%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWV251-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.21s 0.33s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV251-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n015.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 10:22:01 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.33 Command-line arguments: --flatten --complete-subsets
% 0.21/0.33
% 0.21/0.33 % SZS status Unsatisfiable
% 0.21/0.33
% 0.21/0.33 % SZS output start Proof
% 0.21/0.33 Axiom 1 (cls_Set_Osubset__refl_0): c_lessequals(X, X, tc_set(Y)) = true.
% 0.21/0.33 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.21/0.33 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.33 Axiom 4 (cls_conjecture_0): c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = true.
% 0.21/0.34 Axiom 5 (cls_Set_OUn__Diff__cancel_0): c_union(X, c_minus(Y, X, tc_set(Z)), Z) = c_union(X, Y, Z).
% 0.21/0.34 Axiom 6 (cls_conjecture_1): c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = true.
% 0.21/0.34 Axiom 7 (cls_Message_Oanalz__mono_0): ifeq(c_lessequals(X, Y, tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(X), c_Message_Oanalz(Y), tc_set(tc_Message_Omsg)), true) = true.
% 0.21/0.34 Axiom 8 (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.
% 0.21/0.34 Axiom 9 (cls_Set_Oinsert__Diff1_0): ifeq2(c_in(X, Y, Z), true, c_minus(c_insert(X, W, Z), Y, tc_set(Z)), c_minus(W, Y, tc_set(Z))) = c_minus(W, Y, tc_set(Z)).
% 0.21/0.34 Axiom 10 (cls_Set_OsubsetD_0): ifeq(c_in(X, Y, Z), true, ifeq(c_lessequals(Y, W, tc_set(Z)), true, c_in(X, W, Z), true), true) = true.
% 0.21/0.34
% 0.21/0.34 Goal 1 (cls_conjecture_2): c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg) = true.
% 0.21/0.34 Proof:
% 0.21/0.34 c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg)
% 0.21/0.34 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.34 ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.34 ifeq(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 7 (cls_Message_Oanalz__mono_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), true), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 4 (cls_conjecture_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 4 (cls_conjecture_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 5 (cls_Set_OUn__Diff__cancel_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_minus(v_H, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 9 (cls_Set_Oinsert__Diff1_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), ifeq2(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), true, c_minus(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), c_minus(v_H, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 4 (cls_conjecture_0) R->L }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), ifeq2(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_minus(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), c_minus(v_H, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 2 (ifeq_axiom) }
% 0.21/0.34 ifeq(ifeq(c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_minus(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 5 (cls_Set_OUn__Diff__cancel_0) }
% 0.21/0.34 ifeq(ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.34 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.34 ifeq(ifeq(ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(ifeq(ifeq(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 1 (cls_Set_Osubset__refl_0) R->L }
% 0.21/0.35 ifeq(ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(ifeq(ifeq(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)), true, c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_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_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 8 (cls_Set_OUn__subset__iff_1) }
% 0.21/0.35 ifeq(ifeq(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) R->L }
% 0.21/0.35 ifeq(ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.35 ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.35 ifeq(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(true, c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 6 (cls_conjecture_1) R->L }
% 0.21/0.35 ifeq(c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), true, ifeq(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)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), true, ifeq(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)), true, c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), true, ifeq(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)), true, c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), true), c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))
% 0.21/0.35 = { by axiom 4 (cls_conjecture_0) }
% 0.21/0.35 ifeq(c_in(v_x, c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), true, ifeq(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)), true, c_in(v_x, c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), v_H, tc_Message_Omsg)), tc_Message_Omsg), true), true)
% 0.21/0.36 = { by axiom 10 (cls_Set_OsubsetD_0) }
% 0.21/0.36 true
% 0.21/0.36 % SZS output end Proof
% 0.21/0.36
% 0.21/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------