TSTP Solution File: SWV236+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 15:10:29 EDT 2022
% Result : Theorem 1.61s 1.29s
% Output : Proof 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 01:46:17 EDT 2022
% 0.13/0.34 % 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.
% 1.61/1.29 % SZS status Theorem
% 1.61/1.29 % SZS output start Proof
% 1.61/1.29 tff(p_type, type, (
% 1.61/1.29 p: $i > $o)).
% 1.61/1.29 tff(xor_type, type, (
% 1.61/1.29 xor: ( $i * $i ) > $i)).
% 1.61/1.29 tff(data_type, type, (
% 1.61/1.29 data: $i)).
% 1.61/1.29 tff(kp_type, type, (
% 1.61/1.29 kp: $i)).
% 1.61/1.29 tff(crypt_type, type, (
% 1.61/1.29 crypt: ( $i * $i ) > $i)).
% 1.61/1.29 tff(exp_type, type, (
% 1.61/1.29 exp: $i)).
% 1.61/1.29 tff(km_type, type, (
% 1.61/1.29 km: $i)).
% 1.61/1.29 tff(id_type, type, (
% 1.61/1.29 id: $i)).
% 1.61/1.29 tff(decrypt_type, type, (
% 1.61/1.29 decrypt: ( $i * $i ) > $i)).
% 1.61/1.29 tff(eurk_type, type, (
% 1.61/1.29 eurk: $i)).
% 1.61/1.29 tff(1,plain,
% 1.61/1.29 (^[X1: $i, X2: $i] : refl((xor(X1, X2) = xor(X2, X1)) <=> (xor(X1, X2) = xor(X2, X1)))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(2,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1)) <=> ![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[1])).
% 1.61/1.29 tff(3,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1)) <=> ![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(4,axiom,(![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xor_commutative')).
% 1.61/1.29 tff(5,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.61/1.29 tff(6,plain,(
% 1.61/1.29 ![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))),
% 1.61/1.29 inference(skolemize,[status(sab)],[5])).
% 1.61/1.29 tff(7,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.61/1.29 tff(8,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))) | (xor(data, kp) = xor(kp, data))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(9,plain,
% 1.61/1.29 (xor(data, kp) = xor(kp, data)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.61/1.29 tff(10,plain,
% 1.61/1.29 (xor(kp, data) = xor(data, kp)),
% 1.61/1.29 inference(symmetry,[status(thm)],[9])).
% 1.61/1.29 tff(11,plain,
% 1.61/1.29 (p(xor(kp, data)) <=> p(xor(data, kp))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[10])).
% 1.61/1.29 tff(12,plain,
% 1.61/1.29 (p(xor(data, kp)) <=> p(xor(kp, data))),
% 1.61/1.29 inference(symmetry,[status(thm)],[11])).
% 1.61/1.29 tff(13,plain,
% 1.61/1.29 (p(data) <=> p(data)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(14,axiom,(p(data)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','initial_knowledge_of_intruder_3')).
% 1.61/1.29 tff(15,plain,
% 1.61/1.29 (p(data)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.61/1.29 tff(16,plain,
% 1.61/1.29 (p(kp) <=> p(kp)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(17,axiom,(p(kp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','initial_knowledge_of_intruder_1')).
% 1.61/1.29 tff(18,plain,
% 1.61/1.29 (p(kp)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.61/1.29 tff(19,plain,
% 1.61/1.29 (^[X1: $i, X2: $i] : refl((p(xor(X1, X2)) | (~p(X1)) | (~p(X2))) <=> (p(xor(X1, X2)) | (~p(X1)) | (~p(X2))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(20,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2))) <=> ![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[19])).
% 1.61/1.29 tff(21,plain,
% 1.61/1.29 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(X1) & p(X2)) <=> (~((~p(X1)) | (~p(X2))))), ((~(p(X1) & p(X2))) <=> (~(~((~p(X1)) | (~p(X2))))))), rewrite((~(~((~p(X1)) | (~p(X2))))) <=> ((~p(X1)) | (~p(X2)))), ((~(p(X1) & p(X2))) <=> ((~p(X1)) | (~p(X2))))), ((p(xor(X1, X2)) | (~(p(X1) & p(X2)))) <=> (p(xor(X1, X2)) | ((~p(X1)) | (~p(X2)))))), rewrite((p(xor(X1, X2)) | ((~p(X1)) | (~p(X2)))) <=> (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))), ((p(xor(X1, X2)) | (~(p(X1) & p(X2)))) <=> (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(22,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2)))) <=> ![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[21])).
% 1.61/1.29 tff(23,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2)))) <=> ![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2))))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(24,plain,
% 1.61/1.29 (^[X1: $i, X2: $i] : rewrite(((p(X1) & p(X2)) => p(xor(X1, X2))) <=> (p(xor(X1, X2)) | (~(p(X1) & p(X2)))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(25,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : ((p(X1) & p(X2)) => p(xor(X1, X2))) <=> ![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[24])).
% 1.61/1.29 tff(26,axiom,(![X1: $i, X2: $i] : ((p(X1) & p(X2)) => p(xor(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','combine_with_XOR')).
% 1.61/1.29 tff(27,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.61/1.29 tff(28,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.61/1.29 tff(29,plain,(
% 1.61/1.29 ![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~(p(X1) & p(X2))))),
% 1.61/1.29 inference(skolemize,[status(sab)],[28])).
% 1.61/1.29 tff(30,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.61/1.29 tff(31,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[30, 20])).
% 1.61/1.29 tff(32,plain,
% 1.61/1.29 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | ((~p(data)) | p(xor(data, kp)) | (~p(kp)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(data)) | p(xor(data, kp)) | (~p(kp)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(33,plain,
% 1.61/1.29 ((p(xor(data, kp)) | (~p(data)) | (~p(kp))) <=> ((~p(data)) | p(xor(data, kp)) | (~p(kp)))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(34,plain,
% 1.61/1.29 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(data, kp)) | (~p(data)) | (~p(kp)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | ((~p(data)) | p(xor(data, kp)) | (~p(kp))))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[33])).
% 1.61/1.29 tff(35,plain,
% 1.61/1.29 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(data, kp)) | (~p(data)) | (~p(kp)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(data)) | p(xor(data, kp)) | (~p(kp)))),
% 1.61/1.29 inference(transitivity,[status(thm)],[34, 32])).
% 1.61/1.29 tff(36,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(data, kp)) | (~p(data)) | (~p(kp)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(37,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(data)) | p(xor(data, kp)) | (~p(kp))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.61/1.29 tff(38,plain,
% 1.61/1.29 (p(xor(data, kp))),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[37, 31, 18, 15])).
% 1.61/1.29 tff(39,plain,
% 1.61/1.29 (p(xor(kp, data))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[38, 12])).
% 1.61/1.29 tff(40,plain,
% 1.61/1.29 (^[X1: $i] : refl((xor(X1, id) = X1) <=> (xor(X1, id) = X1))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(41,plain,
% 1.61/1.29 (![X1: $i] : (xor(X1, id) = X1) <=> ![X1: $i] : (xor(X1, id) = X1)),
% 1.61/1.29 inference(quant_intro,[status(thm)],[40])).
% 1.61/1.29 tff(42,plain,
% 1.61/1.29 (![X1: $i] : (xor(X1, id) = X1) <=> ![X1: $i] : (xor(X1, id) = X1)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(43,axiom,(![X1: $i] : (xor(X1, id) = X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xor_rules_1')).
% 1.61/1.29 tff(44,plain,
% 1.61/1.29 (![X1: $i] : (xor(X1, id) = X1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.61/1.29 tff(45,plain,(
% 1.61/1.29 ![X1: $i] : (xor(X1, id) = X1)),
% 1.61/1.29 inference(skolemize,[status(sab)],[44])).
% 1.61/1.29 tff(46,plain,
% 1.61/1.29 (![X1: $i] : (xor(X1, id) = X1)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.61/1.29 tff(47,plain,
% 1.61/1.29 ((~![X1: $i] : (xor(X1, id) = X1)) | (xor(kp, id) = kp)),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(48,plain,
% 1.61/1.29 (xor(kp, id) = kp),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[47, 46])).
% 1.61/1.29 tff(49,plain,
% 1.61/1.29 (xor(xor(kp, id), data) = xor(kp, data)),
% 1.61/1.29 inference(monotonicity,[status(thm)],[48])).
% 1.61/1.29 tff(50,plain,
% 1.61/1.29 (^[X1: $i, X2: $i] : refl((decrypt(X1, crypt(X1, X2)) = X2) <=> (decrypt(X1, crypt(X1, X2)) = X2))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(51,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2) <=> ![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)),
% 1.61/1.29 inference(quant_intro,[status(thm)],[50])).
% 1.61/1.29 tff(52,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2) <=> ![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(53,axiom,(![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','encryption_decryption_cancellation')).
% 1.61/1.29 tff(54,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.61/1.29 tff(55,plain,(
% 1.61/1.29 ![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)),
% 1.61/1.29 inference(skolemize,[status(sab)],[54])).
% 1.61/1.29 tff(56,plain,
% 1.61/1.29 (![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.61/1.29 tff(57,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i] : (decrypt(X1, crypt(X1, X2)) = X2)) | (decrypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp)) = exp)),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(58,plain,
% 1.61/1.29 (decrypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp)) = exp),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[57, 56])).
% 1.61/1.29 tff(59,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))) | (xor(km, kp) = xor(kp, km))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(60,plain,
% 1.61/1.29 (xor(km, kp) = xor(kp, km)),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[59, 7])).
% 1.61/1.29 tff(61,plain,
% 1.61/1.29 (xor(kp, km) = xor(km, kp)),
% 1.61/1.29 inference(symmetry,[status(thm)],[60])).
% 1.61/1.29 tff(62,plain,
% 1.61/1.29 (xor(xor(kp, km), crypt(xor(km, exp), eurk)) = xor(xor(km, kp), crypt(xor(km, exp), eurk))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[61])).
% 1.61/1.29 tff(63,plain,
% 1.61/1.29 (xor(xor(km, kp), crypt(xor(km, exp), eurk)) = xor(xor(kp, km), crypt(xor(km, exp), eurk))),
% 1.61/1.29 inference(symmetry,[status(thm)],[62])).
% 1.61/1.29 tff(64,plain,
% 1.61/1.29 (^[X1: $i, X2: $i, X3: $i] : refl((xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3)) <=> (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3)))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(65,plain,
% 1.61/1.29 (![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3)) <=> ![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[64])).
% 1.61/1.29 tff(66,plain,
% 1.61/1.29 (![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3)) <=> ![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(67,axiom,(![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xor_associative')).
% 1.61/1.29 tff(68,plain,
% 1.61/1.29 (![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.61/1.29 tff(69,plain,(
% 1.61/1.29 ![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))),
% 1.61/1.29 inference(skolemize,[status(sab)],[68])).
% 1.61/1.29 tff(70,plain,
% 1.61/1.29 (![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[69, 65])).
% 1.61/1.29 tff(71,plain,
% 1.61/1.29 ((~![X1: $i, X2: $i, X3: $i] : (xor(X1, xor(X2, X3)) = xor(xor(X1, X2), X3))) | (xor(km, xor(kp, crypt(xor(km, exp), eurk))) = xor(xor(km, kp), crypt(xor(km, exp), eurk)))),
% 1.61/1.29 inference(quant_inst,[status(thm)],[])).
% 1.61/1.29 tff(72,plain,
% 1.61/1.29 (xor(km, xor(kp, crypt(xor(km, exp), eurk))) = xor(xor(km, kp), crypt(xor(km, exp), eurk))),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[71, 70])).
% 1.61/1.29 tff(73,plain,
% 1.61/1.29 (xor(km, xor(kp, crypt(xor(km, exp), eurk))) = xor(xor(kp, km), crypt(xor(km, exp), eurk))),
% 1.61/1.29 inference(transitivity,[status(thm)],[72, 63])).
% 1.61/1.29 tff(74,plain,
% 1.61/1.29 (crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp) = crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)),
% 1.61/1.29 inference(monotonicity,[status(thm)],[73])).
% 1.61/1.29 tff(75,plain,
% 1.61/1.29 (decrypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp)) = decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))),
% 1.61/1.29 inference(monotonicity,[status(thm)],[73, 74])).
% 1.61/1.29 tff(76,plain,
% 1.61/1.29 (decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)) = decrypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp))),
% 1.61/1.30 inference(symmetry,[status(thm)],[75])).
% 1.61/1.30 tff(77,plain,
% 1.61/1.30 (decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)) = exp),
% 1.61/1.30 inference(transitivity,[status(thm)],[76, 58])).
% 1.61/1.30 tff(78,plain,
% 1.61/1.30 (xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))) = xor(km, exp)),
% 1.61/1.30 inference(monotonicity,[status(thm)],[77])).
% 1.61/1.30 tff(79,plain,
% 1.61/1.30 (crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data)) = crypt(xor(km, exp), xor(kp, data))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[78, 49])).
% 1.61/1.30 tff(80,plain,
% 1.61/1.30 (p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) <=> p(crypt(xor(km, exp), xor(kp, data)))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[79])).
% 1.61/1.30 tff(81,plain,
% 1.61/1.30 (p(crypt(xor(km, exp), xor(kp, data))) <=> p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data)))),
% 1.61/1.30 inference(symmetry,[status(thm)],[80])).
% 1.61/1.30 tff(82,plain,
% 1.61/1.30 ((~p(crypt(xor(km, exp), xor(kp, data)))) <=> (~p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[81])).
% 1.61/1.30 tff(83,assumption,(~p(crypt(xor(km, exp), xor(kp, data)))), introduced(assumption)).
% 1.61/1.30 tff(84,plain,
% 1.61/1.30 (~p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data)))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.61/1.30 tff(85,plain,
% 1.61/1.30 (xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp) = xor(exp, kp)),
% 1.61/1.30 inference(monotonicity,[status(thm)],[77])).
% 1.61/1.30 tff(86,plain,
% 1.61/1.30 (xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)) = xor(km, xor(exp, kp))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[85])).
% 1.61/1.30 tff(87,plain,
% 1.61/1.30 (xor(km, xor(exp, kp)) = xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp))),
% 1.61/1.30 inference(symmetry,[status(thm)],[86])).
% 1.61/1.30 tff(88,plain,
% 1.61/1.30 (kp = xor(kp, id)),
% 1.61/1.30 inference(symmetry,[status(thm)],[48])).
% 1.61/1.30 tff(89,plain,
% 1.61/1.30 (exp = decrypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), crypt(xor(km, xor(kp, crypt(xor(km, exp), eurk))), exp))),
% 1.61/1.30 inference(symmetry,[status(thm)],[58])).
% 1.61/1.30 tff(90,plain,
% 1.61/1.30 (exp = decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))),
% 1.61/1.30 inference(transitivity,[status(thm)],[89, 75])).
% 1.61/1.30 tff(91,plain,
% 1.61/1.30 (xor(exp, kp) = xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), xor(kp, id))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[90, 88])).
% 1.61/1.30 tff(92,plain,
% 1.61/1.30 (xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), xor(kp, id)) = xor(exp, kp)),
% 1.61/1.30 inference(symmetry,[status(thm)],[91])).
% 1.61/1.30 tff(93,plain,
% 1.61/1.30 ((~![X1: $i, X2: $i] : (xor(X1, X2) = xor(X2, X1))) | (xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), xor(kp, id)) = xor(xor(kp, id), decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(94,plain,
% 1.61/1.30 (xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), xor(kp, id)) = xor(xor(kp, id), decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[93, 7])).
% 1.61/1.30 tff(95,plain,
% 1.61/1.30 (xor(xor(kp, id), decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))) = xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), xor(kp, id))),
% 1.61/1.30 inference(symmetry,[status(thm)],[94])).
% 1.61/1.30 tff(96,plain,
% 1.61/1.30 (xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))) = xor(xor(kp, id), decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[88])).
% 1.61/1.30 tff(97,plain,
% 1.61/1.30 (xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))) = xor(exp, kp)),
% 1.61/1.30 inference(transitivity,[status(thm)],[96, 95, 92])).
% 1.61/1.30 tff(98,plain,
% 1.61/1.30 (xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) = xor(km, xor(exp, kp))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[97])).
% 1.61/1.30 tff(99,plain,
% 1.61/1.30 (xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) = xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp))),
% 1.61/1.30 inference(transitivity,[status(thm)],[98, 87])).
% 1.61/1.30 tff(100,plain,
% 1.61/1.30 (crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id)) = crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[99])).
% 1.61/1.30 tff(101,plain,
% 1.61/1.30 (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) <=> p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[100])).
% 1.61/1.30 tff(102,plain,
% 1.61/1.30 (p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id))) <=> p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id)))),
% 1.61/1.30 inference(symmetry,[status(thm)],[101])).
% 1.61/1.30 tff(103,plain,
% 1.61/1.30 ((~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) <=> (~p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[102])).
% 1.61/1.30 tff(104,assumption,(~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))), introduced(assumption)).
% 1.61/1.30 tff(105,plain,
% 1.61/1.30 (~p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id)))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.61/1.30 tff(106,plain,
% 1.61/1.30 (p(id) <=> p(id)),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(107,axiom,(p(id)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','initial_knowledge_of_intruder_4')).
% 1.61/1.30 tff(108,plain,
% 1.61/1.30 (p(id)),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.61/1.30 tff(109,plain,
% 1.61/1.30 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | ((~p(kp)) | p(xor(kp, id)) | (~p(id)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(kp)) | p(xor(kp, id)) | (~p(id)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(110,plain,
% 1.61/1.30 ((p(xor(kp, id)) | (~p(kp)) | (~p(id))) <=> ((~p(kp)) | p(xor(kp, id)) | (~p(id)))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(111,plain,
% 1.61/1.31 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(kp, id)) | (~p(kp)) | (~p(id)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | ((~p(kp)) | p(xor(kp, id)) | (~p(id))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[110])).
% 1.61/1.31 tff(112,plain,
% 1.61/1.31 (((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(kp, id)) | (~p(kp)) | (~p(id)))) <=> ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(kp)) | p(xor(kp, id)) | (~p(id)))),
% 1.61/1.31 inference(transitivity,[status(thm)],[111, 109])).
% 1.61/1.31 tff(113,plain,
% 1.61/1.31 ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (p(xor(kp, id)) | (~p(kp)) | (~p(id)))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(114,plain,
% 1.61/1.31 ((~![X1: $i, X2: $i] : (p(xor(X1, X2)) | (~p(X1)) | (~p(X2)))) | (~p(kp)) | p(xor(kp, id)) | (~p(id))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.61/1.31 tff(115,plain,
% 1.61/1.31 (p(xor(kp, id))),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[114, 31, 18, 108])).
% 1.61/1.31 tff(116,plain,
% 1.61/1.31 (p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))) <=> p(exp)),
% 1.61/1.31 inference(monotonicity,[status(thm)],[77])).
% 1.61/1.31 tff(117,plain,
% 1.61/1.31 (p(exp) <=> p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))),
% 1.61/1.31 inference(symmetry,[status(thm)],[116])).
% 1.61/1.31 tff(118,plain,
% 1.61/1.31 (p(exp) <=> p(exp)),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(119,axiom,(p(exp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','initial_knowledge_of_intruder_9')).
% 1.61/1.31 tff(120,plain,
% 1.61/1.31 (p(exp)),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.61/1.31 tff(121,plain,
% 1.61/1.31 (p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[120, 117])).
% 1.61/1.31 tff(122,plain,
% 1.61/1.31 (^[Xk: $i, Xtype: $i] : refl((p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype))) <=> (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(123,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype))) <=> ![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[122])).
% 1.61/1.31 tff(124,plain,
% 1.61/1.31 (^[Xk: $i, Xtype: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(Xk) & p(Xtype)) <=> (~((~p(Xk)) | (~p(Xtype))))), ((~(p(Xk) & p(Xtype))) <=> (~(~((~p(Xk)) | (~p(Xtype))))))), rewrite((~(~((~p(Xk)) | (~p(Xtype))))) <=> ((~p(Xk)) | (~p(Xtype)))), ((~(p(Xk) & p(Xtype))) <=> ((~p(Xk)) | (~p(Xtype))))), (((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> (((~p(Xk)) | (~p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))))), rewrite((((~p(Xk)) | (~p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))), (((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(125,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> ![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[124])).
% 1.61/1.31 tff(126,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> ![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk)))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(127,plain,
% 1.61/1.31 (^[Xk: $i, Xtype: $i] : rewrite(((p(Xk) & p(Xtype)) => p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(128,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : ((p(Xk) & p(Xtype)) => p(crypt(xor(km, xor(kp, Xtype)), Xk))) <=> ![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk)))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[127])).
% 1.61/1.31 tff(129,axiom,(![Xk: $i, Xtype: $i] : ((p(Xk) & p(Xtype)) => p(crypt(xor(km, xor(kp, Xtype)), Xk)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','key_part_import___part_1')).
% 1.61/1.31 tff(130,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.61/1.31 tff(131,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.61/1.31 tff(132,plain,(
% 1.61/1.31 ![Xk: $i, Xtype: $i] : ((~(p(Xk) & p(Xtype))) | p(crypt(xor(km, xor(kp, Xtype)), Xk)))),
% 1.61/1.31 inference(skolemize,[status(sab)],[131])).
% 1.61/1.31 tff(133,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[132, 125])).
% 1.61/1.31 tff(134,plain,
% 1.61/1.31 (![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[133, 123])).
% 1.61/1.31 tff(135,plain,
% 1.61/1.31 (((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id))))) <=> ((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id))))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(136,plain,
% 1.61/1.31 ((p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))))) <=> (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id))))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(137,plain,
% 1.61/1.31 (((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))) <=> ((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id)))))),
% 1.61/1.31 inference(monotonicity,[status(thm)],[136])).
% 1.61/1.31 tff(138,plain,
% 1.61/1.31 (((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))) <=> ((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id))))),
% 1.61/1.31 inference(transitivity,[status(thm)],[137, 135])).
% 1.61/1.31 tff(139,plain,
% 1.61/1.31 ((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))),
% 1.61/1.31 inference(quant_inst,[status(thm)],[])).
% 1.61/1.31 tff(140,plain,
% 1.61/1.31 ((~![Xk: $i, Xtype: $i] : (p(crypt(xor(km, xor(kp, Xtype)), Xk)) | (~p(Xk)) | (~p(Xtype)))) | p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(xor(kp, id)))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.61/1.31 tff(141,plain,
% 1.61/1.31 (p(crypt(xor(km, xor(kp, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))), xor(kp, id)))),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[140, 134, 121, 115])).
% 1.61/1.31 tff(142,plain,
% 1.61/1.31 ($false),
% 1.61/1.31 inference(unit_resolution,[status(thm)],[141, 105])).
% 1.61/1.31 tff(143,plain,(p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.31 tff(144,plain,
% 1.61/1.31 (^[Xk1: $i, Xtype: $i, Xk2: $i] : refl((p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(145,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))) <=> ![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[144])).
% 1.61/1.31 tff(146,plain,
% 1.61/1.31 (^[Xk1: $i, Xtype: $i, Xk2: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)) <=> (~((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))))), ((~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))) <=> (~(~((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))))))), rewrite((~(~((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))))) <=> ((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))), ((~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))) <=> ((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2)))))), ((p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | ((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))))), rewrite((p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | ((~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))), ((p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(147,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)))) <=> ![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[146])).
% 1.61/1.31 tff(148,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)))) <=> ![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))),
% 1.61/1.31 inference(rewrite,[status(thm)],[])).
% 1.61/1.31 tff(149,plain,
% 1.61/1.31 (^[Xk1: $i, Xtype: $i, Xk2: $i] : trans(monotonicity(rewrite(((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2))) & p(Xtype)) <=> (p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))), ((((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2))) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1)))) <=> ((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1)))))), rewrite(((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1)))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))), ((((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2))) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1)))) <=> (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))))),
% 1.61/1.31 inference(bind,[status(th)],[])).
% 1.61/1.31 tff(150,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2))) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1)))) <=> ![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))),
% 1.61/1.31 inference(quant_intro,[status(thm)],[149])).
% 1.61/1.31 tff(151,axiom,(![Xk1: $i, Xtype: $i, Xk2: $i] : (((p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2))) & p(Xtype)) => p(crypt(xor(km, Xtype), xor(Xk2, Xk1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','key_part_import___part_3')).
% 1.61/1.31 tff(152,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.61/1.31 tff(153,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.61/1.31 tff(154,plain,(
% 1.61/1.31 ![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~(p(Xk1) & p(crypt(xor(km, xor(Xtype, kp)), Xk2)) & p(Xtype))))),
% 1.61/1.31 inference(skolemize,[status(sab)],[153])).
% 1.61/1.31 tff(155,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.61/1.31 tff(156,plain,
% 1.61/1.31 (![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))),
% 1.61/1.31 inference(modus_ponens,[status(thm)],[155, 145])).
% 1.61/1.31 tff(157,plain,
% 1.61/1.31 (((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | ((~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))) <=> ((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(158,plain,
% 1.61/1.32 ((p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id))))) <=> ((~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(159,plain,
% 1.61/1.32 (((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))))) <=> ((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | ((~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))))))),
% 1.61/1.32 inference(monotonicity,[status(thm)],[158])).
% 1.61/1.32 tff(160,plain,
% 1.61/1.32 (((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))))) <=> ((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))))),
% 1.61/1.32 inference(transitivity,[status(thm)],[159, 157])).
% 1.61/1.32 tff(161,plain,
% 1.61/1.32 ((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))))),
% 1.61/1.32 inference(quant_inst,[status(thm)],[])).
% 1.61/1.32 tff(162,plain,
% 1.61/1.32 ((~![Xk1: $i, Xtype: $i, Xk2: $i] : (p(crypt(xor(km, Xtype), xor(Xk2, Xk1))) | (~p(Xtype)) | (~p(Xk1)) | (~p(crypt(xor(km, xor(Xtype, kp)), Xk2))))) | (~p(data)) | (~p(crypt(xor(km, xor(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp)), kp)), xor(kp, id)))) | p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data))) | (~p(decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.61/1.32 tff(163,plain,
% 1.61/1.32 (p(crypt(xor(km, decrypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), crypt(xor(xor(kp, km), crypt(xor(km, exp), eurk)), exp))), xor(xor(kp, id), data)))),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[162, 156, 15, 121, 143])).
% 1.61/1.32 tff(164,plain,
% 1.61/1.32 ($false),
% 1.61/1.32 inference(unit_resolution,[status(thm)],[163, 84])).
% 1.61/1.32 tff(165,plain,(p(crypt(xor(km, exp), xor(kp, data)))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.32 tff(166,plain,
% 1.61/1.32 (^[X: $i] : refl(((~p(crypt(xor(km, exp), X))) | (~p(X))) <=> ((~p(crypt(xor(km, exp), X))) | (~p(X))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(167,plain,
% 1.61/1.32 (![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X))) <=> ![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[166])).
% 1.61/1.32 tff(168,plain,
% 1.61/1.32 (^[X: $i] : trans(monotonicity(rewrite((p(crypt(xor(km, exp), X)) & p(X)) <=> (~((~p(crypt(xor(km, exp), X))) | (~p(X))))), ((~(p(crypt(xor(km, exp), X)) & p(X))) <=> (~(~((~p(crypt(xor(km, exp), X))) | (~p(X))))))), rewrite((~(~((~p(crypt(xor(km, exp), X))) | (~p(X))))) <=> ((~p(crypt(xor(km, exp), X))) | (~p(X)))), ((~(p(crypt(xor(km, exp), X)) & p(X))) <=> ((~p(crypt(xor(km, exp), X))) | (~p(X)))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(169,plain,
% 1.61/1.32 (![X: $i] : (~(p(crypt(xor(km, exp), X)) & p(X))) <=> ![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))),
% 1.61/1.32 inference(quant_intro,[status(thm)],[168])).
% 1.61/1.32 tff(170,plain,
% 1.61/1.32 ((~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))) <=> (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X)))),
% 1.61/1.32 inference(rewrite,[status(thm)],[])).
% 1.61/1.32 tff(171,axiom,(~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','find_known_exporter')).
% 1.61/1.32 tff(172,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.61/1.32 tff(173,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[172, 170])).
% 1.61/1.32 tff(174,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[173, 170])).
% 1.61/1.32 tff(175,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[174, 170])).
% 1.61/1.32 tff(176,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[175, 170])).
% 1.61/1.32 tff(177,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[176, 170])).
% 1.61/1.32 tff(178,plain,
% 1.61/1.32 (~?[X: $i] : (p(crypt(xor(km, exp), X)) & p(X))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[177, 170])).
% 1.61/1.32 tff(179,plain,
% 1.61/1.32 (^[X: $i] : refl($oeq((~(p(crypt(xor(km, exp), X)) & p(X))), (~(p(crypt(xor(km, exp), X)) & p(X)))))),
% 1.61/1.32 inference(bind,[status(th)],[])).
% 1.61/1.32 tff(180,plain,(
% 1.61/1.32 ![X: $i] : (~(p(crypt(xor(km, exp), X)) & p(X)))),
% 1.61/1.32 inference(nnf-neg,[status(sab)],[178, 179])).
% 1.61/1.32 tff(181,plain,
% 1.61/1.32 (![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[180, 169])).
% 1.61/1.32 tff(182,plain,
% 1.61/1.32 (![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))),
% 1.61/1.32 inference(modus_ponens,[status(thm)],[181, 167])).
% 1.61/1.32 tff(183,plain,
% 1.61/1.32 (((~![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))) | ((~p(crypt(xor(km, exp), xor(kp, data)))) | (~p(xor(kp, data))))) <=> ((~![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))) | (~p(crypt(xor(km, exp), xor(kp, data)))) | (~p(xor(kp, data))))),
% 1.71/1.32 inference(rewrite,[status(thm)],[])).
% 1.71/1.32 tff(184,plain,
% 1.71/1.32 ((~![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))) | ((~p(crypt(xor(km, exp), xor(kp, data)))) | (~p(xor(kp, data))))),
% 1.71/1.32 inference(quant_inst,[status(thm)],[])).
% 1.71/1.32 tff(185,plain,
% 1.71/1.32 ((~![X: $i] : ((~p(crypt(xor(km, exp), X))) | (~p(X)))) | (~p(crypt(xor(km, exp), xor(kp, data)))) | (~p(xor(kp, data)))),
% 1.71/1.32 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.71/1.32 tff(186,plain,
% 1.71/1.32 ($false),
% 1.71/1.32 inference(unit_resolution,[status(thm)],[185, 182, 165, 39])).
% 1.71/1.32 % SZS output end Proof
%------------------------------------------------------------------------------