%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV275-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:31:57 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV275-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 09:34:33 EDT 2025
% 0.20/0.35 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(c_in_type, type, (
% 0.20/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tc_Message_Omsg_type, type, (
% 0.20/0.39 tc_Message_Omsg: $i)).
% 0.20/0.39 tff(c_insert_type, type, (
% 0.20/0.39 c_insert: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(v_H_type, type, (
% 0.20/0.39 v_H: $i)).
% 0.20/0.39 tff(v_X_type, type, (
% 0.20/0.39 v_X: $i)).
% 0.20/0.39 tff(c_Main_OsubsetI__1_type, type, (
% 0.20/0.39 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(c_lessequals_type, type, (
% 0.20/0.39 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tc_set_type, type, (
% 0.20/0.39 tc_set: $i > $i)).
% 0.20/0.39 tff(c_Message_Osynth_type, type, (
% 0.20/0.39 c_Message_Osynth: $i > $i)).
% 0.20/0.39 tff(1,assumption,(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) <=> c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) <=> c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.39 inference(symmetry,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.39 tff(9,plain,(
% 0.20/0.39 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.39 inference(skolemize,[status(sab)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,axiom,(~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(20,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.39 tff(22,plain,(
% 0.20/0.39 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 23, 16])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Osynth_OInj_0')).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,(
% 0.20/0.39 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(skolemize,[status(sab)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 34, 27])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 13])).
% 0.20/0.40 tff(40,plain,(~(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(44,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.40 tff(46,plain,(
% 0.20/0.40 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.40 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 47, 16])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : refl((c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : rewrite((((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OinsertE_0')).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.40 tff(63,plain,(
% 0.20/0.40 ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[62])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 40])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.40 tff(75,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.40 tff(78,plain,(
% 0.20/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[77])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[82, 79, 27, 69])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(87,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Osynth__mono_0')).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.41 tff(89,plain,(
% 0.20/0.41 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[88])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 83])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 23, 95])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.20/0.41 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 47, 95])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (^[V_b: $i, V_a: $i, T_a: $i, V_B: $i] : refl(((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(110,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OinsertCI_0')).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.41 tff(112,plain,(
% 0.20/0.41 ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.20/0.41 inference(skolemize,[status(sab)],[111])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 113, 106, 99])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------