TSTP Solution File: SWV247-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV247-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:10:33 EDT 2022
% Result : Unsatisfiable 12.44s 8.28s
% Output : Proof 12.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV247-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun Sep 4 02:14:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 12.44/8.28 % SZS status Unsatisfiable
% 12.44/8.28 % SZS output start Proof
% 12.44/8.28 tff(c_in_type, type, (
% 12.44/8.28 c_in: ( $i * $i * $i ) > $o)).
% 12.44/8.28 tff(tc_Message_Omsg_type, type, (
% 12.44/8.28 tc_Message_Omsg: $i)).
% 12.44/8.28 tff(c_union_type, type, (
% 12.44/8.28 c_union: ( $i * $i * $i ) > $i)).
% 12.44/8.28 tff(v_H_type, type, (
% 12.44/8.28 v_H: $i)).
% 12.44/8.28 tff(v_G_type, type, (
% 12.44/8.28 v_G: $i)).
% 12.44/8.28 tff(c_Message_Omsg_OKey_type, type, (
% 12.44/8.28 c_Message_Omsg_OKey: $i > $i)).
% 12.44/8.28 tff(c_Message_OinvKey_type, type, (
% 12.44/8.28 c_Message_OinvKey: $i > $i)).
% 12.44/8.28 tff(v_K_type, type, (
% 12.44/8.28 v_K: $i)).
% 12.44/8.28 tff(c_Message_Oanalz_type, type, (
% 12.44/8.28 c_Message_Oanalz: $i > $i)).
% 12.44/8.28 tff(c_Message_Omsg_OCrypt_type, type, (
% 12.44/8.28 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 12.44/8.28 tff(v_X_type, type, (
% 12.44/8.28 v_X: $i)).
% 12.44/8.28 tff(c_Message_Osynth_type, type, (
% 12.44/8.28 c_Message_Osynth: $i > $i)).
% 12.44/8.28 tff(1,plain,
% 12.44/8.28 ((~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))),
% 12.44/8.28 inference(rewrite,[status(thm)],[])).
% 12.44/8.28 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/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 12.44/8.28 tff(3,plain,
% 12.44/8.28 (~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)),
% 12.44/8.28 inference(modus_ponens,[status(thm)],[2, 1])).
% 12.44/8.28 tff(4,plain,
% 12.44/8.28 (^[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)))),
% 12.44/8.28 inference(bind,[status(th)],[])).
% 12.44/8.28 tff(5,plain,
% 12.44/8.28 (![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))),
% 12.44/8.28 inference(quant_intro,[status(thm)],[4])).
% 12.44/8.28 tff(6,plain,
% 12.44/8.28 (![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))),
% 12.44/8.28 inference(rewrite,[status(thm)],[])).
% 12.44/8.28 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/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OUnCI_0')).
% 12.44/8.28 tff(8,plain,
% 12.44/8.28 (![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))),
% 12.44/8.28 inference(modus_ponens,[status(thm)],[7, 6])).
% 12.44/8.28 tff(9,plain,(
% 12.44/8.28 ![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))),
% 12.44/8.28 inference(skolemize,[status(sab)],[8])).
% 12.44/8.28 tff(10,plain,
% 12.44/8.28 (![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))),
% 12.44/8.28 inference(modus_ponens,[status(thm)],[9, 5])).
% 12.44/8.28 tff(11,plain,
% 12.44/8.28 (((~![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))),
% 12.44/8.28 inference(rewrite,[status(thm)],[])).
% 12.44/8.28 tff(12,plain,
% 12.44/8.28 ((~![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))),
% 12.44/8.28 inference(quant_inst,[status(thm)],[])).
% 12.44/8.28 tff(13,plain,
% 12.44/8.28 ((~![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)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[12, 11])).
% 12.44/8.29 tff(14,plain,
% 12.44/8.29 (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 12.44/8.29 tff(15,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)).
% 12.44/8.29 tff(16,plain,
% 12.44/8.29 (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)),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(17,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 12.44/8.29 tff(18,plain,
% 12.44/8.29 (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)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[17, 16])).
% 12.44/8.29 tff(19,plain,
% 12.44/8.29 (^[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))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(20,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[19])).
% 12.44/8.29 tff(21,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(22,plain,
% 12.44/8.29 (^[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))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(23,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[22])).
% 12.44/8.29 tff(24,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/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OUnE_0')).
% 12.44/8.29 tff(25,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[24, 23])).
% 12.44/8.29 tff(26,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[25, 21])).
% 12.44/8.29 tff(27,plain,(
% 12.44/8.29 ![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)))),
% 12.44/8.29 inference(skolemize,[status(sab)],[26])).
% 12.44/8.29 tff(28,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[27, 20])).
% 12.44/8.29 tff(29,plain,
% 12.44/8.29 (((~![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)))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(30,plain,
% 12.44/8.29 ((~![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)))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(31,plain,
% 12.44/8.29 ((~![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))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[30, 29])).
% 12.44/8.29 tff(32,plain,
% 12.44/8.29 (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)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 12.44/8.29 tff(33,plain,
% 12.44/8.29 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[32, 15])).
% 12.44/8.29 tff(34,plain,
% 12.44/8.29 (^[V_H: $i, V_X: $i, V_K: $i] : refl((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), 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), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(35,plain,
% 12.44/8.29 (![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[34])).
% 12.44/8.29 tff(36,plain,
% 12.44/8.29 (![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(37,plain,
% 12.44/8.29 (^[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(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), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(38,plain,
% 12.44/8.29 (![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(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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[37])).
% 12.44/8.29 tff(39,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/sandbox/benchmark/Axioms/SWV004-0.ax','cls_Message_OCrypt__synth_1')).
% 12.44/8.29 tff(40,plain,
% 12.44/8.29 (![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[39, 38])).
% 12.44/8.29 tff(41,plain,
% 12.44/8.29 (![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[40, 36])).
% 12.44/8.29 tff(42,plain,(
% 12.44/8.29 ![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(skolemize,[status(sab)],[41])).
% 12.44/8.29 tff(43,plain,
% 12.44/8.29 (![V_H: $i, V_X: $i, V_K: $i] : (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), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[42, 35])).
% 12.44/8.29 tff(44,plain,
% 12.44/8.29 (((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(45,plain,
% 12.44/8.29 ((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))) <=> (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(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(46,plain,
% 12.44/8.29 (((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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(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), 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), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)))),
% 12.44/8.29 inference(monotonicity,[status(thm)],[45])).
% 12.44/8.29 tff(47,plain,
% 12.44/8.29 (((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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(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), 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), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg))),
% 12.44/8.29 inference(transitivity,[status(thm)],[46, 44])).
% 12.44/8.29 tff(48,plain,
% 12.44/8.29 ((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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)))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(49,plain,
% 12.44/8.29 ((~![V_H: $i, V_X: $i, V_K: $i] : (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), 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), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[48, 47])).
% 12.44/8.29 tff(50,plain,
% 12.44/8.29 (c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[49, 43, 33, 14])).
% 12.44/8.29 tff(51,plain,
% 12.44/8.29 (^[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)))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(52,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[51])).
% 12.44/8.29 tff(53,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(54,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/sandbox/benchmark/Axioms/SWV004-0.ax','cls_Message_Oanalz_OInj_0')).
% 12.44/8.29 tff(55,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[54, 53])).
% 12.44/8.29 tff(56,plain,(
% 12.44/8.29 ![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))),
% 12.44/8.29 inference(skolemize,[status(sab)],[55])).
% 12.44/8.29 tff(57,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[56, 52])).
% 12.44/8.29 tff(58,plain,
% 12.44/8.29 (((~![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(59,plain,
% 12.44/8.29 ((~![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))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(60,plain,
% 12.44/8.29 ((~![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)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[59, 58])).
% 12.44/8.29 tff(61,plain,
% 12.44/8.29 (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[60, 57, 15])).
% 12.44/8.29 tff(62,plain,
% 12.44/8.29 (^[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)))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(63,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[62])).
% 12.44/8.29 tff(64,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(65,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/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OUnCI_1')).
% 12.44/8.29 tff(66,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[65, 64])).
% 12.44/8.29 tff(67,plain,(
% 12.44/8.29 ![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))),
% 12.44/8.29 inference(skolemize,[status(sab)],[66])).
% 12.44/8.29 tff(68,plain,
% 12.44/8.29 (![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))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[67, 63])).
% 12.44/8.29 tff(69,plain,
% 12.44/8.29 (((~![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(70,plain,
% 12.44/8.29 ((~![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))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(71,plain,
% 12.44/8.29 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[70, 69])).
% 12.44/8.29 tff(72,plain,
% 12.44/8.29 ($false),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[71, 68, 61, 50])).
% 12.44/8.29 tff(73,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,[]))).
% 12.44/8.29 tff(74,plain,
% 12.44/8.29 (((~![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(75,plain,
% 12.44/8.29 ((~![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))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(76,plain,
% 12.44/8.29 ((~![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)),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[75, 74])).
% 12.44/8.29 tff(77,plain,
% 12.44/8.29 (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[76, 68, 3])).
% 12.44/8.29 tff(78,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)).
% 12.44/8.29 tff(79,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)).
% 12.44/8.29 tff(80,plain,
% 12.44/8.29 (^[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))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(81,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[80])).
% 12.44/8.29 tff(82,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(83,plain,
% 12.44/8.29 (^[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))))),
% 12.44/8.29 inference(bind,[status(th)],[])).
% 12.44/8.29 tff(84,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(quant_intro,[status(thm)],[83])).
% 12.44/8.29 tff(85,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/sandbox/benchmark/Axioms/SWV004-0.ax','cls_Message_Oanalz_ODecrypt__dest_0')).
% 12.44/8.29 tff(86,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[85, 84])).
% 12.44/8.29 tff(87,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[86, 82])).
% 12.44/8.29 tff(88,plain,(
% 12.44/8.29 ![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)))),
% 12.44/8.29 inference(skolemize,[status(sab)],[87])).
% 12.44/8.29 tff(89,plain,
% 12.44/8.29 (![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)))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[88, 81])).
% 12.44/8.29 tff(90,plain,
% 12.44/8.29 (((~![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)))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(91,plain,
% 12.44/8.29 ((~![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)))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(92,plain,
% 12.44/8.29 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)), c_Message_Oanalz(V_H), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Oanalz(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(c_Message_Omsg_OCrypt(v_K, v_X), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 12.44/8.29 inference(modus_ponens,[status(thm)],[91, 90])).
% 12.44/8.29 tff(93,plain,
% 12.44/8.29 ($false),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[92, 89, 79, 78, 77])).
% 12.44/8.29 tff(94,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)) | (~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,[]))).
% 12.44/8.29 tff(95,plain,
% 12.44/8.29 (~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)),
% 12.44/8.29 inference(unit_resolution,[status(thm)],[94, 73])).
% 12.44/8.29 tff(96,plain,
% 12.44/8.29 (((~![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))),
% 12.44/8.29 inference(rewrite,[status(thm)],[])).
% 12.44/8.29 tff(97,plain,
% 12.44/8.29 ((~![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))),
% 12.44/8.29 inference(quant_inst,[status(thm)],[])).
% 12.44/8.29 tff(98,plain,
% 12.44/8.29 ((~![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)),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[97, 96])).
% 12.44/8.30 tff(99,plain,
% 12.44/8.30 (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 12.44/8.30 inference(unit_resolution,[status(thm)],[98, 57, 95])).
% 12.44/8.30 tff(100,plain,
% 12.44/8.30 (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)),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(101,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 12.44/8.30 tff(102,plain,
% 12.44/8.30 (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)),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[101, 100])).
% 12.44/8.30 tff(103,plain,
% 12.44/8.30 (((~![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_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_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))) <=> ((~![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_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_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))),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(104,plain,
% 12.44/8.30 ((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_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_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))),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(105,plain,
% 12.44/8.30 (((~![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_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_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)))),
% 12.44/8.30 inference(monotonicity,[status(thm)],[104])).
% 12.44/8.30 tff(106,plain,
% 12.44/8.30 (((~![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_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_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))),
% 12.44/8.30 inference(transitivity,[status(thm)],[105, 103])).
% 12.44/8.30 tff(107,plain,
% 12.44/8.30 ((~![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)))),
% 12.44/8.30 inference(quant_inst,[status(thm)],[])).
% 12.44/8.30 tff(108,plain,
% 12.44/8.30 ((~![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_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_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)),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[107, 106])).
% 12.44/8.30 tff(109,plain,
% 12.44/8.30 (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)),
% 12.44/8.30 inference(unit_resolution,[status(thm)],[108, 28, 102])).
% 12.44/8.30 tff(110,plain,
% 12.44/8.30 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 12.44/8.30 inference(unit_resolution,[status(thm)],[109, 95])).
% 12.44/8.30 tff(111,plain,
% 12.44/8.30 (^[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)))),
% 12.44/8.30 inference(bind,[status(th)],[])).
% 12.44/8.30 tff(112,plain,
% 12.44/8.30 (![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))),
% 12.44/8.30 inference(quant_intro,[status(thm)],[111])).
% 12.44/8.30 tff(113,plain,
% 12.44/8.30 (![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))),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(114,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/sandbox/benchmark/Axioms/SWV004-0.ax','cls_Message_OKey__synth_0')).
% 12.44/8.30 tff(115,plain,
% 12.44/8.30 (![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))),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[114, 113])).
% 12.44/8.30 tff(116,plain,(
% 12.44/8.30 ![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))),
% 12.44/8.30 inference(skolemize,[status(sab)],[115])).
% 12.44/8.30 tff(117,plain,
% 12.44/8.30 (![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))),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[116, 112])).
% 12.44/8.30 tff(118,plain,
% 12.44/8.30 (((~![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))),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(119,plain,
% 12.44/8.30 ((~![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))),
% 12.44/8.30 inference(quant_inst,[status(thm)],[])).
% 12.44/8.30 tff(120,plain,
% 12.44/8.30 ((~![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)),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[119, 118])).
% 12.44/8.30 tff(121,plain,
% 12.44/8.30 (c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)),
% 12.44/8.30 inference(unit_resolution,[status(thm)],[120, 117, 110])).
% 12.44/8.30 tff(122,plain,
% 12.44/8.30 (((~![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))),
% 12.44/8.30 inference(rewrite,[status(thm)],[])).
% 12.44/8.30 tff(123,plain,
% 12.44/8.30 ((~![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))),
% 12.44/8.30 inference(quant_inst,[status(thm)],[])).
% 12.44/8.30 tff(124,plain,
% 12.44/8.30 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 12.44/8.30 inference(modus_ponens,[status(thm)],[123, 122])).
% 12.44/8.30 tff(125,plain,
% 12.44/8.30 ($false),
% 12.44/8.30 inference(unit_resolution,[status(thm)],[124, 68, 121, 99])).
% 12.53/8.34 % SZS output end Proof
%------------------------------------------------------------------------------