%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV247-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:31:51 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV247-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 09:32:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(c_in_type, type, (
% 0.12/0.37 c_in: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tc_Message_Omsg_type, type, (
% 0.12/0.37 tc_Message_Omsg: $i)).
% 0.12/0.37 tff(c_union_type, type, (
% 0.12/0.37 c_union: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(v_H_type, type, (
% 0.12/0.37 v_H: $i)).
% 0.12/0.37 tff(v_G_type, type, (
% 0.12/0.37 v_G: $i)).
% 0.12/0.37 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.12/0.37 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.12/0.37 tff(v_X_type, type, (
% 0.12/0.37 v_X: $i)).
% 0.12/0.37 tff(v_K_type, type, (
% 0.12/0.37 v_K: $i)).
% 0.12/0.37 tff(c_Message_Oanalz_type, type, (
% 0.12/0.37 c_Message_Oanalz: $i > $i)).
% 0.12/0.37 tff(c_Message_Omsg_OKey_type, type, (
% 0.12/0.37 c_Message_Omsg_OKey: $i > $i)).
% 0.12/0.37 tff(c_Message_OinvKey_type, type, (
% 0.12/0.37 c_Message_OinvKey: $i > $i)).
% 0.12/0.37 tff(c_Message_Osynth_type, type, (
% 0.12/0.37 c_Message_Osynth: $i > $i)).
% 0.12/0.37 tff(1,assumption,(~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(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_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(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_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz_OInj_0')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,(
% 0.12/0.37 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(skolemize,[status(sab)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, 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_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, 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_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.38 tff(21,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnE_0')).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.38 tff(24,plain,(
% 0.12/0.38 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[V_H: $i, V_K: $i] : refl(((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,axiom,(![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OKey__synth_0')).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg))) <=> ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 33])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnCI_1')).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,plain,(
% 0.12/0.38 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(skolemize,[status(sab)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[55, 52, 45, 12])).
% 0.12/0.39 tff(57,plain,(c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)) <=> (~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(59,axiom,(~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 52, 60])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (^[V_H: $i, V_X: $i, V_K: $i] : refl((c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (^[V_H: $i, V_X: $i, V_K: $i] : rewrite((((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.39 tff(70,axiom,(![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz_ODecrypt__dest_0')).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.39 tff(73,plain,(
% 0.12/0.39 ![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | (c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | (c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ((~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 64])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[79, 57])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, 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_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[83, 8, 80])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(86,axiom,(c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[90, 25, 87])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[91, 80])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(96,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnCI_0')).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.40 tff(98,plain,(
% 0.12/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(skolemize,[status(sab)],[97])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[102, 99, 60])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (^[V_H: $i, V_X: $i, V_K: $i] : refl((c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (^[V_H: $i, V_X: $i, V_K: $i] : rewrite((((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.40 tff(109,axiom,(![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OCrypt__synth_1')).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.19/0.40 tff(112,plain,(
% 0.19/0.40 ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 103])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[118, 92])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 52, 119, 84])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------