%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWV252-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 87.88s 11.39s
% Output : Proof 88.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV252-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 10:20:26 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.88/11.39 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
% 87.88/11.39
% 87.88/11.39 % SZS status Unsatisfiable
% 87.88/11.39
% 88.68/11.45 % SZS output start Proof
% 88.68/11.45 Axiom 1 (clsarity_set_2): class_Orderings_Oorder(tc_set(X)) = true.
% 88.68/11.45 Axiom 2 (cls_Message_Oparts__analz_0): c_Message_Oparts(c_Message_Oanalz(X)) = c_Message_Oparts(X).
% 88.68/11.45 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 88.68/11.45 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 88.68/11.45 Axiom 5 (cls_Message_Oparts__synth_0): c_Message_Oparts(c_Message_Osynth(X)) = c_union(c_Message_Oparts(X), c_Message_Osynth(X), tc_Message_Omsg).
% 88.68/11.45 Axiom 6 (cls_conjecture_0): c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg) = true.
% 88.68/11.45 Axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0): ifeq(class_Orderings_Oorder(X), true, c_lessequals(Y, Y, X), true) = true.
% 88.68/11.45 Axiom 8 (cls_Message_Oparts__subset__iff_1): ifeq(c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true) = true.
% 88.68/11.45 Axiom 9 (cls_Message_Oparts__subset__iff_0): ifeq(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true) = true.
% 88.68/11.45 Axiom 10 (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.
% 88.68/11.45 Axiom 11 (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.
% 88.68/11.45 Axiom 12 (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.
% 88.68/11.45 Axiom 13 (cls_Set_Oinsert__subset_0): ifeq(c_lessequals(c_insert(X, Y, Z), W, tc_set(Z)), true, c_in(X, W, Z), true) = true.
% 88.68/11.45 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.
% 88.68/11.45 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.
% 88.68/11.45 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.
% 88.68/11.45
% 88.68/11.45 Lemma 17: c_union(c_Message_Oparts(X), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))).
% 88.68/11.45 Proof:
% 88.68/11.45 c_union(c_Message_Oparts(X), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg)
% 88.68/11.45 = { by axiom 2 (cls_Message_Oparts__analz_0) R->L }
% 88.68/11.45 c_union(c_Message_Oparts(c_Message_Oanalz(X)), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg)
% 88.68/11.45 = { by axiom 5 (cls_Message_Oparts__synth_0) R->L }
% 88.68/11.45 c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X)))
% 88.68/11.45
% 88.68/11.45 Goal 1 (cls_conjecture_1): c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)) = true.
% 88.68/11.45 Proof:
% 88.68/11.45 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 88.68/11.45 = { by axiom 14 (cls_Set_Osubset__antisym_0) R->L }
% 88.68/11.45 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.45 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.45 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.45 = { by axiom 11 (cls_Set_OUn__subset__iff_1) R->L }
% 88.68/11.45 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.45 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.45 c_lessequals(c_Message_Oparts(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_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.46 c_lessequals(c_Message_Oparts(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_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by lemma 17 R->L }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(true, true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 10 (cls_Set_OUn__subset__iff_0) R->L }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.46 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), 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_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.46 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), 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_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 15 (cls_Set_OUn__subset__iff_2) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(true, true, ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 4 (ifeq_axiom) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 10 (cls_Set_OUn__subset__iff_0) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(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_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by lemma 17 }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(true, true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 9 (cls_Message_Oparts__subset__iff_0) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(ifeq(true, true, c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.47 c_lessequals(c_Message_Oparts(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_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.47 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.47 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.48 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.48 = { by axiom 15 (cls_Set_OUn__subset__iff_2) }
% 88.68/11.48 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), ifeq2(true, true, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 88.68/11.48 = { by axiom 4 (ifeq_axiom) }
% 88.68/11.48 c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg))
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.48 ifeq(true, true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 16 (cls_Set_Oinsert__subset_2) R->L }
% 88.68/11.48 ifeq(ifeq(c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.48 ifeq(ifeq(ifeq(true, true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 10 (cls_Set_OUn__subset__iff_0) R->L }
% 88.68/11.48 ifeq(ifeq(ifeq(ifeq(c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.48 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.48 ifeq(ifeq(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.48 ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.48 ifeq(ifeq(ifeq(c_lessequals(c_Message_Oparts(v_H), c_union(c_Message_Oparts(v_H), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by lemma 17 }
% 88.68/11.48 ifeq(ifeq(ifeq(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 9 (cls_Message_Oparts__subset__iff_0) }
% 88.68/11.48 ifeq(ifeq(true, true, ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 14 (cls_Set_Osubset__antisym_0) R->L }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 1 (clsarity_set_2) }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true, ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 6 (cls_conjecture_0) R->L }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true, ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), true), true), true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.48 = { by axiom 16 (cls_Set_Oinsert__subset_2) }
% 88.68/11.48 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(true, true, ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 4 (ifeq_axiom) }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(true, true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(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_H)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 1 (clsarity_set_2) }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(ifeq(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true), true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 12 (cls_Set_Oinsert__subset_1) }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(ifeq2(true, true, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 4 (ifeq_axiom) }
% 88.68/11.49 ifeq(ifeq(c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.49 ifeq(ifeq(ifeq(true, true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 9 (cls_Message_Oparts__subset__iff_0) R->L }
% 88.68/11.49 ifeq(ifeq(ifeq(ifeq(c_lessequals(c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) R->L }
% 88.68/11.49 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 1 (clsarity_set_2) R->L }
% 88.68/11.49 ifeq(ifeq(ifeq(ifeq(ifeq(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 88.68/11.49 ifeq(ifeq(ifeq(ifeq(true, true, c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.49 ifeq(ifeq(ifeq(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true, c_in(v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), true), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 13 (cls_Set_Oinsert__subset_0) }
% 88.68/11.49 ifeq(ifeq(true, true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 3 (ifeq_axiom) }
% 88.68/11.49 ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), true)
% 88.68/11.49 = { by axiom 8 (cls_Message_Oparts__subset__iff_1) }
% 88.68/11.49 true
% 88.68/11.49 % SZS output end Proof
% 88.68/11.49
% 88.68/11.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------