TSTP Solution File: SWV249-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV249-2 : 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 : n013.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 23:03:11 EDT 2023
% Result : Unsatisfiable 3.65s 0.86s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV249-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % 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 : n013.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 04:18:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.65/0.86 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.65/0.86
% 3.65/0.86 % SZS status Unsatisfiable
% 3.65/0.86
% 3.65/0.87 % SZS output start Proof
% 3.65/0.87 Take the following subset of the input axioms:
% 3.65/0.87 fof(cls_Message_Oanalz__analz__Un_0, axiom, ![V_G, V_H]: c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg))=c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg))).
% 3.65/0.87 fof(cls_Message_Oanalz__mono_0, axiom, ![V_G2, V_H2]: (~c_lessequals(V_G2, V_H2, tc_set(tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(V_G2), c_Message_Oanalz(V_H2), tc_set(tc_Message_Omsg)))).
% 3.65/0.88 fof(cls_Message_Oanalz__synth__Un_0, axiom, ![V_G2, V_H2]: c_Message_Oanalz(c_union(c_Message_Osynth(V_G2), V_H2, tc_Message_Omsg))=c_union(c_Message_Oanalz(c_union(V_G2, V_H2, tc_Message_Omsg)), c_Message_Osynth(V_G2), tc_Message_Omsg)).
% 3.65/0.88 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))).
% 3.65/0.88 fof(cls_Set_OUn__Diff__cancel2_0, axiom, ![V_B, V_A, T_a2]: c_union(c_minus(V_B, V_A, tc_set(T_a2)), V_A, T_a2)=c_union(V_B, V_A, T_a2)).
% 3.65/0.88 fof(cls_Set_OUn__Diff__cancel_0, axiom, ![T_a2, V_B2, V_A2]: c_union(V_A2, c_minus(V_B2, V_A2, tc_set(T_a2)), T_a2)=c_union(V_A2, V_B2, T_a2)).
% 3.65/0.88 fof(cls_Set_OUn__insert__left_0, axiom, ![V_a, V_C, T_a2, V_B2]: c_union(c_insert(V_a, V_B2, T_a2), V_C, T_a2)=c_insert(V_a, c_union(V_B2, V_C, T_a2), T_a2)).
% 3.65/0.88 fof(cls_Set_OUn__insert__right_0, axiom, ![T_a2, V_B2, V_A2, V_a2]: c_union(V_A2, c_insert(V_a2, V_B2, T_a2), T_a2)=c_insert(V_a2, c_union(V_A2, V_B2, T_a2), T_a2)).
% 3.65/0.88 fof(cls_Set_OUn__subset__iff_0, 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_A2, V_C2, tc_set(T_a2)))).
% 3.65/0.88 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)))).
% 3.65/0.88 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))))).
% 3.65/0.88 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)))).
% 3.65/0.88 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))))).
% 3.65/0.88 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))).
% 3.65/0.88 fof(cls_conjecture_0, negated_conjecture, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)).
% 3.65/0.88 fof(cls_conjecture_1, negated_conjecture, ~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))).
% 3.65/0.88 fof(clsarity_set_2, axiom, ![T_1]: class_Orderings_Oorder(tc_set(T_1))).
% 3.65/0.88
% 3.65/0.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.65/0.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.65/0.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.65/0.88 fresh(y, y, x1...xn) = u
% 3.65/0.88 C => fresh(s, t, x1...xn) = v
% 3.65/0.88 where fresh is a fresh function symbol and x1..xn are the free
% 3.65/0.88 variables of u and v.
% 3.65/0.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.65/0.88 input problem has no model of domain size 1).
% 3.65/0.88
% 3.65/0.88 The encoding turns the above axioms into the following unit equations and goals:
% 3.65/0.88
% 3.65/0.88 Axiom 1 (clsarity_set_2): class_Orderings_Oorder(tc_set(X)) = true.
% 3.65/0.88 Axiom 2 (cls_Set_Osubset__antisym_0): fresh(X, X, Y, Z) = Y.
% 3.65/0.88 Axiom 3 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh11(X, X, Y, Z) = true.
% 3.65/0.88 Axiom 4 (cls_Message_Oanalz__mono_0): fresh10(X, X, Y, Z) = true.
% 3.65/0.88 Axiom 5 (cls_Message_Oanalz__analz__Un_0): c_Message_Oanalz(c_union(c_Message_Oanalz(X), Y, tc_Message_Omsg)) = c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)).
% 3.65/0.88 Axiom 6 (cls_conjecture_0): c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = true.
% 3.65/0.88 Axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0): fresh11(class_Orderings_Oorder(X), true, X, Y) = c_lessequals(Y, Y, X).
% 3.65/0.88 Axiom 8 (cls_Set_OUn__subset__iff_0): fresh9(X, X, Y, Z, W) = true.
% 3.65/0.88 Axiom 9 (cls_Set_OUn__subset__iff_1): fresh8(X, X, Y, Z, W) = true.
% 3.65/0.88 Axiom 10 (cls_Set_Oinsert__subset_1): fresh5(X, X, Y, Z, W) = true.
% 3.65/0.88 Axiom 11 (cls_Set_Osubset__antisym_0): fresh2(X, X, Y, Z, W) = Z.
% 3.65/0.88 Axiom 12 (cls_Set_OUn__insert__left_0): c_union(c_insert(X, Y, Z), W, Z) = c_insert(X, c_union(Y, W, Z), Z).
% 3.65/0.88 Axiom 13 (cls_Set_OUn__insert__right_0): c_union(X, c_insert(Y, Z, W), W) = c_insert(Y, c_union(X, Z, W), W).
% 3.65/0.88 Axiom 14 (cls_Set_OUn__subset__iff_2): fresh6(X, X, Y, Z, W, V) = true.
% 3.65/0.88 Axiom 15 (cls_Set_Oinsert__subset_2): fresh3(X, X, Y, Z, W, V) = true.
% 3.65/0.88 Axiom 16 (cls_Set_OUn__Diff__cancel_0): c_union(X, c_minus(Y, X, tc_set(Z)), Z) = c_union(X, Y, Z).
% 3.65/0.88 Axiom 17 (cls_Set_OUn__Diff__cancel2_0): c_union(c_minus(X, Y, tc_set(Z)), Y, Z) = c_union(X, Y, Z).
% 3.65/0.88 Axiom 18 (cls_Set_OUn__subset__iff_2): fresh7(X, X, Y, Z, W, V) = c_lessequals(c_union(V, Y, W), Z, tc_set(W)).
% 3.65/0.88 Axiom 19 (cls_Set_Oinsert__subset_2): fresh4(X, X, Y, Z, W, V) = c_lessequals(c_insert(Y, V, W), Z, tc_set(W)).
% 3.65/0.88 Axiom 20 (cls_Message_Oanalz__synth__Un_0): c_Message_Oanalz(c_union(c_Message_Osynth(X), Y, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X, Y, tc_Message_Omsg)), c_Message_Osynth(X), tc_Message_Omsg).
% 3.65/0.88 Axiom 21 (cls_Message_Oanalz__mono_0): fresh10(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), true, X, Y) = c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg)).
% 3.65/0.88 Axiom 22 (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).
% 3.65/0.88 Axiom 23 (cls_Set_OUn__subset__iff_2): fresh7(c_lessequals(X, Y, tc_set(Z)), true, W, Y, Z, X) = fresh6(c_lessequals(W, Y, tc_set(Z)), true, W, Y, Z, X).
% 3.65/0.88 Axiom 24 (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).
% 3.65/0.88 Axiom 25 (cls_Set_OUn__subset__iff_0): fresh9(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, X, Z, W) = c_lessequals(X, W, tc_set(Z)).
% 3.65/0.88 Axiom 26 (cls_Set_OUn__subset__iff_1): fresh8(c_lessequals(c_union(X, Y, Z), W, tc_set(Z)), true, Y, Z, W) = c_lessequals(Y, W, tc_set(Z)).
% 3.65/0.88 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)).
% 3.65/0.88
% 3.65/0.88 Lemma 28: fresh7(X, X, Y, c_union(Z, Y, W), W, Z) = true.
% 3.65/0.88 Proof:
% 3.65/0.88 fresh7(X, X, Y, c_union(Z, Y, W), W, Z)
% 3.65/0.88 = { by axiom 18 (cls_Set_OUn__subset__iff_2) }
% 3.65/0.88 c_lessequals(c_union(Z, Y, W), c_union(Z, Y, W), tc_set(W))
% 3.65/0.88 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 3.65/0.88 fresh11(class_Orderings_Oorder(tc_set(W)), true, tc_set(W), c_union(Z, Y, W))
% 3.65/0.88 = { by axiom 1 (clsarity_set_2) }
% 3.65/0.88 fresh11(true, true, tc_set(W), c_union(Z, Y, W))
% 3.65/0.88 = { by axiom 3 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 3.65/0.88 true
% 3.65/0.88
% 3.65/0.88 Lemma 29: c_lessequals(X, c_union(Y, X, Z), tc_set(Z)) = true.
% 3.65/0.88 Proof:
% 3.65/0.88 c_lessequals(X, c_union(Y, X, Z), tc_set(Z))
% 3.65/0.88 = { by axiom 26 (cls_Set_OUn__subset__iff_1) R->L }
% 3.65/0.88 fresh8(c_lessequals(c_union(Y, X, Z), c_union(Y, X, Z), tc_set(Z)), true, X, Z, c_union(Y, X, Z))
% 3.65/0.88 = { by axiom 18 (cls_Set_OUn__subset__iff_2) R->L }
% 3.65/0.88 fresh8(fresh7(W, W, X, c_union(Y, X, Z), Z, Y), true, X, Z, c_union(Y, X, Z))
% 3.65/0.88 = { by lemma 28 }
% 3.65/0.88 fresh8(true, true, X, Z, c_union(Y, X, Z))
% 3.65/0.88 = { by axiom 9 (cls_Set_OUn__subset__iff_1) }
% 3.65/0.88 true
% 3.65/0.88
% 3.65/0.88 Lemma 30: c_lessequals(c_union(X, Y, Z), c_union(Y, X, Z), tc_set(Z)) = true.
% 3.65/0.88 Proof:
% 3.65/0.88 c_lessequals(c_union(X, Y, Z), c_union(Y, X, Z), tc_set(Z))
% 3.65/0.88 = { by axiom 17 (cls_Set_OUn__Diff__cancel2_0) R->L }
% 3.65/0.88 c_lessequals(c_union(c_minus(X, Y, tc_set(Z)), Y, Z), c_union(Y, X, Z), tc_set(Z))
% 3.65/0.88 = { by axiom 18 (cls_Set_OUn__subset__iff_2) R->L }
% 3.65/0.88 fresh7(true, true, Y, c_union(Y, X, Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 16 (cls_Set_OUn__Diff__cancel_0) R->L }
% 3.65/0.88 fresh7(true, true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by lemma 29 R->L }
% 3.65/0.88 fresh7(c_lessequals(c_minus(X, Y, tc_set(Z)), c_union(Y, c_minus(X, Y, tc_set(Z)), Z), tc_set(Z)), true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 23 (cls_Set_OUn__subset__iff_2) }
% 3.65/0.88 fresh6(c_lessequals(Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), tc_set(Z)), true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 25 (cls_Set_OUn__subset__iff_0) R->L }
% 3.65/0.88 fresh6(fresh9(c_lessequals(c_union(Y, c_minus(X, Y, tc_set(Z)), Z), c_union(Y, c_minus(X, Y, tc_set(Z)), Z), tc_set(Z)), true, Y, Z, c_union(Y, c_minus(X, Y, tc_set(Z)), Z)), true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 18 (cls_Set_OUn__subset__iff_2) R->L }
% 3.65/0.88 fresh6(fresh9(fresh7(W, W, c_minus(X, Y, tc_set(Z)), c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, Y), true, Y, Z, c_union(Y, c_minus(X, Y, tc_set(Z)), Z)), true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by lemma 28 }
% 3.65/0.88 fresh6(fresh9(true, true, Y, Z, c_union(Y, c_minus(X, Y, tc_set(Z)), Z)), true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 8 (cls_Set_OUn__subset__iff_0) }
% 3.65/0.88 fresh6(true, true, Y, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), Z, c_minus(X, Y, tc_set(Z)))
% 3.65/0.88 = { by axiom 14 (cls_Set_OUn__subset__iff_2) }
% 3.65/0.88 true
% 3.65/0.88
% 3.65/0.88 Goal 1 (cls_conjecture_1): c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) = true.
% 3.65/0.88 Proof:
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 11 (cls_Set_Osubset__antisym_0) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), fresh2(true, true, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by lemma 30 R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), fresh2(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 22 (cls_Set_Osubset__antisym_0) }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), fresh(c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by lemma 30 }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), fresh(true, true, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 2 (cls_Set_Osubset__antisym_0) }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 5 (cls_Message_Oanalz__analz__Un_0) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 20 (cls_Message_Oanalz__synth__Un_0) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 2 (cls_Set_Osubset__antisym_0) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(true, true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 10 (cls_Set_Oinsert__subset_1) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(fresh5(true, true, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 3 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(fresh5(fresh11(true, true, tc_set(tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 1 (clsarity_set_2) R->L }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(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_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(fresh5(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 27 (cls_Set_Oinsert__subset_1) }
% 3.65/0.88 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.88 = { by axiom 22 (cls_Set_Osubset__antisym_0) R->L }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 19 (cls_Set_Oinsert__subset_2) R->L }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh4(true, true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 3 (cls_Orderings_Oorder__class_Oaxioms__1_0) R->L }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh4(fresh11(true, true, tc_set(tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 1 (clsarity_set_2) R->L }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh4(fresh11(class_Orderings_Oorder(tc_set(tc_Message_Omsg)), true, tc_set(tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G))), true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 7 (cls_Orderings_Oorder__class_Oaxioms__1_0) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh4(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 24 (cls_Set_Oinsert__subset_2) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh3(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 6 (cls_conjecture_0) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(fresh3(true, true, v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg, c_Message_Osynth(c_Message_Oanalz(v_G))), true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 15 (cls_Set_Oinsert__subset_2) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(fresh2(true, true, c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 11 (cls_Set_Osubset__antisym_0) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 12 (cls_Set_OUn__insert__left_0) }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_insert(v_X, c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 13 (cls_Set_OUn__insert__right_0) R->L }
% 3.65/0.89 c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))
% 3.65/0.89 = { by axiom 21 (cls_Message_Oanalz__mono_0) R->L }
% 3.65/0.89 fresh10(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))
% 3.65/0.89 = { by lemma 29 }
% 3.65/0.89 fresh10(true, true, c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))
% 3.65/0.89 = { by axiom 4 (cls_Message_Oanalz__mono_0) }
% 3.65/0.89 true
% 3.65/0.89 % SZS output end Proof
% 3.65/0.89
% 3.65/0.89 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------