TSTP Solution File: LAT353+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT353+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:22 EDT 2022
% Result : Theorem 3.64s 2.63s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT353+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 15:59:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 3.64/2.63 % SZS status Theorem
% 3.64/2.63 % SZS output start Proof
% 3.64/2.63 tff(k1_yellow_0_type, type, (
% 3.64/2.63 k1_yellow_0: ( $i * $i ) > $i)).
% 3.64/2.63 tff(k10_relat_1_type, type, (
% 3.64/2.63 k10_relat_1: ( $i * $i ) > $i)).
% 3.64/2.63 tff(k6_waybel_0_type, type, (
% 3.64/2.63 k6_waybel_0: ( $i * $i ) > $i)).
% 3.64/2.63 tff(tptp_fun_D_3_type, type, (
% 3.64/2.63 tptp_fun_D_3: $i)).
% 3.64/2.63 tff(tptp_fun_A_0_type, type, (
% 3.64/2.63 tptp_fun_A_0: $i)).
% 3.64/2.63 tff(tptp_fun_C_2_type, type, (
% 3.64/2.63 tptp_fun_C_2: $i)).
% 3.64/2.63 tff(tptp_fun_B_1_type, type, (
% 3.64/2.63 tptp_fun_B_1: $i)).
% 3.64/2.63 tff(k1_funct_1_type, type, (
% 3.64/2.63 k1_funct_1: ( $i * $i ) > $i)).
% 3.64/2.63 tff(k2_waybel34_type, type, (
% 3.64/2.63 k2_waybel34: ( $i * $i * $i ) > $i)).
% 3.64/2.63 tff(k5_pre_topc_type, type, (
% 3.64/2.63 k5_pre_topc: ( $i * $i * $i * $i ) > $i)).
% 3.64/2.63 tff(k7_yellow_2_type, type, (
% 3.64/2.63 k7_yellow_2: ( $i * $i * $i * $i ) > $i)).
% 3.64/2.63 tff(u1_struct_0_type, type, (
% 3.64/2.63 u1_struct_0: $i > $i)).
% 3.64/2.63 tff(m1_relset_1_type, type, (
% 3.64/2.63 m1_relset_1: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(m2_relset_1_type, type, (
% 3.64/2.63 m2_relset_1: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(m1_subset_1_type, type, (
% 3.64/2.63 m1_subset_1: ( $i * $i ) > $o)).
% 3.64/2.63 tff(v18_waybel_0_type, type, (
% 3.64/2.63 v18_waybel_0: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(v1_funct_2_type, type, (
% 3.64/2.63 v1_funct_2: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(v1_funct_1_type, type, (
% 3.64/2.63 v1_funct_1: $i > $o)).
% 3.64/2.63 tff(l1_orders_2_type, type, (
% 3.64/2.63 l1_orders_2: $i > $o)).
% 3.64/2.63 tff(v3_lattice3_type, type, (
% 3.64/2.63 v3_lattice3: $i > $o)).
% 3.64/2.63 tff(v2_lattice3_type, type, (
% 3.64/2.63 v2_lattice3: $i > $o)).
% 3.64/2.63 tff(v1_lattice3_type, type, (
% 3.64/2.63 v1_lattice3: $i > $o)).
% 3.64/2.63 tff(v4_orders_2_type, type, (
% 3.64/2.63 v4_orders_2: $i > $o)).
% 3.64/2.63 tff(v3_orders_2_type, type, (
% 3.64/2.63 v3_orders_2: $i > $o)).
% 3.64/2.63 tff(v2_orders_2_type, type, (
% 3.64/2.63 v2_orders_2: $i > $o)).
% 3.64/2.63 tff(l1_struct_0_type, type, (
% 3.64/2.63 l1_struct_0: $i > $o)).
% 3.64/2.63 tff(v1_xboole_0_type, type, (
% 3.64/2.63 v1_xboole_0: $i > $o)).
% 3.64/2.63 tff(v3_struct_0_type, type, (
% 3.64/2.63 v3_struct_0: $i > $o)).
% 3.64/2.63 tff(r2_hidden_type, type, (
% 3.64/2.63 r2_hidden: ( $i * $i ) > $o)).
% 3.64/2.63 tff(r1_yellow_0_type, type, (
% 3.64/2.63 r1_yellow_0: ( $i * $i ) > $o)).
% 3.64/2.63 tff(r4_waybel_1_type, type, (
% 3.64/2.63 r4_waybel_1: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(v5_orders_3_type, type, (
% 3.64/2.63 v5_orders_3: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(v3_waybel_1_type, type, (
% 3.64/2.63 v3_waybel_1: ( $i * $i * $i ) > $o)).
% 3.64/2.63 tff(k1_waybel_1_type, type, (
% 3.64/2.63 k1_waybel_1: ( $i * $i * $i * $i ) > $i)).
% 3.64/2.63 tff(tptp_fun_E_27_type, type, (
% 3.64/2.63 tptp_fun_E_27: ( $i * $i * $i * $i ) > $i)).
% 3.64/2.63 tff(1,plain,
% 3.64/2.63 (^[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)))),
% 3.64/2.63 inference(bind,[status(th)],[])).
% 3.64/2.63 tff(2,plain,
% 3.64/2.63 (![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))),
% 3.64/2.63 inference(quant_intro,[status(thm)],[1])).
% 3.64/2.63 tff(3,plain,
% 3.64/2.63 (![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))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 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')).
% 3.64/2.63 tff(5,plain,
% 3.64/2.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.64/2.63 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.64/2.63 tff(6,plain,(
% 3.64/2.63 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.64/2.63 inference(skolemize,[status(sab)],[5])).
% 3.64/2.63 tff(7,plain,
% 3.64/2.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.64/2.63 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.64/2.63 tff(8,plain,
% 3.64/2.63 ((~![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)))),
% 3.64/2.63 inference(quant_inst,[status(thm)],[])).
% 3.64/2.63 tff(9,plain,
% 3.64/2.63 (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))),
% 3.64/2.63 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.64/2.63 tff(10,plain,
% 3.64/2.63 (((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)))))))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(11,plain,
% 3.64/2.63 (((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)))))))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(12,plain,
% 3.64/2.63 (((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)))))))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(13,plain,
% 3.64/2.63 ((~(~(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))))) <=> (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)))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(14,plain,
% 3.64/2.63 (((~(~(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)))))))),
% 3.64/2.63 inference(monotonicity,[status(thm)],[13])).
% 3.64/2.63 tff(15,plain,
% 3.64/2.63 (((~(~(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)))))))),
% 3.64/2.63 inference(transitivity,[status(thm)],[14, 12])).
% 3.64/2.63 tff(16,plain,
% 3.64/2.63 ((~(~(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)))) <=> (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))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(17,plain,
% 3.64/2.63 (((~(~(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))))))))),
% 3.64/2.63 inference(monotonicity,[status(thm)],[16, 15])).
% 3.64/2.63 tff(18,plain,
% 3.64/2.63 (((~(~(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)))))))),
% 3.64/2.63 inference(transitivity,[status(thm)],[17, 11])).
% 3.64/2.63 tff(19,plain,
% 3.64/2.63 ((~(~(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(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))),
% 3.64/2.63 inference(rewrite,[status(thm)],[])).
% 3.64/2.63 tff(20,plain,
% 3.64/2.63 (((~(~(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))))))))),
% 3.64/2.64 inference(monotonicity,[status(thm)],[19, 18])).
% 3.64/2.64 tff(21,plain,
% 3.64/2.64 (((~(~(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)))))))),
% 3.64/2.64 inference(transitivity,[status(thm)],[20, 10])).
% 3.64/2.64 tff(22,plain,
% 3.64/2.64 ((~![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)))))))))),
% 3.64/2.64 inference(rewrite,[status(thm)],[])).
% 3.64/2.64 tff(23,plain,
% 3.64/2.64 ((~![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)))))))))),
% 3.64/2.64 inference(rewrite,[status(thm)],[])).
% 3.64/2.64 tff(24,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')).
% 3.64/2.64 tff(25,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.64/2.64 tff(26,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[25, 22])).
% 3.64/2.64 tff(27,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[26, 22])).
% 3.64/2.64 tff(28,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[27, 22])).
% 3.64/2.64 tff(29,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[28, 22])).
% 3.64/2.64 tff(30,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[29, 22])).
% 3.64/2.64 tff(31,plain,
% 3.64/2.64 (~![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))))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[30, 22])).
% 3.64/2.64 tff(32,plain,
% 3.64/2.64 (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))))))),
% 3.64/2.64 inference(modus_ponens,[status(thm)],[31, 21])).
% 3.64/2.64 tff(33,plain,
% 3.64/2.64 (m2_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 3.64/2.64 inference(and_elim,[status(thm)],[32])).
% 3.64/2.64 tff(34,plain,
% 3.64/2.64 ((~(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))),
% 3.64/2.64 inference(tautology,[status(thm)],[])).
% 3.64/2.64 tff(35,plain,
% 3.64/2.64 ((~(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))),
% 3.64/2.64 inference(unit_resolution,[status(thm)],[34, 33])).
% 3.64/2.64 tff(36,plain,
% 3.64/2.64 (m1_relset_1(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 3.64/2.64 inference(unit_resolution,[status(thm)],[35, 9])).
% 3.64/2.64 tff(37,plain,
% 3.64/2.64 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 3.64/2.64 inference(bind,[status(th)],[])).
% 3.64/2.64 tff(38,plain,
% 3.64/2.64 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.64/2.64 inference(quant_intro,[status(thm)],[37])).
% 3.64/2.64 tff(39,plain,
% 3.64/2.64 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.64/2.64 inference(rewrite,[status(thm)],[])).
% 3.64/2.64 tff(40,plain,
% 3.64/2.64 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 3.64/2.64 inference(bind,[status(th)],[])).
% 3.64/2.64 tff(41,plain,
% 3.64/2.64 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.64/2.64 inference(quant_intro,[status(thm)],[40])).
% 3.79/2.64 tff(42,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 3.79/2.64 tff(43,plain,
% 3.79/2.64 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[42, 41])).
% 3.79/2.64 tff(44,plain,
% 3.79/2.64 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[43, 39])).
% 3.79/2.64 tff(45,plain,(
% 3.79/2.64 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.79/2.64 inference(skolemize,[status(sab)],[44])).
% 3.79/2.64 tff(46,plain,
% 3.79/2.64 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[45, 38])).
% 3.79/2.64 tff(47,plain,
% 3.79/2.64 (l1_orders_2(B!1)),
% 3.79/2.64 inference(and_elim,[status(thm)],[32])).
% 3.79/2.64 tff(48,plain,
% 3.79/2.64 (((~![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)))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(49,plain,
% 3.79/2.64 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(B!1) | (~l1_orders_2(B!1)))),
% 3.79/2.64 inference(quant_inst,[status(thm)],[])).
% 3.79/2.64 tff(50,plain,
% 3.79/2.64 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(B!1) | (~l1_orders_2(B!1))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[49, 48])).
% 3.79/2.64 tff(51,plain,
% 3.79/2.64 (l1_struct_0(B!1)),
% 3.79/2.64 inference(unit_resolution,[status(thm)],[50, 47, 46])).
% 3.79/2.64 tff(52,plain,
% 3.79/2.64 (l1_orders_2(A!0)),
% 3.79/2.64 inference(and_elim,[status(thm)],[32])).
% 3.79/2.64 tff(53,plain,
% 3.79/2.64 (((~![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)))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(54,plain,
% 3.79/2.64 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 3.79/2.64 inference(quant_inst,[status(thm)],[])).
% 3.79/2.64 tff(55,plain,
% 3.79/2.64 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[54, 53])).
% 3.79/2.64 tff(56,plain,
% 3.79/2.64 (l1_struct_0(A!0)),
% 3.79/2.64 inference(unit_resolution,[status(thm)],[55, 52, 46])).
% 3.79/2.64 tff(57,plain,
% 3.79/2.64 (^[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))))),
% 3.79/2.64 inference(bind,[status(th)],[])).
% 3.79/2.64 tff(58,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(quant_intro,[status(thm)],[57])).
% 3.79/2.64 tff(59,plain,
% 3.79/2.64 (^[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)))))),
% 3.79/2.64 inference(bind,[status(th)],[])).
% 3.79/2.64 tff(60,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(quant_intro,[status(thm)],[59])).
% 3.79/2.64 tff(61,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(62,plain,
% 3.79/2.64 (^[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)))))),
% 3.79/2.64 inference(bind,[status(th)],[])).
% 3.79/2.64 tff(63,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(quant_intro,[status(thm)],[62])).
% 3.79/2.64 tff(64,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')).
% 3.79/2.64 tff(65,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[64, 63])).
% 3.79/2.64 tff(66,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[65, 61])).
% 3.79/2.64 tff(67,plain,(
% 3.79/2.64 ![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)))),
% 3.79/2.64 inference(skolemize,[status(sab)],[66])).
% 3.79/2.64 tff(68,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[67, 60])).
% 3.79/2.64 tff(69,plain,
% 3.79/2.64 (![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)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[68, 58])).
% 3.79/2.64 tff(70,plain,
% 3.79/2.64 (v1_funct_2(C!2, u1_struct_0(B!1), u1_struct_0(A!0))),
% 3.79/2.64 inference(and_elim,[status(thm)],[32])).
% 3.79/2.64 tff(71,plain,
% 3.79/2.64 (v1_funct_1(C!2)),
% 3.79/2.64 inference(and_elim,[status(thm)],[32])).
% 3.79/2.64 tff(72,plain,
% 3.79/2.64 (((~![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))))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(73,plain,
% 3.79/2.64 (((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))))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(74,plain,
% 3.79/2.64 (((~![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)))))),
% 3.79/2.64 inference(monotonicity,[status(thm)],[73])).
% 3.79/2.64 tff(75,plain,
% 3.79/2.64 (((~![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))))),
% 3.79/2.64 inference(transitivity,[status(thm)],[74, 72])).
% 3.79/2.64 tff(76,plain,
% 3.79/2.64 ((~![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)))),
% 3.79/2.64 inference(quant_inst,[status(thm)],[])).
% 3.79/2.64 tff(77,plain,
% 3.79/2.64 ((~![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)))),
% 3.79/2.64 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.79/2.64 tff(78,plain,
% 3.79/2.64 ((~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)))),
% 3.79/2.64 inference(unit_resolution,[status(thm)],[77, 71, 70, 69, 56, 51])).
% 3.79/2.64 tff(79,plain,
% 3.79/2.64 (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))),
% 3.79/2.64 inference(unit_resolution,[status(thm)],[78, 36])).
% 3.79/2.64 tff(80,plain,
% 3.79/2.64 (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))),
% 3.79/2.64 inference(symmetry,[status(thm)],[79])).
% 3.79/2.64 tff(81,plain,
% 3.79/2.64 (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)))),
% 3.79/2.64 inference(monotonicity,[status(thm)],[80])).
% 3.79/2.64 tff(82,plain,
% 3.79/2.64 (^[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)))))))),
% 3.79/2.64 inference(bind,[status(th)],[])).
% 3.79/2.64 tff(83,plain,
% 3.79/2.64 (![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))))))),
% 3.79/2.64 inference(quant_intro,[status(thm)],[82])).
% 3.79/2.64 tff(84,plain,
% 3.79/2.64 (^[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))))))))),
% 3.79/2.64 inference(bind,[status(th)],[])).
% 3.79/2.64 tff(85,plain,
% 3.79/2.64 (![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))))))),
% 3.79/2.64 inference(quant_intro,[status(thm)],[84])).
% 3.79/2.64 tff(86,plain,
% 3.79/2.64 (![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))))),
% 3.79/2.64 inference(rewrite,[status(thm)],[])).
% 3.79/2.64 tff(87,plain,
% 3.79/2.64 (^[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))))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(88,plain,
% 3.79/2.65 (![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))))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[87])).
% 3.79/2.65 tff(89,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')).
% 3.79/2.65 tff(90,plain,
% 3.79/2.65 (![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))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[89, 88])).
% 3.79/2.65 tff(91,plain,
% 3.79/2.65 (![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))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[90, 86])).
% 3.79/2.65 tff(92,plain,(
% 3.79/2.65 ![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))))),
% 3.79/2.65 inference(skolemize,[status(sab)],[91])).
% 3.79/2.65 tff(93,plain,
% 3.79/2.65 (![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))))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[92, 85])).
% 3.79/2.65 tff(94,plain,
% 3.79/2.65 (![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))))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[93, 83])).
% 3.79/2.65 tff(95,plain,
% 3.79/2.65 (v2_lattice3(B!1)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(96,plain,
% 3.79/2.65 (v1_lattice3(B!1)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(97,plain,
% 3.79/2.65 (v4_orders_2(B!1)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(98,plain,
% 3.79/2.65 (v3_orders_2(B!1)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(99,plain,
% 3.79/2.65 (v2_orders_2(B!1)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(100,plain,
% 3.79/2.65 (v2_lattice3(A!0)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(101,plain,
% 3.79/2.65 (v1_lattice3(A!0)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(102,plain,
% 3.79/2.65 (v4_orders_2(A!0)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(103,plain,
% 3.79/2.65 (v3_orders_2(A!0)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(104,plain,
% 3.79/2.65 (v2_orders_2(A!0)),
% 3.79/2.65 inference(and_elim,[status(thm)],[32])).
% 3.79/2.65 tff(105,plain,
% 3.79/2.65 (((~![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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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))))))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(106,plain,
% 3.79/2.65 (((~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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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))))))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(107,plain,
% 3.79/2.65 ((~((~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)))))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(108,plain,
% 3.79/2.65 (((~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))))))),
% 3.79/2.65 inference(monotonicity,[status(thm)],[107])).
% 3.79/2.65 tff(109,plain,
% 3.79/2.65 (((~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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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))))))),
% 3.79/2.65 inference(transitivity,[status(thm)],[108, 106])).
% 3.79/2.65 tff(110,plain,
% 3.79/2.65 (((~![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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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)))))))),
% 3.79/2.65 inference(monotonicity,[status(thm)],[109])).
% 3.79/2.65 tff(111,plain,
% 3.79/2.65 (((~![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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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))))))),
% 3.79/2.65 inference(transitivity,[status(thm)],[110, 105])).
% 3.79/2.65 tff(112,plain,
% 3.79/2.65 ((~![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))))))),
% 3.79/2.65 inference(quant_inst,[status(thm)],[])).
% 3.79/2.65 tff(113,plain,
% 3.79/2.65 ((~![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)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_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)))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.79/2.65 tff(114,plain,
% 3.79/2.65 ((~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)))))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[113, 104, 103, 102, 101, 100, 52, 99, 98, 97, 96, 95, 47, 71, 70, 94])).
% 3.79/2.65 tff(115,plain,
% 3.79/2.65 (~((~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))))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[114, 36])).
% 3.79/2.65 tff(116,plain,
% 3.79/2.65 (((~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))),
% 3.79/2.65 inference(tautology,[status(thm)],[])).
% 3.79/2.65 tff(117,plain,
% 3.79/2.65 (v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[116, 115])).
% 3.79/2.65 tff(118,plain,
% 3.79/2.65 (((~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))),
% 3.79/2.65 inference(tautology,[status(thm)],[])).
% 3.79/2.65 tff(119,plain,
% 3.79/2.65 (v1_funct_1(k2_waybel34(A!0, B!1, C!2))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[118, 115])).
% 3.79/2.65 tff(120,plain,
% 3.79/2.65 ((~![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)))),
% 3.79/2.65 inference(quant_inst,[status(thm)],[])).
% 3.79/2.65 tff(121,plain,
% 3.79/2.65 (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))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[120, 7])).
% 3.79/2.65 tff(122,plain,
% 3.79/2.65 (((~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))),
% 3.79/2.65 inference(tautology,[status(thm)],[])).
% 3.79/2.65 tff(123,plain,
% 3.79/2.65 (m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[122, 115])).
% 3.79/2.65 tff(124,plain,
% 3.79/2.65 ((~(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))),
% 3.79/2.65 inference(tautology,[status(thm)],[])).
% 3.79/2.65 tff(125,plain,
% 3.79/2.65 ((~(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))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[124, 123])).
% 3.79/2.65 tff(126,plain,
% 3.79/2.65 (m1_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[125, 121])).
% 3.79/2.65 tff(127,plain,
% 3.79/2.65 (^[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))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(128,plain,
% 3.79/2.65 (![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)))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[127])).
% 3.79/2.65 tff(129,plain,
% 3.79/2.65 (![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)))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(130,plain,
% 3.79/2.65 (^[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)))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(131,plain,
% 3.79/2.65 (![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)))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[130])).
% 3.79/2.65 tff(132,axiom,(![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_lattice3')).
% 3.79/2.65 tff(133,plain,
% 3.79/2.65 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[132, 131])).
% 3.79/2.65 tff(134,plain,
% 3.79/2.65 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[133, 129])).
% 3.79/2.65 tff(135,plain,(
% 3.79/2.65 ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 3.79/2.65 inference(skolemize,[status(sab)],[134])).
% 3.79/2.65 tff(136,plain,
% 3.79/2.65 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[135, 128])).
% 3.79/2.65 tff(137,plain,
% 3.79/2.65 (((~![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)))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(138,plain,
% 3.79/2.65 (((~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)))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(139,plain,
% 3.79/2.65 (((~![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))))),
% 3.79/2.65 inference(monotonicity,[status(thm)],[138])).
% 3.79/2.65 tff(140,plain,
% 3.79/2.65 (((~![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)))),
% 3.79/2.65 inference(transitivity,[status(thm)],[139, 137])).
% 3.79/2.65 tff(141,plain,
% 3.79/2.65 ((~![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)))),
% 3.79/2.65 inference(quant_inst,[status(thm)],[])).
% 3.79/2.65 tff(142,plain,
% 3.79/2.65 ((~![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))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[141, 140])).
% 3.79/2.65 tff(143,plain,
% 3.79/2.65 (~v3_struct_0(A!0)),
% 3.79/2.65 inference(unit_resolution,[status(thm)],[142, 100, 52, 136])).
% 3.79/2.65 tff(144,plain,
% 3.79/2.65 (^[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))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(145,plain,
% 3.79/2.65 (![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)))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[144])).
% 3.79/2.65 tff(146,plain,
% 3.79/2.65 (^[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)))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(147,plain,
% 3.79/2.65 (![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)))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[146])).
% 3.79/2.65 tff(148,plain,
% 3.79/2.65 (![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))))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(149,plain,
% 3.79/2.65 (^[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)))))),
% 3.79/2.65 inference(bind,[status(th)],[])).
% 3.79/2.65 tff(150,plain,
% 3.79/2.65 (![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))))),
% 3.79/2.65 inference(quant_intro,[status(thm)],[149])).
% 3.79/2.65 tff(151,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')).
% 3.79/2.65 tff(152,plain,
% 3.79/2.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[151, 150])).
% 3.79/2.65 tff(153,plain,
% 3.79/2.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[152, 148])).
% 3.79/2.65 tff(154,plain,(
% 3.79/2.65 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.79/2.65 inference(skolemize,[status(sab)],[153])).
% 3.79/2.65 tff(155,plain,
% 3.79/2.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[154, 147])).
% 3.79/2.65 tff(156,plain,
% 3.79/2.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.79/2.65 inference(modus_ponens,[status(thm)],[155, 145])).
% 3.79/2.65 tff(157,plain,
% 3.79/2.65 (((~![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))))),
% 3.79/2.65 inference(rewrite,[status(thm)],[])).
% 3.79/2.65 tff(158,plain,
% 3.79/2.65 ((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))))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(159,plain,
% 3.79/2.66 (((~![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)))))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[158])).
% 3.79/2.66 tff(160,plain,
% 3.79/2.66 (((~![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))))),
% 3.79/2.66 inference(transitivity,[status(thm)],[159, 157])).
% 3.79/2.66 tff(161,plain,
% 3.79/2.66 ((~![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)))),
% 3.79/2.66 inference(quant_inst,[status(thm)],[])).
% 3.79/2.66 tff(162,plain,
% 3.79/2.66 ((~![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[161, 160])).
% 3.79/2.66 tff(163,plain,
% 3.79/2.66 (~v1_xboole_0(u1_struct_0(A!0))),
% 3.79/2.66 inference(unit_resolution,[status(thm)],[162, 156, 143, 56])).
% 3.79/2.66 tff(164,plain,
% 3.79/2.66 (((~![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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(165,plain,
% 3.79/2.66 (((~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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(166,plain,
% 3.79/2.66 (((~![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))))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[165])).
% 3.79/2.66 tff(167,plain,
% 3.79/2.66 (((~![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)))),
% 3.79/2.66 inference(transitivity,[status(thm)],[166, 164])).
% 3.79/2.66 tff(168,plain,
% 3.79/2.66 ((~![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)))),
% 3.79/2.66 inference(quant_inst,[status(thm)],[])).
% 3.79/2.66 tff(169,plain,
% 3.79/2.66 ((~![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))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.79/2.66 tff(170,plain,
% 3.79/2.66 (~v3_struct_0(B!1)),
% 3.79/2.66 inference(unit_resolution,[status(thm)],[169, 95, 47, 136])).
% 3.79/2.66 tff(171,plain,
% 3.79/2.66 (^[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))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(172,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[171])).
% 3.79/2.66 tff(173,plain,
% 3.79/2.66 (^[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)))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(174,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[173])).
% 3.79/2.66 tff(175,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(176,plain,
% 3.79/2.66 (^[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)))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(177,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[176])).
% 3.79/2.66 tff(178,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')).
% 3.79/2.66 tff(179,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[178, 177])).
% 3.79/2.66 tff(180,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[179, 175])).
% 3.79/2.66 tff(181,plain,(
% 3.79/2.66 ![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)))),
% 3.79/2.66 inference(skolemize,[status(sab)],[180])).
% 3.79/2.66 tff(182,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[181, 174])).
% 3.79/2.66 tff(183,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[182, 172])).
% 3.79/2.66 tff(184,plain,
% 3.79/2.66 (~((~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)))))),
% 3.79/2.66 inference(and_elim,[status(thm)],[32])).
% 3.79/2.66 tff(185,plain,
% 3.79/2.66 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 3.79/2.66 inference(or_elim,[status(thm)],[184])).
% 3.79/2.66 tff(186,plain,
% 3.79/2.66 (((~![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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(187,plain,
% 3.79/2.66 ((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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(188,plain,
% 3.79/2.66 (((~![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))))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[187])).
% 3.79/2.66 tff(189,plain,
% 3.79/2.66 (((~![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)))),
% 3.79/2.66 inference(transitivity,[status(thm)],[188, 186])).
% 3.79/2.66 tff(190,plain,
% 3.79/2.66 ((~![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))))),
% 3.79/2.66 inference(quant_inst,[status(thm)],[])).
% 3.79/2.66 tff(191,plain,
% 3.79/2.66 ((~![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))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[190, 189])).
% 3.79/2.66 tff(192,plain,
% 3.79/2.66 ((~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))),
% 3.79/2.66 inference(unit_resolution,[status(thm)],[191, 185, 183, 170, 51, 163])).
% 3.79/2.66 tff(193,plain,
% 3.79/2.66 (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)),
% 3.79/2.66 inference(unit_resolution,[status(thm)],[192, 126, 119, 117])).
% 3.79/2.66 tff(194,plain,
% 3.79/2.66 (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)),
% 3.79/2.66 inference(symmetry,[status(thm)],[193])).
% 3.79/2.66 tff(195,plain,
% 3.79/2.66 ((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))))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[194, 81])).
% 3.79/2.66 tff(196,plain,
% 3.79/2.66 ((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))))),
% 3.79/2.66 inference(symmetry,[status(thm)],[195])).
% 3.79/2.66 tff(197,plain,
% 3.79/2.66 ((~(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)))))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[196])).
% 3.79/2.66 tff(198,plain,
% 3.79/2.66 (~(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))))),
% 3.79/2.66 inference(or_elim,[status(thm)],[184])).
% 3.79/2.66 tff(199,plain,
% 3.79/2.66 (~(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))))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[198, 197])).
% 3.79/2.66 tff(200,plain,
% 3.79/2.66 (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))),
% 3.79/2.66 inference(monotonicity,[status(thm)],[194])).
% 3.79/2.66 tff(201,plain,
% 3.79/2.66 (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))),
% 3.79/2.66 inference(symmetry,[status(thm)],[200])).
% 3.79/2.66 tff(202,plain,
% 3.79/2.66 (^[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))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(203,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[202])).
% 3.79/2.66 tff(204,plain,
% 3.79/2.66 (^[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)))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(205,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[204])).
% 3.79/2.66 tff(206,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(207,plain,
% 3.79/2.66 (^[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)))))),
% 3.79/2.66 inference(bind,[status(th)],[])).
% 3.79/2.66 tff(208,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(quant_intro,[status(thm)],[207])).
% 3.79/2.66 tff(209,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')).
% 3.79/2.66 tff(210,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[209, 208])).
% 3.79/2.66 tff(211,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[210, 206])).
% 3.79/2.66 tff(212,plain,(
% 3.79/2.66 ![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)))),
% 3.79/2.66 inference(skolemize,[status(sab)],[211])).
% 3.79/2.66 tff(213,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[212, 205])).
% 3.79/2.66 tff(214,plain,
% 3.79/2.66 (![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)))),
% 3.79/2.66 inference(modus_ponens,[status(thm)],[213, 203])).
% 3.79/2.66 tff(215,plain,
% 3.79/2.66 (((~![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))))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(216,plain,
% 3.79/2.66 ((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))))),
% 3.79/2.66 inference(rewrite,[status(thm)],[])).
% 3.79/2.66 tff(217,plain,
% 3.79/2.66 (((~![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)))))),
% 3.79/2.67 inference(monotonicity,[status(thm)],[216])).
% 3.79/2.67 tff(218,plain,
% 3.79/2.67 (((~![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))))),
% 3.79/2.67 inference(transitivity,[status(thm)],[217, 215])).
% 3.79/2.67 tff(219,plain,
% 3.79/2.67 ((~![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))))),
% 3.79/2.67 inference(quant_inst,[status(thm)],[])).
% 3.79/2.67 tff(220,plain,
% 3.79/2.67 ((~![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)))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.79/2.67 tff(221,plain,
% 3.79/2.67 ((~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)))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[220, 185, 214, 170, 51, 163])).
% 3.79/2.67 tff(222,plain,
% 3.79/2.67 (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))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[221, 126, 119, 117])).
% 3.79/2.67 tff(223,plain,
% 3.79/2.67 (m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[222, 201])).
% 3.79/2.67 tff(224,plain,
% 3.79/2.67 (^[A: $i] : refl((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))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(225,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[224])).
% 3.79/2.67 tff(226,plain,
% 3.79/2.67 (^[A: $i] : 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))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(227,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[226])).
% 3.79/2.67 tff(228,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(transitivity,[status(thm)],[227, 225])).
% 3.79/2.67 tff(229,plain,
% 3.79/2.67 (^[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] : (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)))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(230,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[229])).
% 3.79/2.67 tff(231,plain,
% 3.79/2.67 (![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)))))),
% 3.79/2.67 inference(rewrite,[status(thm)],[])).
% 3.79/2.67 tff(232,plain,
% 3.79/2.67 (^[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)))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(233,plain,
% 3.79/2.67 (![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)))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[232])).
% 3.79/2.67 tff(234,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')).
% 3.79/2.67 tff(235,plain,
% 3.79/2.67 (![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)))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[234, 233])).
% 3.79/2.67 tff(236,plain,
% 3.79/2.67 (![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)))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[235, 231])).
% 3.79/2.67 tff(237,plain,(
% 3.79/2.67 ![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)))))),
% 3.79/2.67 inference(skolemize,[status(sab)],[236])).
% 3.79/2.67 tff(238,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[237, 230])).
% 3.79/2.67 tff(239,plain,
% 3.79/2.67 (![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)))))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[238, 228])).
% 3.79/2.67 tff(240,plain,
% 3.79/2.67 (((~![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)))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, 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)))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C)))))))),
% 3.79/2.67 inference(rewrite,[status(thm)],[])).
% 3.79/2.67 tff(241,plain,
% 3.79/2.67 ((~![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)))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C)))))))),
% 3.79/2.67 inference(quant_inst,[status(thm)],[])).
% 3.79/2.67 tff(242,plain,
% 3.79/2.67 ((~![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)))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[241, 240])).
% 3.79/2.67 tff(243,plain,
% 3.79/2.67 (v3_struct_0(B!1) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[242, 47, 239])).
% 3.79/2.67 tff(244,plain,
% 3.79/2.67 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[243, 170])).
% 3.79/2.67 tff(245,plain,
% 3.79/2.67 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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)))))))),
% 3.79/2.67 inference(rewrite,[status(thm)],[])).
% 3.79/2.67 tff(246,plain,
% 3.79/2.67 (((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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)))))) <=> ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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)))))))),
% 3.79/2.67 inference(rewrite,[status(thm)],[])).
% 3.79/2.67 tff(247,plain,
% 3.79/2.67 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))))),
% 3.79/2.67 inference(monotonicity,[status(thm)],[246])).
% 3.79/2.67 tff(248,plain,
% 3.79/2.67 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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)))))))),
% 3.79/2.67 inference(transitivity,[status(thm)],[247, 245])).
% 3.79/2.67 tff(249,plain,
% 3.79/2.67 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))),
% 3.79/2.67 inference(quant_inst,[status(thm)],[])).
% 3.79/2.67 tff(250,plain,
% 3.79/2.67 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, B, C) <=> (~((~r1_yellow_0(B!1, C)) | (~(B = k1_yellow_0(B!1, C))) | (~r2_hidden(k1_yellow_0(B!1, C), C))))))) | (~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))),
% 3.79/2.67 inference(modus_ponens,[status(thm)],[249, 248])).
% 3.79/2.67 tff(251,plain,
% 3.79/2.67 ((~m1_subset_1(k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), u1_struct_0(B!1))) | ![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[250, 244])).
% 3.79/2.67 tff(252,plain,
% 3.79/2.67 (![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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))))))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[251, 223])).
% 3.79/2.67 tff(253,plain,
% 3.79/2.67 ((~![C: $i] : (r4_waybel_1(B!1, k1_funct_1(k2_waybel34(A!0, B!1, C!2), D!3), C) <=> (~((~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), 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))))))))),
% 3.79/2.67 inference(quant_inst,[status(thm)],[])).
% 3.79/2.67 tff(254,plain,
% 3.79/2.67 (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)))))))),
% 3.79/2.67 inference(unit_resolution,[status(thm)],[253, 252])).
% 3.79/2.67 tff(255,plain,
% 3.79/2.67 (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)))),
% 3.79/2.67 inference(monotonicity,[status(thm)],[194, 80])).
% 3.79/2.67 tff(256,plain,
% 3.79/2.67 (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)))),
% 3.79/2.67 inference(symmetry,[status(thm)],[255])).
% 3.79/2.67 tff(257,plain,
% 3.79/2.67 (^[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))))))))))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(258,plain,
% 3.79/2.67 (![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)))))))))))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[257])).
% 3.79/2.67 tff(259,plain,
% 3.79/2.67 (^[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)))))))))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(260,plain,
% 3.79/2.67 (![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))))))))))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[259])).
% 3.79/2.67 tff(261,plain,
% 3.79/2.67 (^[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)))))))))))))))),
% 3.79/2.67 inference(bind,[status(th)],[])).
% 3.79/2.67 tff(262,plain,
% 3.79/2.67 (![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))))))))))))))),
% 3.79/2.67 inference(quant_intro,[status(thm)],[261])).
% 3.79/2.67 tff(263,plain,
% 3.79/2.67 (![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))))))))))))))),
% 3.79/2.68 inference(transitivity,[status(thm)],[262, 260])).
% 3.79/2.68 tff(264,plain,
% 3.79/2.68 (^[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))))))))))))))))),
% 3.79/2.68 inference(bind,[status(th)],[])).
% 3.79/2.68 tff(265,plain,
% 3.79/2.68 (![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))))))))))))))),
% 3.79/2.68 inference(quant_intro,[status(thm)],[264])).
% 3.79/2.68 tff(266,plain,
% 3.79/2.68 (^[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)))))))))))))),
% 3.79/2.68 inference(bind,[status(th)],[])).
% 3.79/2.68 tff(267,plain,
% 3.79/2.68 (![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))))))))))))),
% 3.79/2.68 inference(quant_intro,[status(thm)],[266])).
% 3.79/2.68 tff(268,plain,
% 3.79/2.68 (![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))))))))))),
% 3.79/2.68 inference(rewrite,[status(thm)],[])).
% 3.79/2.68 tff(269,plain,
% 3.79/2.68 (^[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))))))))))))),
% 3.79/2.68 inference(bind,[status(th)],[])).
% 3.79/2.68 tff(270,plain,
% 3.79/2.68 (![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))))))))))),
% 3.79/2.68 inference(quant_intro,[status(thm)],[269])).
% 3.79/2.68 tff(271,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')).
% 3.79/2.68 tff(272,plain,
% 3.79/2.68 (![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))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[271, 270])).
% 3.79/2.68 tff(273,plain,
% 3.79/2.68 (![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))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[272, 268])).
% 3.79/2.68 tff(274,plain,(
% 3.79/2.68 ![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)))))))))))))),
% 3.79/2.68 inference(skolemize,[status(sab)],[273])).
% 3.79/2.68 tff(275,plain,
% 3.79/2.68 (![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))))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[274, 267])).
% 3.79/2.68 tff(276,plain,
% 3.79/2.68 (![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))))))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[275, 265])).
% 3.79/2.68 tff(277,plain,
% 3.79/2.68 (![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))))))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[276, 263])).
% 3.79/2.68 tff(278,plain,
% 3.79/2.68 (![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)))))))))))))))),
% 3.79/2.68 inference(modus_ponens,[status(thm)],[277, 258])).
% 3.79/2.68 tff(279,plain,
% 3.79/2.68 (((~![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)) | (~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)))))))))))))))),
% 3.79/2.68 inference(rewrite,[status(thm)],[])).
% 3.79/2.68 tff(280,plain,
% 3.79/2.68 ((~![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)))))))))))))))),
% 3.79/2.69 inference(quant_inst,[status(thm)],[])).
% 3.79/2.69 tff(281,plain,
% 3.79/2.69 ((~![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))))))))))))))),
% 3.79/2.69 inference(modus_ponens,[status(thm)],[280, 279])).
% 3.79/2.69 tff(282,plain,
% 3.79/2.69 (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)) | (~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))))))))))))))),
% 3.79/2.69 inference(unit_resolution,[status(thm)],[281, 104, 103, 102, 52, 278])).
% 3.79/2.69 tff(283,plain,
% 3.79/2.69 (![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))))))))))))))),
% 3.79/2.69 inference(unit_resolution,[status(thm)],[282, 143])).
% 3.79/2.69 tff(284,plain,
% 3.79/2.69 (((~![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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))))))))))))))),
% 3.79/2.69 inference(rewrite,[status(thm)],[])).
% 3.79/2.69 tff(285,plain,
% 3.79/2.69 ((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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(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)) | (~((~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)))))))))))))) <=> (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))))))))))))))),
% 3.79/2.69 inference(rewrite,[status(thm)],[])).
% 3.79/2.69 tff(286,plain,
% 3.79/2.69 (((~![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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(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)) | (~((~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)) | (~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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)))))))))))))))),
% 3.79/2.69 inference(monotonicity,[status(thm)],[285])).
% 3.79/2.69 tff(287,plain,
% 3.79/2.69 (((~![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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(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)) | (~((~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)) | (~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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))))))))))))))),
% 3.79/2.69 inference(transitivity,[status(thm)],[286, 284])).
% 3.79/2.69 tff(288,plain,
% 3.79/2.69 ((~![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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B!1), u1_struct_0(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)) | (~((~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))))))))))))))),
% 3.79/2.69 inference(quant_inst,[status(thm)],[])).
% 3.79/2.69 tff(289,plain,
% 3.79/2.69 ((~![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(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)))))))))))))),
% 3.79/2.69 inference(modus_ponens,[status(thm)],[288, 287])).
% 3.79/2.69 tff(290,plain,
% 3.79/2.69 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)))))))))))))),
% 3.79/2.69 inference(unit_resolution,[status(thm)],[289, 99, 98, 97, 47, 283, 170])).
% 3.79/2.69 tff(291,plain,
% 3.79/2.69 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)))))))))))))),
% 3.85/2.70 inference(rewrite,[status(thm)],[])).
% 3.85/2.70 tff(292,plain,
% 3.85/2.70 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)))))))))))))),
% 3.85/2.70 inference(quant_inst,[status(thm)],[])).
% 3.85/2.70 tff(293,plain,
% 3.85/2.70 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))))))))))))),
% 3.85/2.70 inference(modus_ponens,[status(thm)],[292, 291])).
% 3.85/2.70 tff(294,plain,
% 3.85/2.70 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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))))))))))))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[293, 119, 117, 123, 290])).
% 3.85/2.70 tff(295,plain,
% 3.85/2.70 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~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))) | (~((~((~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)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~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))) | (~((~((~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))))))))))))),
% 3.85/2.70 inference(rewrite,[status(thm)],[])).
% 3.85/2.70 tff(296,plain,
% 3.85/2.70 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~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))) | (~((~((~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))))))))))))),
% 3.85/2.70 inference(quant_inst,[status(thm)],[])).
% 3.85/2.70 tff(297,plain,
% 3.85/2.70 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B!1), u1_struct_0(A!0))) | (~m2_relset_1(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)) | (~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))) | (~((~((~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)))))))))))),
% 3.85/2.70 inference(modus_ponens,[status(thm)],[296, 295])).
% 3.85/2.70 tff(298,plain,
% 3.85/2.70 (~((~((~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))))))))))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[297, 71, 70, 33, 294])).
% 3.85/2.70 tff(299,plain,
% 3.85/2.70 (((~((~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))))))))),
% 3.85/2.70 inference(tautology,[status(thm)],[])).
% 3.85/2.70 tff(300,plain,
% 3.85/2.70 ((~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)))))))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[299, 298])).
% 3.85/2.70 tff(301,plain,
% 3.85/2.70 (^[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))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(302,plain,
% 3.85/2.70 (![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)))))))),
% 3.85/2.71 inference(quant_intro,[status(thm)],[301])).
% 3.85/2.71 tff(303,plain,
% 3.85/2.71 (^[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)))))))),
% 3.85/2.71 inference(bind,[status(th)],[])).
% 3.85/2.71 tff(304,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(quant_intro,[status(thm)],[303])).
% 3.85/2.71 tff(305,plain,
% 3.85/2.71 (^[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)))))))),
% 3.85/2.71 inference(bind,[status(th)],[])).
% 3.85/2.71 tff(306,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(quant_intro,[status(thm)],[305])).
% 3.85/2.71 tff(307,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(transitivity,[status(thm)],[306, 304])).
% 3.85/2.71 tff(308,plain,
% 3.85/2.71 (^[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))))))))),
% 3.85/2.71 inference(bind,[status(th)],[])).
% 3.85/2.71 tff(309,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(quant_intro,[status(thm)],[308])).
% 3.85/2.71 tff(310,plain,
% 3.85/2.71 (![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)))))))),
% 3.85/2.71 inference(rewrite,[status(thm)],[])).
% 3.85/2.71 tff(311,plain,
% 3.85/2.71 (^[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)))))))))),
% 3.85/2.71 inference(bind,[status(th)],[])).
% 3.85/2.71 tff(312,plain,
% 3.85/2.71 (![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)))))))),
% 3.85/2.71 inference(quant_intro,[status(thm)],[311])).
% 3.85/2.71 tff(313,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')).
% 3.85/2.71 tff(314,plain,
% 3.85/2.71 (![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)))))))),
% 3.85/2.71 inference(modus_ponens,[status(thm)],[313, 312])).
% 3.85/2.71 tff(315,plain,
% 3.85/2.71 (![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)))))))),
% 3.85/2.71 inference(modus_ponens,[status(thm)],[314, 310])).
% 3.85/2.71 tff(316,plain,(
% 3.85/2.71 ![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)))))))),
% 3.85/2.71 inference(skolemize,[status(sab)],[315])).
% 3.85/2.71 tff(317,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(modus_ponens,[status(thm)],[316, 309])).
% 3.85/2.71 tff(318,plain,
% 3.85/2.71 (![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))))))),
% 3.85/2.71 inference(modus_ponens,[status(thm)],[317, 307])).
% 3.85/2.71 tff(319,plain,
% 3.85/2.71 (![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)))))))),
% 3.85/2.71 inference(modus_ponens,[status(thm)],[318, 302])).
% 3.85/2.71 tff(320,plain,
% 3.85/2.71 (((~![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)) | (~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] : ((~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)) | (~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] : ((~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)))))))),
% 3.85/2.71 inference(rewrite,[status(thm)],[])).
% 3.85/2.71 tff(321,plain,
% 3.85/2.71 (((~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)) | (~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] : ((~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)))))))),
% 3.85/2.71 inference(rewrite,[status(thm)],[])).
% 3.85/2.71 tff(322,plain,
% 3.85/2.71 (((~![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)) | (~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] : ((~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))))))))),
% 3.85/2.71 inference(monotonicity,[status(thm)],[321])).
% 3.85/2.71 tff(323,plain,
% 3.85/2.71 (((~![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)) | (~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] : ((~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)))))))),
% 3.85/2.71 inference(transitivity,[status(thm)],[322, 320])).
% 3.85/2.71 tff(324,plain,
% 3.85/2.71 ((~![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)))))))),
% 3.85/2.72 inference(quant_inst,[status(thm)],[])).
% 3.85/2.72 tff(325,plain,
% 3.85/2.72 ((~![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)) | (~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] : ((~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))))))),
% 3.85/2.72 inference(modus_ponens,[status(thm)],[324, 323])).
% 3.85/2.72 tff(326,plain,
% 3.85/2.72 (![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)) | (~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] : ((~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))))))),
% 3.85/2.72 inference(unit_resolution,[status(thm)],[325, 104, 103, 102, 101, 100, 52, 319])).
% 3.85/2.72 tff(327,plain,
% 3.85/2.72 (((~![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)) | (~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] : ((~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)) | (~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] : ((~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)))))),
% 3.85/2.72 inference(rewrite,[status(thm)],[])).
% 3.85/2.72 tff(328,plain,
% 3.85/2.72 (((~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)) | (~v18_waybel_0(C, B!1, A!0)) | (~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))) | ![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)))))),
% 3.85/2.72 inference(rewrite,[status(thm)],[])).
% 3.85/2.72 tff(329,plain,
% 3.85/2.72 (((~![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)) | (~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] : ((~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)) | (~v18_waybel_0(C, B!1, A!0)) | (~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))) | ![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)) | (~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] : ((~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))))))),
% 3.85/2.72 inference(monotonicity,[status(thm)],[328])).
% 3.85/2.72 tff(330,plain,
% 3.85/2.72 (((~![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)) | (~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] : ((~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)) | (~v18_waybel_0(C, B!1, A!0)) | (~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))) | ![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)) | (~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] : ((~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)))))),
% 3.85/2.72 inference(transitivity,[status(thm)],[329, 327])).
% 3.85/2.72 tff(331,plain,
% 3.85/2.72 ((~![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)) | (~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] : ((~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)) | (~v18_waybel_0(C, B!1, A!0)) | (~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))) | ![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))))))),
% 3.85/2.72 inference(quant_inst,[status(thm)],[])).
% 3.85/2.72 tff(332,plain,
% 3.85/2.72 ((~![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)) | (~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] : ((~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))))),
% 3.85/2.72 inference(modus_ponens,[status(thm)],[331, 330])).
% 3.85/2.72 tff(333,plain,
% 3.85/2.72 (![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))))),
% 3.85/2.72 inference(unit_resolution,[status(thm)],[332, 99, 98, 97, 96, 95, 47, 326])).
% 3.85/2.72 tff(334,plain,
% 3.85/2.72 (v18_waybel_0(C!2, B!1, A!0)),
% 3.85/2.72 inference(and_elim,[status(thm)],[32])).
% 3.85/2.72 tff(335,plain,
% 3.85/2.72 (v3_lattice3(B!1)),
% 3.85/2.72 inference(and_elim,[status(thm)],[32])).
% 3.85/2.72 tff(336,plain,
% 3.85/2.72 (v3_lattice3(A!0)),
% 3.85/2.72 inference(and_elim,[status(thm)],[32])).
% 3.85/2.72 tff(337,plain,
% 3.85/2.72 (((~![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))))),
% 3.85/2.72 inference(rewrite,[status(thm)],[])).
% 3.85/2.72 tff(338,plain,
% 3.85/2.72 (((~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))))),
% 3.85/2.72 inference(rewrite,[status(thm)],[])).
% 3.85/2.72 tff(339,plain,
% 3.85/2.72 (((~![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)))))),
% 3.85/2.72 inference(monotonicity,[status(thm)],[338])).
% 3.85/2.72 tff(340,plain,
% 3.85/2.72 (((~![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))))),
% 3.85/2.72 inference(transitivity,[status(thm)],[339, 337])).
% 3.85/2.72 tff(341,plain,
% 3.85/2.72 ((~![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))))),
% 3.85/2.72 inference(quant_inst,[status(thm)],[])).
% 3.85/2.72 tff(342,plain,
% 3.85/2.72 ((~![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)))),
% 3.85/2.72 inference(modus_ponens,[status(thm)],[341, 340])).
% 3.85/2.72 tff(343,plain,
% 3.85/2.72 (![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)))),
% 3.85/2.72 inference(unit_resolution,[status(thm)],[342, 336, 335, 71, 70, 334, 33, 333])).
% 3.85/2.72 tff(344,plain,
% 3.85/2.72 (((~![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: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B!1))) | ((D = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, D, C!2), A!0, B!1)))) | (~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 3.85/2.72 inference(rewrite,[status(thm)],[])).
% 3.85/2.72 tff(345,plain,
% 3.85/2.72 (((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> ((~v1_funct_1(k2_waybel34(A!0, B!1, C!2))) | (~v1_funct_2(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(k2_waybel34(A!0, B!1, C!2), u1_struct_0(A!0), u1_struct_0(B!1))) | v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1))),
% 3.85/2.73 inference(rewrite,[status(thm)],[])).
% 3.85/2.73 tff(346,plain,
% 3.85/2.73 (($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)),
% 3.85/2.73 inference(rewrite,[status(thm)],[])).
% 3.85/2.73 tff(347,plain,
% 3.85/2.73 ((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> $true),
% 3.85/2.73 inference(rewrite,[status(thm)],[])).
% 3.85/2.73 tff(348,plain,
% 3.85/2.73 (((k2_waybel34(A!0, B!1, C!2) = k2_waybel34(A!0, B!1, C!2)) <=> v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)) <=> ($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))),
% 3.85/2.73 inference(monotonicity,[status(thm)],[347])).
% 3.85/2.73 tff(349,plain,
% 3.85/2.73 (((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)),
% 3.85/2.73 inference(transitivity,[status(thm)],[348, 346])).
% 3.85/2.73 tff(350,plain,
% 3.85/2.73 (((~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))),
% 3.85/2.73 inference(monotonicity,[status(thm)],[349])).
% 3.85/2.73 tff(351,plain,
% 3.85/2.73 (((~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))),
% 3.85/2.73 inference(transitivity,[status(thm)],[350, 345])).
% 3.85/2.73 tff(352,plain,
% 3.85/2.73 (((~![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)))),
% 3.85/2.73 inference(monotonicity,[status(thm)],[351])).
% 3.85/2.73 tff(353,plain,
% 3.85/2.73 (((~![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))),
% 3.85/2.73 inference(transitivity,[status(thm)],[352, 344])).
% 3.85/2.73 tff(354,plain,
% 3.85/2.73 ((~![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)))),
% 3.85/2.73 inference(quant_inst,[status(thm)],[])).
% 3.85/2.73 tff(355,plain,
% 3.85/2.73 ((~![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)),
% 3.85/2.73 inference(modus_ponens,[status(thm)],[354, 353])).
% 3.85/2.73 tff(356,plain,
% 3.85/2.73 (v3_waybel_1(k1_waybel_1(A!0, B!1, k2_waybel34(A!0, B!1, C!2), C!2), A!0, B!1)),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[355, 119, 117, 123, 343])).
% 3.85/2.73 tff(357,plain,
% 3.85/2.73 ((~((~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)))))))),
% 3.85/2.73 inference(tautology,[status(thm)],[])).
% 3.85/2.73 tff(358,plain,
% 3.85/2.73 (~((~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))))))),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[357, 356, 300])).
% 3.85/2.73 tff(359,plain,
% 3.85/2.73 (((~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))))),
% 3.85/2.73 inference(tautology,[status(thm)],[])).
% 3.85/2.73 tff(360,plain,
% 3.85/2.73 (![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))))),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[359, 358])).
% 3.85/2.73 tff(361,plain,
% 3.85/2.73 (((~![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))))),
% 3.85/2.73 inference(rewrite,[status(thm)],[])).
% 3.85/2.73 tff(362,plain,
% 3.85/2.73 ((~![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))))),
% 3.85/2.73 inference(quant_inst,[status(thm)],[])).
% 3.85/2.73 tff(363,plain,
% 3.85/2.73 ((~![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)))),
% 3.85/2.73 inference(modus_ponens,[status(thm)],[362, 361])).
% 3.85/2.73 tff(364,plain,
% 3.85/2.73 (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)))),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[363, 185, 360])).
% 3.85/2.73 tff(365,plain,
% 3.85/2.73 (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)))),
% 3.85/2.73 inference(modus_ponens,[status(thm)],[364, 256])).
% 3.85/2.73 tff(366,plain,
% 3.85/2.73 ((~(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)))) | (~((~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)))))))),
% 3.85/2.73 inference(tautology,[status(thm)],[])).
% 3.85/2.73 tff(367,plain,
% 3.85/2.73 (~((~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))))))),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[366, 365, 254])).
% 3.85/2.73 tff(368,plain,
% 3.85/2.73 (((~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))))),
% 3.85/2.73 inference(tautology,[status(thm)],[])).
% 3.85/2.73 tff(369,plain,
% 3.85/2.73 ($false),
% 3.85/2.73 inference(unit_resolution,[status(thm)],[368, 367, 199])).
% 3.91/2.76 % SZS output end Proof
%------------------------------------------------------------------------------