%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWV249-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:06:34 PM UTC 2026
% Result : Unsatisfiable 68.54s 9.05s
% Output : Proof 70.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV249-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n017.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Mon Sep 28 10:13:20 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.54/9.05 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 68.54/9.05
% 68.54/9.05 % SZS status Unsatisfiable
% 68.54/9.05
% 70.42/9.17 % SZS output start Proof
% 70.42/9.17 Axiom 1 (clsarity_set_2): class_Orderings_Oorder(tc_set(X)) = true.
% 70.42/9.17 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 70.42/9.17 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 70.42/9.17 Axiom 4 (cls_Message_Oanalz__analz__Un_0): c_Message_Oanalz(c_union(c_Message_Oanalz(X), Y, tc_Message_Omsg)) = c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)).
% 70.42/9.17 Axiom 5 (cls_conjecture_0): c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = true.
% 70.42/9.18 Axiom 6 (cls_Set_OUn__insert__right_0): c_union(X, c_insert(Y, Z, W), W) = c_insert(Y, c_union(X, Z, W), W).
% 70.42/9.18 Axiom 7 (cls_Set_OUn__insert__left_0): c_union(c_insert(X, Y, Z), W, Z) = c_insert(X, c_union(Y, W, Z), Z).
% 70.42/9.18 Axiom 8 (cls_Message_Oanalz__synth__Un_0): c_Message_Oanalz(c_union(c_Message_Osynth(X), Y, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Osynth(X), tc_Message_Omsg).
% 70.42/9.18 Axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0): ifeq(class_Orderings_Oorder(X), true, c_lessequals(Y, Y, X), true) = true.
% 70.42/9.18 Axiom 10 (cls_Message_Oanalz__mono_0): ifeq(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg)), true) = true.
% 70.42/9.18 Axiom 11 (cls_Set_OUn__subset__iff_0): ifeq(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, c_lessequals(X, W, tc_set(Z)), true) = true.
% 70.42/9.18 Axiom 12 (cls_Set_OUn__subset__iff_1): ifeq(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, c_lessequals(Y, W, tc_set(Z)), true) = true.
% 70.42/9.18 Axiom 13 (cls_Set_Oinsert__subset_1): ifeq(c_lessequals(c_insert(X, Y, Z), W, tc_set(Z)), true, c_lessequals(Y, W, tc_set(Z)), true) = true.
% 70.42/9.18 Axiom 14 (cls_Set_Osubset__antisym_0): ifeq2(c_lessequals(X, Y, tc_set(Z)), true, ifeq2(c_lessequals(Y, X, tc_set(Z)), true, X, Y), Y) = Y.
% 70.42/9.18 Axiom 15 (cls_Set_OUn__subset__iff_2): ifeq(c_lessequals(X, Y, tc_set(Z)), true, ifeq(c_lessequals(W, Y, tc_set(Z)), true, c_lessequals(c_union(X, W, Z), Y, tc_set(Z)), true), true) = true.
% 70.42/9.18 Axiom 16 (cls_Set_Oinsert__subset_2): ifeq(c_lessequals(X, Y, tc_set(Z)), true, ifeq(c_in(W, Y, Z), true, c_lessequals(c_insert(W, X, Z), Y, tc_set(Z)), true), true) = true.
% 70.42/9.18
% 70.42/9.18 Lemma 17: c_union(X, X, Y) = X.
% 70.42/9.18 Proof:
% 70.42/9.18 c_union(X, X, Y)
% 70.42/9.18 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.18 ifeq2(true, true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 11 (cls_Set_OUn__subset__iff_0) R->L }
% 70.42/9.18 ifeq2(ifeq(c_lessequals(c_union(X, X, Y), c_union(X, X, Y), tc_set(Y)), true, c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true), true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.18 ifeq2(ifeq(ifeq(true, true, c_lessequals(c_union(X, X, Y), c_union(X, X, Y), tc_set(Y)), true), true, c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true), true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.18 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(Y)), true, c_lessequals(c_union(X, X, Y), c_union(X, X, Y), tc_set(Y)), true), true, c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true), true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.18 ifeq2(ifeq(true, true, c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true), true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.18 ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X)
% 70.42/9.18 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.18 ifeq2(true, true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.18 = { by axiom 15 (cls_Set_OUn__subset__iff_2) R->L }
% 70.42/9.18 ifeq2(ifeq(c_lessequals(X, X, tc_set(Y)), true, ifeq(c_lessequals(X, X, tc_set(Y)), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.18 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.18 ifeq2(ifeq(ifeq(true, true, c_lessequals(X, X, tc_set(Y)), true), true, ifeq(c_lessequals(X, X, tc_set(Y)), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.18 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.18 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(Y)), true, c_lessequals(X, X, tc_set(Y)), true), true, ifeq(c_lessequals(X, X, tc_set(Y)), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.18 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.18 ifeq2(ifeq(true, true, ifeq(c_lessequals(X, X, tc_set(Y)), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, X, tc_set(Y)), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(true, true, c_lessequals(X, X, tc_set(Y)), true), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(Y)), true, c_lessequals(X, X, tc_set(Y)), true), true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.19 ifeq2(ifeq(true, true, c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(c_lessequals(c_union(X, X, Y), X, tc_set(Y)), true, ifeq2(c_lessequals(X, c_union(X, X, Y), tc_set(Y)), true, c_union(X, X, Y), X), X)
% 70.42/9.19 = { by axiom 14 (cls_Set_Osubset__antisym_0) }
% 70.42/9.19 X
% 70.42/9.19
% 70.42/9.19 Lemma 18: c_union(X, c_union(Y, X, Z), Z) = c_union(Y, X, Z).
% 70.42/9.19 Proof:
% 70.42/9.19 c_union(X, c_union(Y, X, Z), Z)
% 70.42/9.19 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(true, true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 12 (cls_Set_OUn__subset__iff_1) R->L }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(true, true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(Z)), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.19 ifeq2(ifeq(true, true, c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(true, true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 15 (cls_Set_OUn__subset__iff_2) R->L }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true, ifeq(c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true, ifeq(ifeq(true, true, c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true, ifeq(ifeq(class_Orderings_Oorder(tc_set(Z)), true, c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true, ifeq(true, true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(true, true, c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(Z)), true, c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 1 (clsarity_set_2) }
% 70.42/9.19 ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(ifeq(ifeq(c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true, c_lessequals(X, c_union(Y, X, Z), tc_set(Z)), true), true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 12 (cls_Set_OUn__subset__iff_1) }
% 70.42/9.19 ifeq2(ifeq(true, true, c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.19 ifeq2(c_lessequals(c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z), tc_set(Z)), true, ifeq2(c_lessequals(c_union(Y, X, Z), c_union(X, c_union(Y, X, Z), Z), tc_set(Z)), true, c_union(X, c_union(Y, X, Z), Z), c_union(Y, X, Z)), c_union(Y, X, Z))
% 70.42/9.19 = { by axiom 14 (cls_Set_Osubset__antisym_0) }
% 70.42/9.19 c_union(Y, X, Z)
% 70.42/9.19
% 70.42/9.19 Lemma 19: c_union(c_insert(X, Y, Z), W, Z) = c_union(Y, c_insert(X, W, Z), Z).
% 70.42/9.19 Proof:
% 70.42/9.19 c_union(c_insert(X, Y, Z), W, Z)
% 70.42/9.19 = { by axiom 7 (cls_Set_OUn__insert__left_0) }
% 70.42/9.19 c_insert(X, c_union(Y, W, Z), Z)
% 70.42/9.19 = { by axiom 6 (cls_Set_OUn__insert__right_0) R->L }
% 70.42/9.19 c_union(Y, c_insert(X, W, Z), Z)
% 70.42/9.19
% 70.42/9.19 Lemma 20: c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg) = c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)).
% 70.42/9.19 Proof:
% 70.42/9.19 c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg)
% 70.42/9.19 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(true, true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.19 = { by axiom 11 (cls_Set_OUn__subset__iff_0) R->L }
% 70.42/9.19 ifeq2(ifeq(c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.19 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.19 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.19 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.19 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.20 ifeq2(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.20 ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 3 (ifeq_axiom) R->L }
% 70.42/9.20 ifeq2(true, true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 15 (cls_Set_OUn__subset__iff_2) R->L }
% 70.42/9.20 ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.20 ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 1 (clsarity_set_2) R->L }
% 70.42/9.20 ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.42/9.20 ifeq2(ifeq(true, true, ifeq(c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 2 (ifeq_axiom) }
% 70.42/9.20 ifeq2(ifeq(c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.20 ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 11 (cls_Set_OUn__subset__iff_0) R->L }
% 70.42/9.20 ifeq2(ifeq(ifeq(ifeq(c_lessequals(c_union(X, Y, tc_Message_Omsg), c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(X, c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 2 (ifeq_axiom) R->L }
% 70.42/9.20 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(X, Y, tc_Message_Omsg), c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(X, c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.42/9.20 = { by axiom 1 (clsarity_set_2) R->L }
% 70.81/9.20 ifeq2(ifeq(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(X, Y, tc_Message_Omsg), c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(X, c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.81/9.20 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.81/9.20 ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(X, c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.81/9.20 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.20 ifeq2(ifeq(ifeq(c_lessequals(X, c_union(X, Y, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.81/9.20 = { by axiom 10 (cls_Message_Oanalz__mono_0) }
% 70.81/9.20 ifeq2(ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.81/9.20 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.20 ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Oanalz(X), tc_Message_Omsg), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))), c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)))
% 70.81/9.20 = { by axiom 14 (cls_Set_Osubset__antisym_0) }
% 70.81/9.21 c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg))
% 70.81/9.21
% 70.81/9.21 Goal 1 (cls_conjecture_1): c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) = true.
% 70.81/9.21 Proof:
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 70.81/9.21 = { by axiom 14 (cls_Set_Osubset__antisym_0) R->L }
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.21 = { by axiom 8 (cls_Message_Oanalz__synth__Un_0) }
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.21 = { by lemma 20 R->L }
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(v_G), tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.21 = { by lemma 18 }
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(v_G), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.21 = { by lemma 20 }
% 70.81/9.21 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 3 (ifeq_axiom) R->L }
% 70.81/9.22 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(true, true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 10 (cls_Message_Oanalz__mono_0) R->L }
% 70.81/9.22 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 4 (cls_Message_Oanalz__analz__Un_0) R->L }
% 70.81/9.22 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.22 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.22 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.22 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 11 (cls_Set_OUn__subset__iff_0) }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by lemma 17 }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 3 (ifeq_axiom) R->L }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(true, true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 10 (cls_Message_Oanalz__mono_0) R->L }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.23 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.23 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(ifeq(c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 11 (cls_Set_OUn__subset__iff_0) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 4 (cls_Message_Oanalz__analz__Un_0) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by lemma 17 }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(ifeq2(c_lessequals(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 14 (cls_Set_Osubset__antisym_0) }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 12 (cls_Set_OUn__subset__iff_1) R->L }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 1 (clsarity_set_2) R->L }
% 70.81/9.24 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.24 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 11 (cls_Set_OUn__subset__iff_0) R->L }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 1 (clsarity_set_2) R->L }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 15 (cls_Set_OUn__subset__iff_2) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(true, true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 3 (ifeq_axiom) }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.25 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.25 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 10 (cls_Message_Oanalz__mono_0) R->L }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 4 (cls_Message_Oanalz__analz__Un_0) R->L }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 11 (cls_Set_OUn__subset__iff_0) }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.26 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.26 = { by lemma 18 }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 12 (cls_Set_OUn__subset__iff_1) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 1 (clsarity_set_2) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(v_G, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 4 (cls_Message_Oanalz__analz__Un_0) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 8 (cls_Message_Oanalz__synth__Un_0) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 15 (cls_Set_OUn__subset__iff_2) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(true, true, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 3 (ifeq_axiom) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by lemma 18 R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 14 (cls_Set_Osubset__antisym_0) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 5 (cls_conjecture_0) R->L }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 16 (cls_Set_Oinsert__subset_2) }
% 70.81/9.27 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(true, true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.27 = { by axiom 3 (ifeq_axiom) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(ifeq(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 13 (cls_Set_Oinsert__subset_1) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(ifeq2(true, true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 3 (ifeq_axiom) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by lemma 19 }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 6 (cls_Set_OUn__insert__right_0) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 4 (cls_Message_Oanalz__analz__Un_0) }
% 70.81/9.28 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.28 ifeq(true, true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 12 (cls_Set_OUn__subset__iff_1) R->L }
% 70.81/9.28 ifeq(ifeq(c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) R->L }
% 70.81/9.28 ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 9 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 70.81/9.28 ifeq(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 1 (clsarity_set_2) }
% 70.81/9.28 ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.28 ifeq(ifeq(ifeq(c_lessequals(c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 11 (cls_Set_OUn__subset__iff_0) }
% 70.81/9.28 ifeq(ifeq(true, true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 2 (ifeq_axiom) }
% 70.81/9.28 ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 6 (cls_Set_OUn__insert__right_0) }
% 70.81/9.28 ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_insert(v_X, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by lemma 19 }
% 70.81/9.28 ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true)
% 70.81/9.28 = { by axiom 10 (cls_Message_Oanalz__mono_0) }
% 70.81/9.28 true
% 70.81/9.28 % SZS output end Proof
% 70.81/9.28
% 70.81/9.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------