TSTP Solution File: SWV247-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV247-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:10:34 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV247-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Sun Sep 4 01:52:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(c_in_type, type, (
% 0.21/0.40 c_in: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tc_Message_Omsg_type, type, (
% 0.21/0.40 tc_Message_Omsg: $i)).
% 0.21/0.40 tff(v_G_type, type, (
% 0.21/0.40 v_G: $i)).
% 0.21/0.40 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.21/0.40 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.21/0.40 tff(v_X_type, type, (
% 0.21/0.40 v_X: $i)).
% 0.21/0.40 tff(v_K_type, type, (
% 0.21/0.40 v_K: $i)).
% 0.21/0.40 tff(c_Message_Osynth_type, type, (
% 0.21/0.40 c_Message_Osynth: $i > $i)).
% 0.21/0.40 tff(c_union_type, type, (
% 0.21/0.40 c_union: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(c_Message_Oanalz_type, type, (
% 0.21/0.40 c_Message_Oanalz: $i > $i)).
% 0.21/0.40 tff(v_H_type, type, (
% 0.21/0.40 v_H: $i)).
% 0.21/0.40 tff(c_Message_Omsg_OKey_type, type, (
% 0.21/0.40 c_Message_Omsg_OKey: $i > $i)).
% 0.21/0.40 tff(c_Message_OinvKey_type, type, (
% 0.21/0.40 c_Message_OinvKey: $i > $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((~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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(2,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')).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (~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)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(7,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')).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.40 tff(9,plain,(
% 0.21/0.40 ![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))),
% 0.21/0.40 inference(skolemize,[status(sab)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (((~![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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ((~![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))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 ((~![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)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (^[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)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![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)) <=> ![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))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![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)) <=> ![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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(18,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')).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.40 tff(20,plain,(
% 0.21/0.40 ![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))),
% 0.21/0.40 inference(skolemize,[status(sab)],[19])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![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))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (((~![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(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))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![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(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))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ((~![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(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)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[24, 21, 3])).
% 0.21/0.40 tff(26,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)).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(28,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')).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (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)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, 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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, 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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.40 tff(35,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')).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.40 tff(38,plain,(
% 0.21/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[37])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, 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_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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((~![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)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (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)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 26])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(48,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')).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.41 tff(50,plain,(
% 0.21/0.41 ![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))),
% 0.21/0.41 inference(skolemize,[status(sab)],[49])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 ((~![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)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,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')).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.41 tff(61,plain,(
% 0.21/0.41 ![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))),
% 0.21/0.41 inference(skolemize,[status(sab)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![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))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![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)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 62, 26])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 21, 66, 55])).
% 0.21/0.41 tff(71,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,[]))).
% 0.21/0.41 tff(72,assumption,(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)), introduced(assumption)).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.41 tff(78,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')).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.41 tff(81,plain,(
% 0.21/0.41 ![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)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[80])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (((~![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 82, 72, 71, 25])).
% 0.21/0.42 tff(87,plain,(~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)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(89,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')).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (((~![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 39, 90])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 87])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.42 tff(101,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')).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.42 tff(104,plain,(
% 0.21/0.42 ![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)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[103])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (((~![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(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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)))) <=> ((~![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(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((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))) <=> (c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (((~![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(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (((~![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(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 ((~![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)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~![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(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | 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))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 105, 95, 14])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~![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)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 62, 87])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[119, 21, 116, 112])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------