56/2.78 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B, A!0), u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, tptp_fun_E_27(D, C, B, A!0)), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~((~v5_orders_3(D, B, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B, k7_yellow_2(u1_struct_0(A!0), B, C, E), k5_pre_topc(B, A!0, D, k6_waybel_0(A!0, E))))))))))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))),
% 2.56/2.78 inference(modus_ponens,[status(thm)],[274, 273])).
% 2.56/2.78 tff(276,plain,
% 2.56/2.78 (![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))),
% 2.56/2.78 inference(unit_resolution,[status(thm)],[275, 49, 48, 47, 44, 272, 139])).
% 2.56/2.78 tff(277,plain,
% 2.56/2.78 (((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))),
% 2.56/2.79 inference(rewrite,[status(thm)],[])).
% 2.56/2.79 tff(278,plain,
% 2.56/2.79 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))),
% 2.56/2.79 inference(quant_inst,[status(thm)],[])).
% 2.56/2.79 tff(279,plain,
% 2.56/2.79 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, tptp_fun_E_27(D, C, B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, C, B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, C, D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, C, E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E)))))))))))))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))),
% 2.56/2.79 inference(modus_ponens,[status(thm)],[278, 277])).
% 2.56/2.79 tff(280,plain,
% 2.56/2.79 (![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))),
% 2.56/2.79 inference(unit_resolution,[status(thm)],[279, 70, 68, 74, 276])).
% 2.56/2.79 tff(281,plain,
% 2.56/2.79 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))))))),
% 2.56/2.79 inference(rewrite,[status(thm)],[])).
% 2.56/2.79 tff(282,plain,
% 2.56/2.79 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))))))),
% 2.56/2.79 inference(quant_inst,[status(thm)],[])).
% 2.56/2.79 tff(283,plain,
% 2.56/2.79 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(D, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, tptp_fun_E_27(D, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), D), A!0, B!1)) | (~((~v5_orders_3(D, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, D, k6_waybel_0(A!0, E))))))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E)))))))))))),
% 2.56/2.79 inference(modus_ponens,[status(thm)],[282, 281])).
% 2.56/2.79 tff(284,plain,
% 2.56/2.79 (~((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))))),
% 2.56/2.79 inference(unit_resolution,[status(thm)],[283, 43, 42, 25, 280])).
% 2.56/2.79 tff(285,plain,
% 2.56/2.79 (((~((~v5_orders_3(C!2, B!1, A!0)) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1) | (~((~m1_subset_1(tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0), u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, tptp_fun_E_27(C!2, k2_waybel34(A!0, B!1, C!2), B!1, A!0)))))))) | (~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E)))))))))) | ((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))),
% 2.56/2.79 inference(tautology,[status(thm)],[])).
% 2.56/2.79 tff(286,plain,
% 2.56/2.79 ((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E)))))))),
% 2.56/2.79 inference(unit_resolution,[status(thm)],[285, 284])).
% 2.56/2.79 tff(287,plain,
% 2.56/2.79 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))))))),
% 2.56/2.79 inference(bind,[status(th)],[])).
% 2.56/2.79 tff(288,plain,
% 2.56/2.79 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))),
% 2.56/2.79 inference(quant_intro,[status(thm)],[287])).
% 2.56/2.79 tff(289,plain,
% 2.56/2.79 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.79 inference(bind,[status(th)],[])).
% 2.56/2.79 tff(290,plain,
% 2.56/2.79 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.79 inference(quant_intro,[status(thm)],[289])).
% 2.56/2.79 tff(291,plain,
% 2.56/2.79 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.79 inference(bind,[status(th)],[])).
% 2.56/2.79 tff(292,plain,
% 2.56/2.79 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.80 inference(quant_intro,[status(thm)],[291])).
% 2.56/2.80 tff(293,plain,
% 2.56/2.80 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.80 inference(transitivity,[status(thm)],[292, 290])).
% 2.56/2.80 tff(294,plain,
% 2.56/2.80 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) <=> (~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> (~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))))), rewrite((~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(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)) & 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))) | (~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)) & 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))) | (~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))) | (~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))) | (~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)) & 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))) | (~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)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(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)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))))), (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), trans(monotonicity(rewrite((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) <=> (~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))), ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) <=> (~(~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))))), rewrite((~(~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))) <=> ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)))), ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) <=> ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))), trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> (![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite((![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite((((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> (((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))),
% 2.56/2.80 inference(bind,[status(th)],[])).
% 2.56/2.80 tff(295,plain,
% 2.56/2.80 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.80 inference(quant_intro,[status(thm)],[294])).
% 2.56/2.80 tff(296,plain,
% 2.56/2.80 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.80 inference(rewrite,[status(thm)],[])).
% 2.56/2.80 tff(297,plain,
% 2.56/2.80 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))), trans(monotonicity(rewrite(((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) <=> (v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(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)) & 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))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), rewrite(((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), (![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))))),
% 2.56/2.80 inference(bind,[status(th)],[])).
% 2.56/2.80 tff(298,plain,
% 2.56/2.80 (![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.80 inference(quant_intro,[status(thm)],[297])).
% 2.56/2.80 tff(299,axiom,(![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_waybel34')).
% 2.56/2.80 tff(300,plain,
% 2.56/2.80 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.80 inference(modus_ponens,[status(thm)],[299, 298])).
% 2.56/2.80 tff(301,plain,
% 2.56/2.80 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.80 inference(modus_ponens,[status(thm)],[300, 296])).
% 2.56/2.80 tff(302,plain,(
% 2.56/2.80 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 2.56/2.80 inference(skolemize,[status(sab)],[301])).
% 2.56/2.80 tff(303,plain,
% 2.56/2.80 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.80 inference(modus_ponens,[status(thm)],[302, 295])).
% 2.56/2.80 tff(304,plain,
% 2.56/2.80 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 2.56/2.80 inference(modus_ponens,[status(thm)],[303, 293])).
% 2.56/2.80 tff(305,plain,
% 2.56/2.80 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))),
% 2.56/2.80 inference(modus_ponens,[status(thm)],[304, 288])).
% 2.56/2.80 tff(306,plain,
% 2.56/2.80 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 2.56/2.80 inference(rewrite,[status(thm)],[])).
% 2.56/2.80 tff(307,plain,
% 2.56/2.80 (((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 2.56/2.80 inference(rewrite,[status(thm)],[])).
% 2.56/2.80 tff(308,plain,
% 2.56/2.80 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))))),
% 2.56/2.80 inference(monotonicity,[status(thm)],[307])).
% 2.56/2.80 tff(309,plain,
% 2.56/2.80 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 2.56/2.80 inference(transitivity,[status(thm)],[308, 306])).
% 2.56/2.80 tff(310,plain,
% 2.56/2.80 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 2.56/2.80 inference(quant_inst,[status(thm)],[])).
% 2.56/2.80 tff(311,plain,
% 2.56/2.80 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))),
% 2.56/2.81 inference(modus_ponens,[status(thm)],[310, 309])).
% 2.56/2.81 tff(312,plain,
% 2.56/2.81 (![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))),
% 2.56/2.81 inference(unit_resolution,[status(thm)],[311, 55, 54, 53, 52, 51, 50, 305])).
% 2.56/2.81 tff(313,plain,
% 2.56/2.81 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)))))),
% 2.56/2.81 inference(rewrite,[status(thm)],[])).
% 2.56/2.81 tff(314,plain,
% 2.56/2.81 (((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B!1)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)))))),
% 2.56/2.81 inference(rewrite,[status(thm)],[])).
% 2.56/2.81 tff(315,plain,
% 2.56/2.81 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B!1)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))))),
% 2.56/2.81 inference(monotonicity,[status(thm)],[314])).
% 2.56/2.81 tff(316,plain,
% 2.56/2.81 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B!1)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)))))),
% 2.56/2.81 inference(transitivity,[status(thm)],[315, 313])).
% 2.56/2.81 tff(317,plain,
% 2.56/2.81 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B!1)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 2.56/2.81 inference(quant_inst,[status(thm)],[])).
% 2.56/2.81 tff(318,plain,
% 2.56/2.81 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(B!1)) | (~v1_lattice3(B!1)) | (~v2_lattice3(B!1)) | (~v2_orders_2(B!1)) | (~v3_orders_2(B!1)) | (~v4_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))),
% 2.56/2.81 inference(modus_ponens,[status(thm)],[317, 316])).
% 2.56/2.81 tff(319,plain,
% 2.56/2.81 (![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))),
% 2.56/2.81 inference(unit_resolution,[status(thm)],[318, 49, 48, 47, 46, 45, 44, 312])).
% 2.56/2.81 tff(320,plain,
% 2.56/2.81 (v18_waybel_0(C!2, B!1, A!0)),
% 2.56/2.81 inference(and_elim,[status(thm)],[24])).
% 2.56/2.81 tff(321,plain,
% 2.56/2.81 (v3_lattice3(B!1)),
% 2.56/2.81 inference(and_elim,[status(thm)],[24])).
% 2.56/2.81 tff(322,plain,
% 2.56/2.81 (v3_lattice3(A!0)),
% 2.56/2.81 inference(and_elim,[status(thm)],[24])).
% 2.56/2.81 tff(323,plain,
% 2.56/2.81 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | ((~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))),
% 2.56/2.81 inference(rewrite,[status(thm)],[])).
% 2.56/2.81 tff(324,plain,
% 2.56/2.81 (((~v1_funct_1(C!2)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) <=> ((~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))),
% 2.56/2.81 inference(rewrite,[status(thm)],[])).
% 2.56/2.81 tff(325,plain,
% 2.56/2.81 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | ((~v1_funct_1(C!2)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | ((~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))))),
% 2.56/2.81 inference(monotonicity,[status(thm)],[324])).
% 2.56/2.81 tff(326,plain,
% 2.56/2.81 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | ((~v1_funct_1(C!2)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))),
% 2.56/2.81 inference(transitivity,[status(thm)],[325, 323])).
% 2.56/2.81 tff(327,plain,
% 2.56/2.81 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | ((~v1_funct_1(C!2)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1))))),
% 2.56/2.81 inference(quant_inst,[status(thm)],[])).
% 2.56/2.81 tff(328,plain,
% 2.65/2.81 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_2(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C, B!1, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C), A!0, B!1))))) | (~v3_lattice3(A!0)) | (~v3_lattice3(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | (~v18_waybel_0(C!2, B!1, A!0)) | (~m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))),
% 2.65/2.81 inference(modus_ponens,[status(thm)],[327, 326])).
% 2.65/2.81 tff(329,plain,
% 2.65/2.81 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))),
% 2.65/2.81 inference(unit_resolution,[status(thm)],[328, 322, 321, 43, 42, 320, 25, 319])).
% 2.65/2.81 tff(330,plain,
% 2.65/2.81 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(331,plain,
% 2.65/2.81 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(332,plain,
% 2.65/2.81 (($true <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(333,plain,
% 2.65/2.81 ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> $true),
% 2.65/2.81 inference(rewrite,[status(thm)],[])).
% 2.65/2.81 tff(334,plain,
% 2.65/2.81 (((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> ($true <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.81 inference(monotonicity,[status(thm)],[333])).
% 2.65/2.81 tff(335,plain,
% 2.65/2.81 (((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)),
% 2.65/2.81 inference(transitivity,[status(thm)],[334, 332])).
% 2.65/2.81 tff(336,plain,
% 2.65/2.81 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))) <=> ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[335])).
% 2.65/2.82 tff(337,plain,
% 2.65/2.82 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))) <=> ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.82 inference(transitivity,[status(thm)],[336, 331])).
% 2.65/2.82 tff(338,plain,
% 2.65/2.82 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[337])).
% 2.65/2.82 tff(339,plain,
% 2.65/2.82 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 2.65/2.82 inference(transitivity,[status(thm)],[338, 330])).
% 2.65/2.82 tff(340,plain,
% 2.65/2.82 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(341,plain,
% 2.65/2.82 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[340, 339])).
% 2.65/2.82 tff(342,plain,
% 2.65/2.82 (v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[341, 70, 68, 74, 329])).
% 2.65/2.82 tff(343,plain,
% 2.65/2.82 ((~((~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))))) | (~v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) | (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E)))))))),
% 2.65/2.82 inference(tautology,[status(thm)],[])).
% 2.65/2.82 tff(344,plain,
% 2.65/2.82 (~((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[343, 342, 286])).
% 2.65/2.82 tff(345,plain,
% 2.65/2.82 (((~v5_orders_3(C!2, B!1, A!0)) | (~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E)))))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))),
% 2.65/2.82 inference(tautology,[status(thm)],[])).
% 2.65/2.82 tff(346,plain,
% 2.65/2.82 (![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[345, 344])).
% 2.65/2.82 tff(347,plain,
% 2.65/2.82 (((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))) <=> ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(rewrite,[status(thm)],[])).
% 2.65/2.82 tff(348,plain,
% 2.65/2.82 ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(quant_inst,[status(thm)],[])).
% 2.65/2.82 tff(349,plain,
% 2.65/2.82 ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), E), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, E))))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[348, 347])).
% 2.65/2.82 tff(350,plain,
% 2.65/2.82 (r4_waybel_1(B!1, k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3), k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[349, 154, 346])).
% 2.65/2.82 tff(351,plain,
% 2.65/2.82 (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[350, 242])).
% 2.65/2.82 tff(352,plain,
% 2.65/2.82 (k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[240])).
% 2.65/2.82 tff(353,plain,
% 2.65/2.82 ((k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) <=> (k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[163, 352])).
% 2.65/2.82 tff(354,plain,
% 2.65/2.82 ((k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3)))) <=> (k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(symmetry,[status(thm)],[353])).
% 2.65/2.82 tff(355,plain,
% 2.65/2.82 ((~(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))) <=> (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))),
% 2.65/2.82 inference(monotonicity,[status(thm)],[354])).
% 2.65/2.82 tff(356,plain,
% 2.65/2.82 (~(k7_yellow_2(u1_struct_0(A!0), B!1, k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k5_pre_topc(B!1, A!0, C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(or_elim,[status(thm)],[153])).
% 2.65/2.82 tff(357,plain,
% 2.65/2.82 (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(modus_ponens,[status(thm)],[356, 355])).
% 2.65/2.82 tff(358,plain,
% 2.65/2.82 (((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))) | (k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(tautology,[status(thm)],[])).
% 2.65/2.82 tff(359,plain,
% 2.65/2.82 ((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))),
% 2.65/2.82 inference(unit_resolution,[status(thm)],[358, 357])).
% 2.65/2.82 tff(360,plain,
% 2.65/2.82 ((((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))))) <=> r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~((~r1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~r2_hidden(k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))), k10_relat_1(C!2, k6_waybel_0(A!0, D!3)))) | (~(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3) = k1_yellow_0(B!1, k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))))) | (~r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), k10_relat_1(C!2, k6_waybel_0(A!0, D!3))))),
% 2.65/2.82 inference(tautology,[status(thm)],[])).
% 2.65/2.82 tff(361,plain,
% 2.65/2.83 ($false),
% 2.65/2.83 inference(unit_resolution,[status(thm)],[360, 359, 351, 218])).
% 2.65/2.83 % SZS output end Proof
% 2.65/2.84 % E exiting
%------------------------------------------------------------------------------