TSTP Solution File: SWV252-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV252-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 23:03:13 EDT 2023
% Result : Unsatisfiable 50.87s 6.88s
% Output : Proof 51.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV252-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 04:57:45 EDT 2023
% 0.14/0.35 % CPUTime :
% 50.87/6.88 Command-line arguments: --flatten
% 50.87/6.88
% 50.87/6.88 % SZS status Unsatisfiable
% 50.87/6.88
% 51.39/6.92 % SZS output start Proof
% 51.39/6.92 Take the following subset of the input axioms:
% 51.39/6.92 fof(cls_Message_Oparts__analz_0, axiom, ![V_H]: c_Message_Oparts(c_Message_Oanalz(V_H))=c_Message_Oparts(V_H)).
% 51.39/6.92 fof(cls_Message_Oparts__subset__iff_0, axiom, ![V_G, V_H2]: (~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)) | c_lessequals(V_G, c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)))).
% 51.39/6.92 fof(cls_Message_Oparts__subset__iff_1, axiom, ![V_H2, V_G2]: (~c_lessequals(V_G2, c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(V_G2), c_Message_Oparts(V_H2), tc_set(tc_Message_Omsg)))).
% 51.39/6.92 fof(cls_Message_Oparts__synth_0, axiom, ![V_H2]: c_Message_Oparts(c_Message_Osynth(V_H2))=c_union(c_Message_Oparts(V_H2), c_Message_Osynth(V_H2), tc_Message_Omsg)).
% 51.39/6.92 fof(cls_Orderings_Oorder__class_Oaxioms__1_0, axiom, ![T_a, V_x]: (~class_Orderings_Oorder(T_a) | c_lessequals(V_x, V_x, T_a))).
% 51.39/6.92 fof(cls_Set_OUn__subset__iff_0, axiom, ![V_B, V_A, V_C, T_a2]: (~c_lessequals(c_union(V_A, V_B, T_a2), V_C, tc_set(T_a2)) | c_lessequals(V_A, V_C, tc_set(T_a2)))).
% 51.39/6.92 fof(cls_Set_OUn__subset__iff_1, axiom, ![T_a2, V_B2, V_A2, V_C2]: (~c_lessequals(c_union(V_A2, V_B2, T_a2), V_C2, tc_set(T_a2)) | c_lessequals(V_B2, V_C2, tc_set(T_a2)))).
% 51.39/6.92 fof(cls_Set_OUn__subset__iff_2, axiom, ![T_a2, V_B2, V_A2, V_C2]: (~c_lessequals(V_B2, V_C2, tc_set(T_a2)) | (~c_lessequals(V_A2, V_C2, tc_set(T_a2)) | c_lessequals(c_union(V_A2, V_B2, T_a2), V_C2, tc_set(T_a2))))).
% 51.39/6.92 fof(cls_Set_Oinsert__subset_0, axiom, ![T_a2, V_B2, V_A2, V_x2]: (~c_lessequals(c_insert(V_x2, V_A2, T_a2), V_B2, tc_set(T_a2)) | c_in(V_x2, V_B2, T_a2))).
% 51.39/6.92 fof(cls_Set_Oinsert__subset_1, axiom, ![T_a2, V_B2, V_A2, V_x2]: (~c_lessequals(c_insert(V_x2, V_A2, T_a2), V_B2, tc_set(T_a2)) | c_lessequals(V_A2, V_B2, tc_set(T_a2)))).
% 51.39/6.92 fof(cls_Set_Oinsert__subset_2, axiom, ![T_a2, V_B2, V_A2, V_x2]: (~c_in(V_x2, V_B2, T_a2) | (~c_lessequals(V_A2, V_B2, tc_set(T_a2)) | c_lessequals(c_insert(V_x2, V_A2, T_a2), V_B2, tc_set(T_a2))))).
% 51.39/6.92 fof(cls_Set_Osubset__antisym_0, axiom, ![T_a2, V_B2, V_A2]: (~c_lessequals(V_B2, V_A2, tc_set(T_a2)) | (~c_lessequals(V_A2, V_B2, tc_set(T_a2)) | V_A2=V_B2))).
% 51.39/6.92 fof(cls_conjecture_0, negated_conjecture, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)).
% 51.39/6.92 fof(cls_conjecture_1, negated_conjecture, ~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))).
% 51.39/6.92 fof(clsarity_set_2, axiom, ![T_1]: class_Orderings_Oorder(tc_set(T_1))).
% 51.39/6.92
% 51.39/6.92 Now clausify the problem and encode Horn clauses using encoding 3 of
% 51.39/6.92 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 51.39/6.92 We repeatedly replace C & s=t => u=v by the two clauses:
% 51.39/6.92 fresh(y, y, x1...xn) = u
% 51.39/6.92 C => fresh(s, t, x1...xn) = v
% 51.39/6.92 where fresh is a fresh function symbol and x1..xn are the free
% 51.39/6.92 variables of u and v.
% 51.39/6.92 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 51.39/6.92 input problem has no model of domain size 1).
% 51.39/6.92
% 51.39/6.92 The encoding turns the above axioms into the following unit equations and goals:
% 51.39/6.92
% 51.39/6.92 Axiom 1 (clsarity_set_2): class_Orderings_Oorder(tc_set(X)) = true.
% 51.39/6.92 Axiom 2 (cls_Message_Oparts__analz_0): c_Message_Oparts(c_Message_Oanalz(X)) = c_Message_Oparts(X).
% 51.39/6.92 Axiom 3 (cls_Set_Osubset__antisym_0): fresh(X, X, Y, Z) = Y.
% 51.39/6.92 Axiom 4 (cls_Message_Oparts__subset__iff_0): fresh14(X, X, Y, Z) = true.
% 51.39/6.92 Axiom 5 (cls_Message_Oparts__subset__iff_1): fresh12(X, X, Y, Z) = true.
% 51.39/6.92 Axiom 6 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh11(X, X, Y, Z) = true.
% 51.39/6.92 Axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh11(class_Orderings_Oorder(X), true, X, Y) = c_lessequals(Y, Y, X).
% 51.39/6.92 Axiom 8 (cls_Set_OUn__subset__iff_0): fresh10(X, X, Y, Z, W) = true.
% 51.39/6.92 Axiom 9 (cls_Set_OUn__subset__iff_1): fresh9(X, X, Y, Z, W) = true.
% 51.39/6.92 Axiom 10 (cls_Set_Oinsert__subset_0): fresh6(X, X, Y, Z, W) = true.
% 51.39/6.92 Axiom 11 (cls_Set_Oinsert__subset_1): fresh5(X, X, Y, Z, W) = true.
% 51.39/6.92 Axiom 12 (cls_Set_Osubset__antisym_0): fresh2(X, X, Y, Z, W) = Z.
% 51.39/6.92 Axiom 13 (cls_conjecture_0): c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg) = true.
% 51.39/6.92 Axiom 14 (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).
% 51.39/6.92 Axiom 15 (cls_Set_OUn__subset__iff_2): fresh7(X, X, Y, Z, W, V) = true.
% 51.39/6.92 Axiom 16 (cls_Set_Oinsert__subset_2): fresh3(X, X, Y, Z, W, V) = true.
% 51.39/6.92 Axiom 17 (cls_Set_Oinsert__subset_2): fresh4(X, X, Y, Z, W, V) = c_lessequals(c_insert(Y, V, W), Z, tc_set(W)).
% 51.39/6.92 Axiom 18 (cls_Set_OUn__subset__iff_2): fresh8(X, X, Y, Z, W, V) = c_lessequals(c_union(V, Y, W), Z, tc_set(W)).
% 51.39/6.92 Axiom 19 (cls_Message_Oparts__subset__iff_1): fresh12(c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)).
% 51.39/6.92 Axiom 20 (cls_Set_Osubset__antisym_0): fresh2(c_lessequals(X, Y, tc_set(Z)), true, Y, X, Z) = fresh(c_lessequals(Y, X, tc_set(Z)), true, Y, X).
% 51.39/6.92 Axiom 21 (cls_Message_Oparts__subset__iff_0): fresh14(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)).
% 51.39/6.92 Axiom 22 (cls_Set_OUn__subset__iff_2): fresh8(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X) = fresh7(c_lessequals(W, Y, tc_set(Z)), true, W, Y, Z, X).
% 51.39/6.92 Axiom 23 (cls_Set_Oinsert__subset_2): fresh4(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X) = fresh3(c_in(W, Y, Z), true, W, Y, Z, X).
% 51.39/6.92 Axiom 24 (cls_Set_OUn__subset__iff_0): fresh10(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, X, Z, W) = c_lessequals(X, W, tc_set(Z)).
% 51.39/6.92 Axiom 25 (cls_Set_OUn__subset__iff_1): fresh9(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, Y, Z, W) = c_lessequals(Y, W, tc_set(Z)).
% 51.39/6.92 Axiom 26 (cls_Set_Oinsert__subset_0): fresh6(c_lessequals(c_insert(X, Y, Z), W, tc_set(Z)), true, X, Z, W) = c_in(X, W, Z).
% 51.39/6.92 Axiom 27 (cls_Set_Oinsert__subset_1): fresh5(c_lessequals(c_insert(X, Y, Z), W, tc_set(Z)), true, Y, Z, W) = c_lessequals(Y, W, tc_set(Z)).
% 51.39/6.92
% 51.39/6.92 Lemma 28: fresh14(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, Y) = c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg)).
% 51.39/6.92 Proof:
% 51.39/6.92 fresh14(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, Y)
% 51.39/6.92 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.92 fresh14(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(Y), tc_set(tc_Message_Omsg)), true, X, Y)
% 51.39/6.92 = { by axiom 21 (cls_Message_Oparts__subset__iff_0) }
% 51.39/6.92 c_lessequals(X, c_Message_Oparts(Y), tc_set(tc_Message_Omsg))
% 51.39/6.92
% 51.39/6.92 Lemma 29: c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg) = class_Orderings_Oorder(tc_set(X)).
% 51.39/6.92 Proof:
% 51.39/6.92 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.92 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.92 true
% 51.39/6.92 = { by axiom 1 (clsarity_set_2) R->L }
% 51.39/6.92 class_Orderings_Oorder(tc_set(X))
% 51.39/6.92
% 51.39/6.92 Lemma 30: c_lessequals(X, c_Message_Oparts(X), tc_set(tc_Message_Omsg)) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.92 Proof:
% 51.39/6.92 c_lessequals(X, c_Message_Oparts(X), tc_set(tc_Message_Omsg))
% 51.39/6.92 = { by lemma 28 R->L }
% 51.39/6.92 fresh14(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(X), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.92 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 51.39/6.92 fresh14(fresh11(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, tc_set(tc_Message_Omsg), c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.92 = { by lemma 29 R->L }
% 51.39/6.92 fresh14(fresh11(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), true, tc_set(tc_Message_Omsg), c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.92 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.92 fresh14(fresh11(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg), c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.92 = { by axiom 6 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 51.39/6.93 fresh14(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh14(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, X)
% 51.39/6.93 = { by axiom 4 (cls_Message_Oparts__subset__iff_0) }
% 51.39/6.93 true
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 31: 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))).
% 51.39/6.93 Proof:
% 51.39/6.93 c_union(c_Message_Oparts(X), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg)
% 51.39/6.93 = { by axiom 2 (cls_Message_Oparts__analz_0) R->L }
% 51.39/6.93 c_union(c_Message_Oparts(c_Message_Oanalz(X)), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg)
% 51.39/6.93 = { by axiom 14 (cls_Message_Oparts__synth_0) R->L }
% 51.39/6.93 c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X)))
% 51.39/6.93
% 51.39/6.93 Lemma 32: fresh7(X, X, Y, Z, W, V) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh7(X, X, Y, Z, W, V)
% 51.39/6.93 = { by axiom 15 (cls_Set_OUn__subset__iff_2) }
% 51.39/6.93 true
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 33: fresh8(X, X, Y, c_union(Z, Y, W), W, Z) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh8(X, X, Y, c_union(Z, Y, W), W, Z)
% 51.39/6.93 = { by axiom 18 (cls_Set_OUn__subset__iff_2) }
% 51.39/6.93 c_lessequals(c_union(Z, Y, W), c_union(Z, Y, W), tc_set(W))
% 51.39/6.93 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 51.39/6.93 fresh11(class_Orderings_Oorder(tc_set(W)), true, tc_set(W), c_union(Z, Y, W))
% 51.39/6.93 = { by axiom 1 (clsarity_set_2) }
% 51.39/6.93 fresh11(true, true, tc_set(W), c_union(Z, Y, W))
% 51.39/6.93 = { by axiom 6 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 51.39/6.93 true
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 34: c_lessequals(X, c_union(X, Y, Z), tc_set(Z)) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.93 Proof:
% 51.39/6.93 c_lessequals(X, c_union(X, Y, Z), tc_set(Z))
% 51.39/6.93 = { by axiom 24 (cls_Set_OUn__subset__iff_0) R->L }
% 51.39/6.93 fresh10(c_lessequals(c_union(X, Y, Z), c_union(X, Y, Z), tc_set(Z)), true, X, Z, c_union(X, Y, Z))
% 51.39/6.93 = { by axiom 18 (cls_Set_OUn__subset__iff_2) R->L }
% 51.39/6.93 fresh10(fresh8(W, W, Y, c_union(X, Y, Z), Z, X), true, X, Z, c_union(X, Y, Z))
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh10(fresh8(W, W, Y, c_union(X, Y, Z), Z, X), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, Z, c_union(X, Y, Z))
% 51.39/6.93 = { by lemma 33 }
% 51.39/6.93 fresh10(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), X, Z, c_union(X, Y, Z))
% 51.39/6.93 = { by axiom 8 (cls_Set_OUn__subset__iff_0) }
% 51.39/6.93 true
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 35: c_lessequals(c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_set(tc_Message_Omsg)) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.93 Proof:
% 51.39/6.93 c_lessequals(c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_set(tc_Message_Omsg))
% 51.39/6.93 = { by lemma 31 R->L }
% 51.39/6.93 c_lessequals(c_Message_Oparts(X), c_union(c_Message_Oparts(X), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 51.39/6.93 = { by lemma 34 }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 36: fresh7(c_lessequals(W, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X) = fresh8(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh7(c_lessequals(W, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.93 fresh7(c_lessequals(W, Y, tc_set(Z)), true, W, Y, Z, X)
% 51.39/6.93 = { by axiom 22 (cls_Set_OUn__subset__iff_2) R->L }
% 51.39/6.93 fresh8(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh8(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X)
% 51.39/6.93
% 51.39/6.93 Lemma 37: fresh2(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), Y, X, Z) = fresh(c_lessequals(Y, X, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), Y, X).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh2(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), Y, X, Z)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.93 fresh2(c_lessequals(X, Y, tc_set(Z)), true, Y, X, Z)
% 51.39/6.93 = { by axiom 20 (cls_Set_Osubset__antisym_0) }
% 51.39/6.93 fresh(c_lessequals(Y, X, tc_set(Z)), true, Y, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh(c_lessequals(Y, X, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), Y, X)
% 51.39/6.93
% 51.39/6.93 Lemma 38: c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))).
% 51.39/6.93 Proof:
% 51.39/6.93 c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg)
% 51.39/6.93 = { by axiom 12 (cls_Set_Osubset__antisym_0) R->L }
% 51.39/6.93 fresh2(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by lemma 32 R->L }
% 51.39/6.93 fresh2(fresh7(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by lemma 35 R->L }
% 51.39/6.93 fresh2(fresh7(c_lessequals(c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by lemma 36 }
% 51.39/6.93 fresh2(fresh8(c_lessequals(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by lemma 30 }
% 51.39/6.93 fresh2(fresh8(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by axiom 18 (cls_Set_OUn__subset__iff_2) }
% 51.39/6.93 fresh2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg)
% 51.39/6.93 = { by lemma 37 }
% 51.39/6.93 fresh(c_lessequals(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by lemma 31 R->L }
% 51.39/6.93 fresh(c_lessequals(c_union(c_Message_Oparts(X), c_Message_Osynth(c_Message_Oanalz(X)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 18 (cls_Set_OUn__subset__iff_2) R->L }
% 51.39/6.93 fresh(fresh8(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.93 fresh(fresh8(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 9 (cls_Set_OUn__subset__iff_1) R->L }
% 51.39/6.93 fresh(fresh8(fresh9(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), tc_Message_Omsg, c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by lemma 33 R->L }
% 51.39/6.93 fresh(fresh8(fresh9(fresh8(Y, Y, c_Message_Oparts(X), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(X), tc_Message_Omsg, c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.93 fresh(fresh8(fresh9(fresh8(Y, Y, c_Message_Oparts(X), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(X))), true, c_Message_Oparts(X), tc_Message_Omsg, c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 18 (cls_Set_OUn__subset__iff_2) }
% 51.39/6.93 fresh(fresh8(fresh9(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_Message_Oparts(X), tc_Message_Omsg, c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 25 (cls_Set_OUn__subset__iff_1) }
% 51.39/6.93 fresh(fresh8(c_lessequals(c_Message_Oparts(X), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by lemma 36 R->L }
% 51.39/6.93 fresh(fresh7(c_lessequals(c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by lemma 34 }
% 51.39/6.93 fresh(fresh7(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(X)), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg), tc_Message_Omsg, c_Message_Oparts(X)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by lemma 32 }
% 51.39/6.93 fresh(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X))), c_union(c_Message_Osynth(c_Message_Oanalz(X)), c_Message_Oparts(X), tc_Message_Omsg))
% 51.39/6.93 = { by axiom 3 (cls_Set_Osubset__antisym_0) }
% 51.39/6.93 c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(X)))
% 51.39/6.93
% 51.39/6.93 Lemma 39: fresh3(X, X, Y, Z, W, V) = c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh3(X, X, Y, Z, W, V)
% 51.39/6.93 = { by axiom 16 (cls_Set_Oinsert__subset_2) }
% 51.39/6.93 true
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)
% 51.39/6.93
% 51.39/6.93 Lemma 40: fresh4(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X) = fresh3(c_in(W, Y, Z), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X).
% 51.39/6.93 Proof:
% 51.39/6.93 fresh4(c_lessequals(X, Y, tc_set(Z)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.93 fresh4(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X)
% 51.39/6.93 = { by axiom 23 (cls_Set_Oinsert__subset_2) }
% 51.39/6.93 fresh3(c_in(W, Y, Z), true, W, Y, Z, X)
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh3(c_in(W, Y, Z), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), W, Y, Z, X)
% 51.39/6.93
% 51.39/6.93 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.
% 51.39/6.93 Proof:
% 51.39/6.93 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))
% 51.39/6.93 = { by lemma 38 }
% 51.39/6.93 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))
% 51.39/6.93 = { by axiom 19 (cls_Message_Oparts__subset__iff_1) R->L }
% 51.39/6.93 fresh12(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_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.93 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.93 fresh12(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.93 = { by lemma 38 R->L }
% 51.39/6.93 fresh12(c_lessequals(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.93 = { by axiom 17 (cls_Set_Oinsert__subset_2) R->L }
% 51.39/6.93 fresh12(fresh4(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh4(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 4 (cls_Message_Oparts__subset__iff_0) R->L }
% 51.39/6.94 fresh12(fresh4(fresh14(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_H, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 35 R->L }
% 51.39/6.94 fresh12(fresh4(fresh14(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_H, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 28 }
% 51.39/6.94 fresh12(fresh4(c_lessequals(v_H, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 38 R->L }
% 51.39/6.94 fresh12(fresh4(c_lessequals(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 40 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 38 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v_H))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 12 (cls_Set_Osubset__antisym_0) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(true, c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 11 (cls_Set_Oinsert__subset_1) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 6 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(fresh11(true, true, tc_set(tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 1 (clsarity_set_2) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(fresh11(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, tc_set(tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 17 (cls_Set_Oinsert__subset_2) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(fresh4(X, X, v_X, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(fresh4(X, X, v_X, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), true, 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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 17 (cls_Set_Oinsert__subset_2) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(fresh5(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_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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 27 (cls_Set_Oinsert__subset_1) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh2(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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 37 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(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)), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 17 (cls_Set_Oinsert__subset_2) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 6 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(fresh11(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), tc_set(tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 13 (cls_conjecture_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(fresh11(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), true, tc_set(tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 29 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(fresh11(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, tc_set(tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh4(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Osynth(c_Message_Oanalz(v_H)), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 40 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(fresh3(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by lemma 39 }
% 51.39/6.94 fresh12(fresh3(c_in(v_X, c_Message_Oparts(fresh(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(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), c_Message_Osynth(c_Message_Oanalz(v_H)))), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 3 (cls_Set_Osubset__antisym_0) }
% 51.39/6.94 fresh12(fresh3(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), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 26 (cls_Set_Oinsert__subset_0) R->L }
% 51.39/6.94 fresh12(fresh3(fresh6(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, v_X, tc_Message_Omsg, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.94 = { by axiom 17 (cls_Set_Oinsert__subset_2) R->L }
% 51.39/6.95 fresh12(fresh3(fresh6(fresh4(Y, Y, v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), true, v_X, tc_Message_Omsg, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.95 fresh12(fresh3(fresh6(fresh4(Y, Y, v_X, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_H))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, tc_Message_Omsg, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by axiom 17 (cls_Set_Oinsert__subset_2) }
% 51.39/6.95 fresh12(fresh3(fresh6(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, tc_Message_Omsg, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by lemma 30 }
% 51.39/6.95 fresh12(fresh3(fresh6(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, tc_Message_Omsg, c_Message_Oparts(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg))), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by axiom 10 (cls_Set_Oinsert__subset_0) }
% 51.39/6.95 fresh12(fresh3(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by axiom 13 (cls_conjecture_0) R->L }
% 51.39/6.95 fresh12(fresh3(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_H)), c_Message_Oparts(v_H), tc_Message_Omsg), tc_Message_Omsg, v_H), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by lemma 39 }
% 51.39/6.95 fresh12(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_H)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_H)))
% 51.39/6.95 = { by axiom 5 (cls_Message_Oparts__subset__iff_1) }
% 51.39/6.95 true
% 51.39/6.95 % SZS output end Proof
% 51.39/6.95
% 51.39/6.95 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------