%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV259-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:31:53 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV259-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:33:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(c_lessequals_type, type, (
% 0.12/0.36 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.12/0.36 tff(tc_set_type, type, (
% 0.12/0.36 tc_set: $i > $i)).
% 0.12/0.36 tff(tc_Message_Omsg_type, type, (
% 0.12/0.36 tc_Message_Omsg: $i)).
% 0.12/0.36 tff(c_Message_Oparts_type, type, (
% 0.12/0.36 c_Message_Oparts: $i > $i)).
% 0.12/0.36 tff(c_insert_type, type, (
% 0.12/0.36 c_insert: ( $i * $i * $i ) > $i)).
% 0.12/0.36 tff(v_H_type, type, (
% 0.12/0.36 v_H: $i)).
% 0.12/0.36 tff(v_X_type, type, (
% 0.12/0.36 v_X: $i)).
% 0.12/0.36 tff(1,assumption,(~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.36 tff(7,plain,(
% 0.12/0.36 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.12/0.36 inference(skolemize,[status(sab)],[6])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.36 tff(11,plain,(c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(15,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts__subset__iff_0')).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.36 tff(17,plain,(
% 0.12/0.36 ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[16])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 ((~c_lessequals(c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[21, 18])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[22, 11])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(27,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts__subset__iff_1')).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.36 tff(29,plain,(
% 0.12/0.36 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[28])).
% 0.12/0.36 tff(30,plain,
% 0.12/0.36 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.36 tff(31,plain,
% 0.12/0.36 ((~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(32,axiom,(~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.12/0.36 tff(33,plain,
% 0.12/0.36 (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.36 tff(34,plain,
% 0.12/0.36 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(35,plain,
% 0.12/0.36 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(36,plain,
% 0.12/0.36 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.36 tff(37,plain,
% 0.12/0.36 (~c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[36, 33, 30])).
% 0.12/0.36 tff(38,plain,
% 0.12/0.36 (^[V_x: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(41,axiom,(![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Oinsert__subset_1')).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,(
% 0.12/0.37 ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[42])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_lessequals(v_H, c_Message_Oparts(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[47, 44, 37, 23])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------