0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : run_Leo-III %s %d THM 0.09/0.30 % Computer : n025.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 1440 0.09/0.30 % WCLimit : 180 0.09/0.30 % DateTime : Thu Jul 4 06:43:40 EDT 2024 0.09/0.30 % CPUTime : 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 2.01/1.24 % [INFO] Parsing done (345ms). 2.01/1.26 % [INFO] Running in sequential loop mode. 2.95/1.61 % [INFO] eprover registered as external prover. 2.95/1.61 % [INFO] Scanning for conjecture ... 3.32/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 3.59/1.89 % [INFO] Axiom selection finished. Selected 265 axioms (removed 90 axioms). 4.72/2.15 % [INFO] Problem is higher-order (TPTP THF). 4.72/2.18 % [INFO] Type checking passed. 4.72/2.18 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 428.11/126.14 % External prover 'e' found a proof! 428.11/126.14 % [INFO] Killing All external provers ... 428.11/126.15 % Time passed: 125686ms (effective reasoning time: 124884ms) 428.11/126.15 % Solved by strategy 428.11/126.15 % Axioms used in derivation (265): fact_289_LocalSecretsComposition__neg1, fact_29_empty__iff, fact_245_UnI2, fact_321_TBtheorem2a, fact_346_eout__def, fact_158_TBtheorem1a, fact_104_insertI1, fact_249_ball__Un, fact_159_TBtheorem3a, fact_350_correctCompositionOut__prop1, fact_97_insertI2, fact_114_insert__not__empty, fact_281_insert__is__Un, fact_1_notKSQ, fact_37_all__not__in__conv, fact_60_equals0D, fact_308_sup__bot__left, fact_244_UnI2, fact_329_TBtheorem5b__notPQ, fact_328_out__exprChannelSingle__Set, fact_139_TBtheorem1b, fact_195_TBtheorem4b__notPQ, fact_129_mem__Collect__eq, fact_208_correctCompositionKS__exprChannel__s__Q, fact_206_LocalSecretsComposition__neg__k, fact_177_LocalSecretsComposition__exprChannel__k, fact_201_ine__nonempty__exprChannelSet, fact_227_Un__insert__right, fact_284_LocalSecretsComposition__ine1__s, fact_292_sup__bot_Oright__neutral, fact_219_Un__iff, fact_199_ine__exprChannelSet__def, fact_299_sup__bot_Oleft__neutral, fact_75_insert__commute, fact_247_bex__Un, fact_352_adv__not__know2, fact_151_is__singleton__the__elem, fact_345_TBtheorem5a__PQ, fact_344_TBtheore54b__P, fact_55_equals0I, fact_313_bot__eq__sup__iff, fact_14_singletonI, fact_190_TBtheorem4b__notP1, fact_220_KS_Oinject_I2_J, fact_275_singleton__Un__iff, fact_63_equals0D, fact_88_insert__ident, fact_98_insertI2, fact_223_Un__empty, fact_6_a1, fact_87_insert__ident, fact_58_equals0I, fact_194_LocalSecretsComposition__ine1__k, fact_307_sup__bot__left, fact_251_Un__assoc, fact_178_ine__def, fact_197_ine__exprChannelSingle__Set, fact_351_TBtheorem45a__P, fact_184_TBtheorem4a__P, fact_246_bex__Un, fact_34_all__not__in__conv, fact_141_Set_Ois__empty__def, fact_64_equals0D, fact_239_UnI1, fact_72_mk__disjoint__insert, fact_173_know_Osimps_I1_J, fact_306_sup__bot__left, fact_94_Set_Oset__insert, fact_229_Un__insert__left, fact_172_TBtheorem4a__empty, fact_71_mk__disjoint__insert, fact_118_singleton__iff, fact_297_sup__bot_Oleft__neutral, fact_305_sup__eq__bot__iff, fact_231_UnE, fact_318_TBtheorem5a__empty, fact_300_sup__bot_Oeq__neutr__iff, fact_315_locStream__def, fact_153_is__singletonI_H, fact_134_Collect__mem__eq, fact_285_LocalSecretsComposition__ine2__s, fact_16_KS_Oinject_I1_J, fact_265_Un__empty__left, fact_23_insert__iff, fact_224_Un__empty, fact_302_sup__bot_Oeq__neutr__iff, fact_5_assms_I3_J, fact_332_not__eout__eoutM, fact_148_not__ine__ineM, fact_123_the__elem__eq, fact_169_TBlemma3b, fact_336_TBtheorem5b__notP1, fact_273_singleton__Un__iff, fact_261_Un__empty__right, fact_294_sup__bot_Oneutr__eq__iff, fact_303_sup__eq__bot__iff, fact_156_is__singletonI_H, fact_214_UnCI, fact_175_LocalSecretsComposition__neg__loc__k, fact_268_KS_Oexhaust, fact_343_TBtheorem5b__PQ, fact_107_insertE, fact_24_insert__iff, fact_314_ineM__Un1, fact_144_correctCompositionIn__L2, fact_18_insertCI, fact_235_UnE, fact_353_adv__not__know1, fact_259_Un__left__commute, fact_82_insert__absorb, fact_4_cCompI, fact_89_insert__ident, fact_215_Un__iff, fact_316_inStream__def, fact_311_sup__bot__right, fact_324_TBtheorem5a__notP1, fact_283_LocalSecretsComposition__neg__s, fact_210_UnCI, fact_310_sup__bot__right, fact_121_singleton__iff, fact_309_sup__bot__right, fact_108_insertE, fact_248_ball__Un, fact_179_ine__ins__neg1, fact_54_ex__in__conv, fact_333_eoutM__eout, fact_279_insert__is__Un, fact_183_TBtheorem4a__PQ, fact_189_correctCompositionKS__exprChannel__k__Q, fact_70_mk__disjoint__insert, fact_203_TBtheorem4a__notP2, fact_264_Un__empty__left, fact_170_correctCompositionIn__L1, fact_69_emptyE, fact_253_Un__absorb, fact_46_singletonD, fact_254_Un__commute, fact_68_emptyE, fact_272_know_Osimps_I2_J, fact_193_LocalSecretsComposition__ine2__k, fact_103_insertI1, fact_347_eoutM__def, fact_27_insert__absorb2, fact_174_correctCompositionKS__exprChannel__k__P, fact_325_TBtheorem5a__notP2, fact_256_Un__left__absorb, fact_262_Un__empty__right, fact_295_sup__bot_Oneutr__eq__iff, fact_304_sup__eq__bot__iff, fact_267_not__know__s__not__ine, fact_188_correctCompositionKS__exprChannel__k__Pex, fact_187_correctCompositionKS__exprChannel__k__Qex, fact_349_out__exprChannelSingle__def, fact_334_TBtheorem2b, fact_348_out__exprChannelSet__def, fact_250_Un__assoc, fact_162_bot__empty__eq, fact_282_LocalSecretsComposition__neg__loc__s, fact_122_singleton__iff, fact_298_sup__bot_Oleft__neutral, fact_240_UnI1, fact_269_KS_Oinduct, fact_125_is__singletonI, fact_17_insertCI, fact_33_empty__iff, fact_128_TBtheorem3b, fact_2_notKSP, fact_205_subcomponents__loc, fact_28_insert__absorb2, fact_160_is__singletonE, fact_236_UnI1, fact_117_doubleton__eq__iff, fact_280_insert__is__Un, fact_317_notSpecKeysSecretsExpr__def, fact_0_cCompKS, fact_291_sup__bot_Oright__neutral, fact_263_Un__empty__right, fact_93_Set_Oset__insert, fact_11_singletonI, fact_102_insertI1, fact_335_TBtheorem5b__notP2, fact_92_Set_Oset__insert, fact_127_a11, fact_274_singleton__Un__iff, fact_278_Un__singleton__iff, fact_252_Un__absorb, fact_9_correctCompositionKS__negP, fact_271_Expression_Odistinct_I1_J, fact_293_sup__bot_Oright__neutral, fact_228_Un__insert__left, fact_260_KS2Expression_Osimps_I2_J, fact_47_singletonD, fact_7_correctCompositionKS__PQ, fact_234_UnE, fact_140_a11ext, fact_10_correctCompositionKS__negQ, fact_145_is__singleton__def, fact_327_out__exprChannelSet__Single, fact_255_Un__commute, fact_59_equals0I, fact_312_bot__eq__sup__iff, fact_196_TBtheorem4b__notP2, fact_15_singletonI, fact_150_not__know__k__not__ine, fact_176_LocalSecretsComposition1, fact_204_TBtheorem4a__notPQ, fact_241_UnI2, fact_76_insert__commute, fact_200_ine__empty__exprChannelSet, fact_225_Un__insert__right, fact_3_subPQ, fact_143_correctCompositionIn__prop1, fact_78_insert__eq__iff, fact_230_Un__insert__left, fact_270_KS_Odistinct_I1_J, fact_22_insert__iff, fact_296_sup__bot_Oneutr__eq__iff, fact_185_TBtheorem4b__PQ, fact_221_Expression_Oinject_I2_J, fact_213_UnCI, fact_147_Expression_Oinject_I1_J, fact_116_doubleton__eq__iff, fact_53_ex__in__conv, fact_192_LocalSecretsComposition__neg1__k, fact_8_correctCompositionKS__neg1, fact_276_Un__singleton__iff, fact_113_singleton__inject, fact_266_Un__empty__left, fact_112_singleton__inject, fact_209_correctCompositionKS__exprChannel__s__Pex, fact_50_ex__in__conv, fact_149_ineM__ine, fact_226_Un__insert__right, fact_287_LocalSecretsComposition__exprChannel__s, fact_290_correctCompositionKS__exprChannel__s__Qex, fact_222_Un__empty, fact_109_insertE, fact_32_empty__iff, fact_257_Un__left__absorb, fact_180_ineM__L1, fact_84_insert__absorb, fact_288_LocalSecretsComposition__neg, fact_191_TBtheorem4a__notP1, fact_38_all__not__in__conv, fact_326_TBtheorem5a__notPQ, fact_218_Un__iff, fact_115_insert__not__empty, fact_202_ine__exprChannelSingle__def, fact_198_ine__exprChannelSet__Single, fact_65_emptyE, fact_186_TBtheorem4b__P, fact_79_insert__eq__iff, fact_43_singletonD, fact_207_correctCompositionKS__exprChannel__s__P, fact_99_insertI2, fact_83_insert__absorb, fact_171_KS2Expression_Osimps_I1_J, fact_301_sup__bot_Oeq__neutr__iff, fact_182_correctCompositionInLoc__exprChannel, fact_258_Un__left__commute, fact_19_insertCI, fact_286_LocalSecretsComposition__neg1__s, fact_181_ineM__def, fact_77_insert__eq__iff, fact_277_Un__singleton__iff 428.11/126.15 % No. of inferences in proof: 1381 428.11/126.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 125686 ms resp. 124884 ms w/o parsing 428.91/126.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 428.91/126.44 thf(list_S529945141ession_type, type, list_S529945141ession: $tType). 428.91/126.44 thf(set_Secrecy_Secrets_type, type, set_Secrecy_Secrets: $tType). 428.91/126.44 thf(set_Secrecy_specID_type, type, set_Secrecy_specID: $tType). 428.91/126.44 thf(set_Secrecy_chanID_type, type, set_Secrecy_chanID: $tType). 428.91/126.44 thf(set_Secrecy_Keys_type, type, set_Secrecy_Keys: $tType). 428.91/126.44 thf(set_Secrecy_KS_type, type, set_Secrecy_KS: $tType). 428.91/126.44 thf(secrecy_Expression_type, type, secrecy_Expression: $tType). 428.91/126.44 thf(secrecy_Secrets_type, type, secrecy_Secrets: $tType). 428.91/126.44 thf(secrecy_specID_type, type, secrecy_specID: $tType). 428.91/126.44 thf(secrecy_chanID_type, type, secrecy_chanID: $tType). 428.91/126.44 thf(secrecy_Keys_type, type, secrecy_Keys: $tType). 428.91/126.44 thf(secrecy_KS_type, type, secrecy_KS: $tType). 428.91/126.44 thf(nat_type, type, nat: $tType). 428.91/126.44 thf(localSecrets_type, type, localSecrets: (secrecy_specID > set_Secrecy_KS)). 428.91/126.44 thf(knowle945212990e_know_type, type, knowle945212990e_know: (secrecy_specID > (secrecy_KS > $o))). 428.91/126.44 thf(sup_su1301156759ecy_KS_type, type, sup_su1301156759ecy_KS: (set_Secrecy_KS > (set_Secrecy_KS > set_Secrecy_KS))). 428.91/126.44 thf(sup_su370684444chanID_type, type, sup_su370684444chanID: (set_Secrecy_chanID > (set_Secrecy_chanID > set_Secrecy_chanID))). 428.91/126.44 thf(sup_su1712599557specID_type, type, sup_su1712599557specID: (set_Secrecy_specID > (set_Secrecy_specID > set_Secrecy_specID))). 428.91/126.44 thf(mem_Se1967555118ession_type, type, mem_Se1967555118ession: (secrecy_Expression > (list_S529945141ession > $o))). 428.91/126.44 thf(bot_bot_Secrecy_KS_o_type, type, bot_bot_Secrecy_KS_o: (secrecy_KS > $o)). 428.91/126.44 thf(bot_bo1943466239ecy_KS_type, type, bot_bo1943466239ecy_KS: set_Secrecy_KS). 428.91/126.44 thf(bot_bo443197316chanID_type, type, bot_bo443197316chanID: set_Secrecy_chanID). 428.91/126.44 thf(bot_bo1785112429specID_type, type, bot_bo1785112429specID: set_Secrecy_specID). 428.91/126.44 thf(ord_le1802272080chanID_type, type, ord_le1802272080chanID: (set_Secrecy_chanID > (set_Secrecy_chanID > $o))). 428.91/126.44 thf(correctCompositionKS_type, type, correctCompositionKS: (secrecy_specID > $o)). 428.91/126.44 thf(eout_type, type, eout: (secrecy_specID > (secrecy_Expression > $o))). 428.91/126.44 thf(eoutM_type, type, eoutM: (secrecy_specID > (set_Secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(exprChannel_type, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))). 428.91/126.44 thf(ine_type, type, ine: (secrecy_specID > (secrecy_Expression > $o))). 428.91/126.44 thf(ineM_type, type, ineM: (secrecy_specID > (set_Secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(ine_exprChannelSet_type, type, ine_exprChannelSet: (secrecy_specID > (set_Secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(ine_ex1303305700Single_type, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(notSpe1586871396tsExpr_type, type, notSpe1586871396tsExpr: (secrecy_specID > (list_S529945141ession > $o))). 428.91/126.44 thf(out_exprChannelSet_type, type, out_exprChannelSet: (secrecy_specID > (set_Secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(out_ex985543062Single_type, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))). 428.91/126.44 thf(specKeysSecrets_type, type, specKeysSecrets: (secrecy_specID > set_Secrecy_KS)). 428.91/126.44 thf(secrecy_kE_type, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)). 428.91/126.44 thf(secrecy_sE_type, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)). 428.91/126.44 thf(secrec1016742679ession_type, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)). 428.91/126.44 thf(secrecy_kKS_type, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)). 428.91/126.44 thf(secrecy_sKS_type, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)). 428.91/126.44 thf(collect_Secrecy_KS_type, type, collect_Secrecy_KS: ((secrecy_KS > $o) > set_Secrecy_KS)). 428.91/126.44 thf(insert_Secrecy_KS_type, type, insert_Secrecy_KS: (secrecy_KS > (set_Secrecy_KS > set_Secrecy_KS))). 428.91/126.44 thf(insert751661162chanID_type, type, insert751661162chanID: (secrecy_chanID > (set_Secrecy_chanID > set_Secrecy_chanID))). 428.91/126.44 thf(insert1671894227specID_type, type, insert1671894227specID: (secrecy_specID > (set_Secrecy_specID > set_Secrecy_specID))). 428.91/126.44 thf(is_emp1849217361specID_type, type, is_emp1849217361specID: (set_Secrecy_specID > $o)). 428.91/126.44 thf(is_sin1442426433ecy_KS_type, type, is_sin1442426433ecy_KS: (set_Secrecy_KS > $o)). 428.91/126.44 thf(is_sin1501507247specID_type, type, is_sin1501507247specID: (set_Secrecy_specID > $o)). 428.91/126.44 thf(the_el827131246specID_type, type, the_el827131246specID: (set_Secrecy_specID > secrecy_specID)). 428.91/126.44 thf(correctCompositionIn_type, type, correctCompositionIn: (secrecy_specID > $o)). 428.91/126.44 thf(correc965049635ionLoc_type, type, correc965049635ionLoc: (secrecy_specID > $o)). 428.91/126.44 thf(correc990227761ionOut_type, type, correc990227761ionOut: (secrecy_specID > $o)). 428.91/126.44 thf(inStream_type, type, inStream: (secrecy_specID > (set_Secrecy_chanID > $o))). 428.91/126.44 thf(ins_type, type, ins: (secrecy_specID > set_Secrecy_chanID)). 428.91/126.44 thf(loc_type, type, loc: (secrecy_specID > set_Secrecy_chanID)). 428.91/126.44 thf(locStream_type, type, locStream: (secrecy_specID > (set_Secrecy_chanID > $o))). 428.91/126.44 thf(out_type, type, out: (secrecy_specID > set_Secrecy_chanID)). 428.91/126.44 thf(subcomponents_type, type, subcomponents: (secrecy_specID > set_Secrecy_specID)). 428.91/126.44 thf(member_Secrecy_KS_type, type, member_Secrecy_KS: (secrecy_KS > (set_Secrecy_KS > $o))). 428.91/126.44 thf(member1967978193chanID_type, type, member1967978193chanID: (secrecy_chanID > (set_Secrecy_chanID > $o))). 428.91/126.44 thf(member740727610specID_type, type, member740727610specID: (secrecy_specID > (set_Secrecy_specID > $o))). 428.91/126.44 thf(p_type, type, p: secrecy_specID). 428.91/126.44 thf(pq_type, type, pq: secrecy_specID). 428.91/126.44 thf(q_type, type, q: secrecy_specID). 428.91/126.44 thf(key_type, type, key: secrecy_Keys). 428.91/126.44 thf(m_type, type, m: secrecy_KS). 428.91/126.44 thf(sk1_type, type, sk1: (set_Secrecy_chanID > (secrecy_chanID > set_Secrecy_chanID))). 428.91/126.44 thf(sk2_type, type, sk2: (set_Secrecy_chanID > (secrecy_chanID > set_Secrecy_chanID))). 428.91/126.44 thf(sk3_type, type, sk3: (set_Secrecy_specID > secrecy_specID)). 428.91/126.44 thf(sk4_type, type, sk4: (set_Secrecy_specID > (secrecy_specID > set_Secrecy_specID))). 428.91/126.44 thf(sk5_type, type, sk5: (set_Secrecy_specID > (secrecy_specID > set_Secrecy_specID))). 428.91/126.44 thf(sk6_type, type, sk6: (set_Secrecy_chanID > secrecy_chanID)). 428.91/126.44 thf(sk7_type, type, sk7: (set_Secrecy_specID > secrecy_specID)). 428.91/126.44 thf(sk8_type, type, sk8: (set_Secrecy_specID > secrecy_specID)). 428.91/126.44 thf(sk39_type, type, sk39: (set_Secrecy_KS > secrecy_KS)). 428.91/126.44 thf(sk49_type, type, sk49: (secrecy_specID > secrecy_specID)). 428.91/126.44 thf(sk50_type, type, sk50: (secrecy_specID > secrecy_specID)). 428.91/126.44 thf(sk60_type, type, sk60: (secrecy_KS > secrecy_KS)). 428.91/126.44 thf(sk62_type, type, sk62: (secrecy_KS > secrecy_KS)). 428.91/126.44 thf(sk63_type, type, sk63: secrecy_KS). 428.91/126.44 thf(sk65_type, type, sk65: secrecy_KS). 428.91/126.44 thf(251,axiom,((! [A:set_Secrecy_KS]: ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_Collect__mem__eq)). 428.91/126.44 thf(1150,plain,((! [A:set_Secrecy_KS]: ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 428.91/126.44 thf(1151,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) = A))),inference(cnf,[status(esa)],[1150])). 428.91/126.44 thf(1152,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) = A))),inference(lifteq,[status(thm)],[1151])). 428.91/126.44 thf(168,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Un__absorb)). 428.91/126.44 thf(803,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 428.91/126.44 thf(804,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ A @ A) = A))),inference(cnf,[status(esa)],[803])). 428.91/126.44 thf(805,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ A @ A) = A))),inference(lifteq,[status(thm)],[804])). 428.91/126.44 thf(1821,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) = B) | (A != (sup_su1301156759ecy_KS @ B @ B)))),inference(paramod_ordered,[status(thm)],[1152,805])). 428.91/126.44 thf(1822,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ A)))) = A))),inference(pattern_uni,[status(thm)],[1821:[bind(A, $thf(sup_su1301156759ecy_KS @ D @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(1823,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ A)))) = A))),inference(simp,[status(thm)],[1822])). 428.91/126.44 thf(245,axiom,((! [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_singletonI)). 428.91/126.44 thf(1137,plain,((! [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 428.91/126.44 thf(1138,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(cnf,[status(esa)],[1137])). 428.91/126.44 thf(1706,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A)))) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,1138])). 428.91/126.44 thf(1707,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(pattern_uni,[status(thm)],[1706:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(1712,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(simp,[status(thm)],[1707])). 428.91/126.44 thf(266,axiom,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ p)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_notKSP)). 428.91/126.44 thf(1205,plain,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ p)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 428.91/126.44 thf(1206,plain,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ p)))),inference(polarity_switch,[status(thm)],[1205])). 428.91/126.44 thf(2656,plain,(! [A:secrecy_KS] : (((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ m @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1712,1206])). 428.91/126.44 thf(2666,plain,(! [A:secrecy_KS] : ((A != m) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[2656])). 428.91/126.44 thf(2672,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[2666])). 428.91/126.44 thf(5561,plain,(! [A:set_Secrecy_KS] : ((A != (specKeysSecrets @ p)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1823,2672])). 428.91/126.44 thf(5591,plain,(((^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) != (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ p) @ (specKeysSecrets @ p)))))),inference(simp,[status(thm)],[5561])). 428.91/126.44 thf(6059,plain,(((^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) != (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ p))))),inference(rewrite,[status(thm)],[5591,805])). 428.91/126.44 thf(6061,plain,(((member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p)))),inference(func_ext,[status(esa)],[6059])). 428.91/126.44 thf(6085,plain,((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | (~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p)))),inference(bool_ext,[status(thm)],[6061])). 428.91/126.44 thf(3,axiom,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (insert751661162chanID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insert__commute)). 428.91/126.44 thf(270,plain,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (insert751661162chanID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 428.91/126.44 thf(271,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (insert751661162chanID @ A @ C))))),inference(cnf,[status(esa)],[270])). 428.91/126.44 thf(272,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (insert751661162chanID @ A @ C))))),inference(lifteq,[status(thm)],[271])). 428.91/126.44 thf(20,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((insert751661162chanID @ A @ B) != bot_bo443197316chanID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insert__not__empty)). 428.91/126.44 thf(323,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ~ ((insert751661162chanID @ A @ B) = bot_bo443197316chanID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 428.91/126.44 thf(324,plain,((~ (? [A:secrecy_chanID,B:set_Secrecy_chanID]: ((insert751661162chanID @ A @ B) = bot_bo443197316chanID)))),inference(miniscope,[status(thm)],[323])). 428.91/126.44 thf(325,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((~ ((insert751661162chanID @ A @ B) = bot_bo443197316chanID)))),inference(cnf,[status(esa)],[324])). 428.91/126.44 thf(326,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ B) != bot_bo443197316chanID))),inference(lifteq,[status(thm)],[325])). 428.91/126.44 thf(1332,plain,(! [E:set_Secrecy_chanID,D:secrecy_chanID,C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ B @ (insert751661162chanID @ A @ C)) != bot_bo443197316chanID) | ((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) != (insert751661162chanID @ D @ E)))),inference(paramod_ordered,[status(thm)],[272,326])). 428.91/126.44 thf(1333,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ B @ (insert751661162chanID @ A @ C)) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[1332:[bind(A, $thf(A)),bind(B, $thf(F)),bind(C, $thf(G)),bind(D, $thf(A)),bind(E, $thf(insert751661162chanID @ F @ G))]])). 428.91/126.44 thf(1337,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ B @ (insert751661162chanID @ A @ C)) != bot_bo443197316chanID))),inference(simp,[status(thm)],[1333])). 428.91/126.44 thf(6355,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1712,6085])). 428.91/126.44 thf(6365,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | (A != sk63) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[6355])). 428.91/126.44 thf(6387,plain,((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | ((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[6365])). 428.91/126.44 thf(217,axiom,((! [A:secrecy_specID,B:secrecy_Secrets]: ((knowle945212990e_know @ A @ (secrecy_sKS @ B)) = ((ine @ A @ (secrecy_sE @ B)) | (member_Secrecy_KS @ (secrecy_sKS @ B) @ (localSecrets @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_know_Osimps_I2_J)). 428.91/126.44 thf(1024,plain,((! [A:secrecy_specID,B:secrecy_Secrets]: ((knowle945212990e_know @ A @ (secrecy_sKS @ B)) = ((ine @ A @ (secrecy_sE @ B)) | (member_Secrecy_KS @ (secrecy_sKS @ B) @ (localSecrets @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 428.91/126.44 thf(105,axiom,((is_emp1849217361specID = (^ [A:set_Secrecy_specID]: (A = bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Set_Ois__empty__def)). 428.91/126.44 thf(584,plain,(((is_emp1849217361specID) = (^ [A:set_Secrecy_specID]: (A = bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 428.91/126.44 thf(585,plain,(((is_emp1849217361specID) = (^ [A:set_Secrecy_specID]: (A = bot_bo1785112429specID)))),inference(lifteq,[status(thm)],[584])). 428.91/126.44 thf(1215,plain,(! [A:set_Secrecy_specID] : (((is_emp1849217361specID @ A) = (A = bot_bo1785112429specID)))),inference(func_ext,[status(esa)],[585])). 428.91/126.44 thf(37,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_Un__empty__left)). 428.91/126.44 thf(377,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 428.91/126.44 thf(378,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),inference(cnf,[status(esa)],[377])). 428.91/126.44 thf(379,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),inference(lifteq,[status(thm)],[378])). 428.91/126.44 thf(39,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: ((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((B = bot_bo1785112429specID) & (A = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_bot__eq__sup__iff)). 428.91/126.44 thf(382,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: ((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((B = bot_bo1785112429specID) & (A = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 428.91/126.44 thf(383,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((B = bot_bo1785112429specID) & (A = bot_bo1785112429specID))))),inference(cnf,[status(esa)],[382])). 428.91/126.44 thf(384,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((B = bot_bo1785112429specID) & (A = bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[383])). 428.91/126.44 thf(7711,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = A) = ((C = bot_bo1785112429specID) & (B = bot_bo1785112429specID))) | ((sup_su1712599557specID @ bot_bo1785112429specID @ A) != (sup_su1712599557specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[379,384])). 428.91/126.44 thf(7712,plain,(! [A:set_Secrecy_specID] : ((((A = bot_bo1785112429specID) & (bot_bo1785112429specID = bot_bo1785112429specID)) = (bot_bo1785112429specID = A)))),inference(pattern_uni,[status(thm)],[7711:[bind(A, $thf(A)),bind(B, $thf(bot_bo1785112429specID)),bind(C, $thf(A))]])). 428.91/126.44 thf(7833,plain,(! [A:set_Secrecy_specID] : (((A = bot_bo1785112429specID) = (bot_bo1785112429specID = A)))),inference(simp,[status(thm)],[7712])). 428.91/126.44 thf(7854,plain,(! [A:set_Secrecy_specID] : (((is_emp1849217361specID @ A) = (bot_bo1785112429specID = A)))),inference(rewrite,[status(thm)],[1215,7833])). 428.91/126.44 thf(231,axiom,(((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_subPQ)). 428.91/126.44 thf(1080,plain,(((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 428.91/126.44 thf(1081,plain,(((insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)) = (subcomponents @ pq))),inference(lifteq,[status(thm)],[1080])). 428.91/126.44 thf(89,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: (((A = C) <= (~ (member740727610specID @ A @ B))) => (member740727610specID @ A @ (insert1671894227specID @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_insertCI)). 428.91/126.44 thf(536,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: (((A = C) | (member740727610specID @ A @ B)) => (member740727610specID @ A @ (insert1671894227specID @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 428.91/126.44 thf(537,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((~ (A = C)) | (member740727610specID @ A @ (insert1671894227specID @ C @ B)))),inference(cnf,[status(esa)],[536])). 428.91/126.44 thf(539,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((A != C) | (member740727610specID @ A @ (insert1671894227specID @ C @ B)))),inference(lifteq,[status(thm)],[537])). 428.91/126.44 thf(540,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (insert1671894227specID @ B @ A)))),inference(simp,[status(thm)],[539])). 428.91/126.44 thf(1922,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (subcomponents @ pq)) | ((insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)) != (insert1671894227specID @ B @ A)))),inference(paramod_ordered,[status(thm)],[1081,540])). 428.91/126.44 thf(1923,plain,((member740727610specID @ p @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[1922:[bind(A, $thf(insert1671894227specID @ q @ bot_bo1785112429specID)),bind(B, $thf(p))]])). 428.91/126.44 thf(45,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: ((member740727610specID @ A @ B) => (member740727610specID @ A @ (insert1671894227specID @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_insertI2)). 428.91/126.44 thf(399,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: ((member740727610specID @ A @ B) => (member740727610specID @ A @ (insert1671894227specID @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 428.91/126.44 thf(400,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => (! [C:secrecy_specID]: (member740727610specID @ A @ (insert1671894227specID @ C @ B)))))),inference(miniscope,[status(thm)],[399])). 428.91/126.44 thf(401,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | (member740727610specID @ A @ (insert1671894227specID @ C @ B)))),inference(cnf,[status(esa)],[400])). 428.91/126.44 thf(8728,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (insert1671894227specID @ C @ B)) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,401])). 428.91/126.44 thf(8729,plain,(! [A:secrecy_specID] : ((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))))),inference(pattern_uni,[status(thm)],[8728:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(8744,plain,(! [A:secrecy_specID] : ((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))))),inference(simp,[status(thm)],[8729])). 428.91/126.44 thf(33,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) <= (member740727610specID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_UnI1)). 428.91/126.44 thf(364,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) | ~ (member740727610specID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 428.91/126.44 thf(365,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: (! [C:set_Secrecy_specID]: (member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) | ~ (member740727610specID @ A @ B)))),inference(miniscope,[status(thm)],[364])). 428.91/126.44 thf(366,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) | (~ (member740727610specID @ A @ B)))),inference(cnf,[status(esa)],[365])). 428.91/126.44 thf(8759,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((member740727610specID @ B @ (sup_su1712599557specID @ C @ D)) | ((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[8744,366])). 428.91/126.44 thf(8760,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (insert1671894227specID @ B @ (subcomponents @ pq)) @ A)))),inference(pattern_uni,[status(thm)],[8759:[bind(A, $thf(E)),bind(B, $thf(p)),bind(C, $thf(insert1671894227specID @ E @ (subcomponents @ pq))),bind(D, $thf(D))]])). 428.91/126.44 thf(8802,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (insert1671894227specID @ B @ (subcomponents @ pq)) @ A)))),inference(simp,[status(thm)],[8760])). 428.91/126.44 thf(32,axiom,((! [A:secrecy_specID]: ~ (member740727610specID @ A @ bot_bo1785112429specID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_empty__iff)). 428.91/126.44 thf(361,plain,((! [A:secrecy_specID]: ~ (member740727610specID @ A @ bot_bo1785112429specID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 428.91/126.44 thf(362,plain,((~ (? [A:secrecy_specID]: (member740727610specID @ A @ bot_bo1785112429specID)))),inference(miniscope,[status(thm)],[361])). 428.91/126.44 thf(363,plain,(! [A:secrecy_specID] : ((~ (member740727610specID @ A @ bot_bo1785112429specID)))),inference(cnf,[status(esa)],[362])). 428.91/126.44 thf(14850,plain,(! [C:secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (insert1671894227specID @ B @ (subcomponents @ pq)) @ A)) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[8802,363])). 428.91/126.44 thf(14886,plain,(! [C:secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((p != C) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ (subcomponents @ pq)) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[14850])). 428.91/126.44 thf(14922,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ (subcomponents @ pq)) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[14886])). 428.91/126.44 thf(27,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ C @ B)) <= ((member1967978193chanID @ A @ C) <= (~ (member1967978193chanID @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_UnCI)). 428.91/126.44 thf(347,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ C @ B)) | ~ ((member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 428.91/126.44 thf(222,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)) <= ((~ (member_Secrecy_KS @ A @ B)) => (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_insertCI)). 428.91/126.44 thf(1050,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)) | ~ ((~ (member_Secrecy_KS @ A @ B)) => (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 428.91/126.44 thf(1052,plain,(! [C:secrecy_KS,B:set_Secrecy_KS,A:secrecy_KS] : ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)) | (~ (A = C)))),inference(cnf,[status(esa)],[1050])). 428.91/126.44 thf(1053,plain,(! [C:secrecy_KS,B:set_Secrecy_KS,A:secrecy_KS] : ((A != C) | (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)))),inference(lifteq,[status(thm)],[1052])). 428.91/126.44 thf(1054,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)))),inference(simp,[status(thm)],[1053])). 428.91/126.44 thf(6099,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))),inference(paramod_ordered,[status(thm)],[1712,6061])). 428.91/126.44 thf(6108,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | (A != sk63) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))),inference(simp,[status(thm)],[6099])). 428.91/126.44 thf(6112,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS)))) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[6108])). 428.91/126.44 thf(10438,plain,(! [A:set_Secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | (A != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,6112])). 428.91/126.44 thf(10439,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[10438:[bind(A, $thf(insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(10481,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)) != (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1054,10439])). 428.91/126.44 thf(10506,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((sk63 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS) | (B != sk63) | ((insert_Secrecy_KS @ B @ A) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[10481])). 428.91/126.44 thf(10520,plain,(! [A:set_Secrecy_KS] : ((sk63 != m) | ((insert_Secrecy_KS @ sk63 @ A) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[10506])). 428.91/126.44 thf(172,axiom,((locStream = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (loc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_locStream__def)). 428.91/126.44 thf(830,plain,(((locStream) = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (loc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 428.91/126.44 thf(831,plain,(((locStream) = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (loc @ A))))),inference(lifteq,[status(thm)],[830])). 428.91/126.44 thf(1237,plain,(! [A:secrecy_specID] : (((locStream @ A) = ((=) @ set_Secrecy_chanID @ (loc @ A))))),inference(func_ext,[status(esa)],[831])). 428.91/126.44 thf(259,axiom,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ q)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_notKSQ)). 428.91/126.44 thf(1178,plain,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ q)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 428.91/126.44 thf(1179,plain,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ q)))),inference(polarity_switch,[status(thm)],[1178])). 428.91/126.44 thf(94,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (((B != bot_bo443197316chanID) => (ine @ A @ C)) <= (ine_exprChannelSet @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ine__nonempty__exprChannelSet)). 428.91/126.44 thf(553,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (((~ (B = bot_bo443197316chanID)) => (ine @ A @ C)) | ~ (ine_exprChannelSet @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 428.91/126.44 thf(554,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((B = bot_bo443197316chanID) | (ine @ A @ C) | (~ (ine_exprChannelSet @ A @ B @ C)))),inference(cnf,[status(esa)],[553])). 428.91/126.44 thf(555,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((B = bot_bo443197316chanID) | (ine @ A @ C) | (~ (ine_exprChannelSet @ A @ B @ C)))),inference(lifteq,[status(thm)],[554])). 428.91/126.44 thf(72,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_sup__bot__right)). 428.91/126.44 thf(481,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 428.91/126.44 thf(262,axiom,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_chanID]: ((((~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (specKeysSecrets @ B))) => (~ (member1967978193chanID @ C @ (loc @ B)))) <= (exprChannel @ C @ (secrecy_sE @ A))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_LocalSecretsComposition__neg__loc__s)). 428.91/126.44 thf(1190,plain,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_chanID]: (((~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (specKeysSecrets @ B))) => (~ (member1967978193chanID @ C @ (loc @ B)))) | ~ (exprChannel @ C @ (secrecy_sE @ A)) | (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 428.91/126.44 thf(23,axiom,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: (((A != B) => (member1967978193chanID @ A @ C)) <= (member1967978193chanID @ A @ (insert751661162chanID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insertE)). 428.91/126.44 thf(333,plain,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: (((~ (A = B)) => (member1967978193chanID @ A @ C)) | ~ (member1967978193chanID @ A @ (insert751661162chanID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 428.91/126.44 thf(219,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ C))) => (((! [E:secrecy_Secrets]: ((~ (ine @ C @ (secrecy_sE @ E)) & ~ (ine @ B @ (secrecy_sE @ E))) <= (D = (secrecy_sKS @ E)))) => ((~ (member_Secrecy_KS @ D @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C)))))) <= (! [E:secrecy_Keys]: ((~ (ine @ B @ (secrecy_kE @ E)) & ~ (ine @ C @ (secrecy_kE @ E))) <= (D = (secrecy_kKS @ E)))))) <= (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ B)))) <= (correctCompositionKS @ A)) <= (correc965049635ionLoc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_LocalSecretsComposition__neg)). 428.91/126.44 thf(1031,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ C))) => (((! [E:secrecy_Secrets]: ((~ (ine @ C @ (secrecy_sE @ E)) & ~ (ine @ B @ (secrecy_sE @ E))) | ~ (D = (secrecy_sKS @ E)))) => (~ (member_Secrecy_KS @ D @ (localSecrets @ A)) | (member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C))))) | ~ (! [E:secrecy_Keys]: ((~ (ine @ B @ (secrecy_kE @ E)) & ~ (ine @ C @ (secrecy_kE @ E))) | ~ (D = (secrecy_kKS @ E)))))) | (member_Secrecy_KS @ D @ (specKeysSecrets @ B)) | ~ (correctCompositionKS @ A) | ~ (correc965049635ionLoc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 428.91/126.44 thf(82,axiom,((! [A:set_Secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) = (insert1671894227specID @ B @ (sup_su1712599557specID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Un__insert__right)). 428.91/126.44 thf(516,plain,((! [A:set_Secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) = (insert1671894227specID @ B @ (sup_su1712599557specID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 428.91/126.44 thf(517,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) = (insert1671894227specID @ B @ (sup_su1712599557specID @ A @ C))))),inference(cnf,[status(esa)],[516])). 428.91/126.44 thf(518,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((insert1671894227specID @ B @ (sup_su1712599557specID @ A @ C)) = (sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C))))),inference(lifteq,[status(thm)],[517])). 428.91/126.44 thf(43,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) = (insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Un__insert__left)). 428.91/126.44 thf(394,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) = (insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 428.91/126.44 thf(395,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) = (insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C))))),inference(cnf,[status(esa)],[394])). 428.91/126.44 thf(396,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C)) = (sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C)))),inference(lifteq,[status(thm)],[395])). 428.91/126.44 thf(16898,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) = (sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C))))),inference(rewrite,[status(thm)],[518,396])). 428.91/126.44 thf(51,axiom,((sup_su370684444chanID = (^ [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Un__commute)). 428.91/126.44 thf(416,plain,(((sup_su370684444chanID) = (^ [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 428.91/126.44 thf(417,plain,(((sup_su370684444chanID) = (^ [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ A)))),inference(lifteq,[status(thm)],[416])). 428.91/126.44 thf(1211,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A) = (^ [B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ A))))),inference(func_ext,[status(esa)],[417])). 428.91/126.44 thf(84,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => ((insert1671894227specID @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__absorb)). 428.91/126.44 thf(521,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => ((insert1671894227specID @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 428.91/126.44 thf(522,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | ((insert1671894227specID @ A @ B) = B))),inference(cnf,[status(esa)],[521])). 428.91/126.44 thf(523,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ B) = B) | (~ (member740727610specID @ A @ B)))),inference(lifteq,[status(thm)],[522])). 428.91/126.44 thf(263,axiom,((! [A:set_Secrecy_KS]: ((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) => (A = bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_equals0I)). 428.91/126.44 thf(1193,plain,((! [A:set_Secrecy_KS]: ((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) => (A = bot_bo1943466239ecy_KS)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 428.91/126.44 thf(1194,plain,((! [A:set_Secrecy_KS]: ((~ (? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) => (A = bot_bo1943466239ecy_KS)))),inference(miniscope,[status(thm)],[1193])). 428.91/126.44 thf(1195,plain,(! [A:set_Secrecy_KS] : ((member_Secrecy_KS @ (sk39 @ A) @ A) | (A = bot_bo1943466239ecy_KS))),inference(cnf,[status(esa)],[1194])). 428.91/126.44 thf(1196,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | (member_Secrecy_KS @ (sk39 @ A) @ A))),inference(lifteq,[status(thm)],[1195])). 428.91/126.44 thf(1,conjecture,((~ (member_Secrecy_KS @ m @ (specKeysSecrets @ pq)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 428.91/126.44 thf(2,negated_conjecture,((~ (~ (member_Secrecy_KS @ m @ (specKeysSecrets @ pq))))),inference(neg_conjecture,[status(cth)],[1])). 428.91/126.44 thf(268,plain,((~ (~ (member_Secrecy_KS @ m @ (specKeysSecrets @ pq))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 428.91/126.44 thf(269,plain,((member_Secrecy_KS @ m @ (specKeysSecrets @ pq))),inference(polarity_switch,[status(thm)],[268])). 428.91/126.44 thf(210,axiom,((! [A:secrecy_KS]: ~ (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_emptyE)). 428.91/126.44 thf(998,plain,((! [A:secrecy_KS]: ~ (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 428.91/126.44 thf(999,plain,((~ (? [A:secrecy_KS]: (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(miniscope,[status(thm)],[998])). 428.91/126.44 thf(1000,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(cnf,[status(esa)],[999])). 428.91/126.44 thf(1288,plain,(! [A:secrecy_KS] : (((member_Secrecy_KS @ m @ (specKeysSecrets @ pq)) != (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[269,1000])). 428.91/126.44 thf(1289,plain,(! [A:secrecy_KS] : ((m != A) | ((specKeysSecrets @ pq) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1288])). 428.91/126.44 thf(1290,plain,(((specKeysSecrets @ pq) != bot_bo1943466239ecy_KS)),inference(simp,[status(thm)],[1289])). 428.91/126.44 thf(3614,plain,(! [A:set_Secrecy_KS] : ((member_Secrecy_KS @ (sk39 @ A) @ A) | (A != (specKeysSecrets @ pq)))),inference(paramod_ordered,[status(thm)],[1196,1290])). 428.91/126.44 thf(3615,plain,((member_Secrecy_KS @ (sk39 @ (specKeysSecrets @ pq)) @ (specKeysSecrets @ pq))),inference(pattern_uni,[status(thm)],[3614:[bind(A, $thf(specKeysSecrets @ pq))]])). 428.91/126.44 thf(6097,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((member_Secrecy_KS @ (sk39 @ (specKeysSecrets @ pq)) @ (specKeysSecrets @ pq)) != (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[3615,6061])). 428.91/126.44 thf(6106,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((sk39 @ (specKeysSecrets @ pq)) != sk63) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[6097])). 428.91/126.44 thf(5590,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ p) @ (specKeysSecrets @ p))))))),inference(simp,[status(thm)],[5561])). 428.91/126.44 thf(6728,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ p)))))),inference(rewrite,[status(thm)],[5590,805])). 428.91/126.44 thf(6743,plain,(! [A:set_Secrecy_KS] : ((A != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ p))))) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,6728])). 428.91/126.44 thf(6744,plain,(((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ p)))))),inference(pattern_uni,[status(thm)],[6743:[bind(A, $thf(insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(209,axiom,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((((correc965049635ionLoc @ B) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ C))) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ D))) => (ine @ C @ (secrecy_kE @ A)))) <= (~ (ine @ D @ (secrecy_kE @ A))))) <= ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID)))) <= (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_LocalSecretsComposition__ine1__k)). 428.91/126.44 thf(994,plain,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: (((correc965049635ionLoc @ B) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ C))) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ D))) => (ine @ C @ (secrecy_kE @ A)))) | (ine @ D @ (secrecy_kE @ A)))) | ~ ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) | ~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 428.91/126.44 thf(1705,plain,(! [B:secrecy_KS,A:secrecy_KS] : (((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1138,1000])). 428.91/126.44 thf(1711,plain,(! [B:secrecy_KS,A:secrecy_KS] : ((A != B) | ((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1705])). 428.91/126.44 thf(1715,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1711])). 428.91/126.44 thf(1770,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != bot_bo1943466239ecy_KS) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,1715])). 428.91/126.44 thf(1771,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[1770:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(1773,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1771])). 428.91/126.44 thf(5373,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((A != bot_bo1943466239ecy_KS) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1823,1773])). 428.91/126.44 thf(5611,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS))))))),inference(simp,[status(thm)],[5373])). 428.91/126.44 thf(5729,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS))))))),inference(simp,[status(thm)],[5611])). 428.91/126.44 thf(139,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_Un__empty__left)). 428.91/126.44 thf(716,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 428.91/126.44 thf(717,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),inference(cnf,[status(esa)],[716])). 428.91/126.44 thf(718,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),inference(lifteq,[status(thm)],[717])). 428.91/126.44 thf(12089,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))),inference(rewrite,[status(thm)],[5729,718])). 428.91/126.44 thf(15,axiom,((! [A:secrecy_chanID]: (member1967978193chanID @ A @ (insert751661162chanID @ A @ bot_bo443197316chanID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_singletonI)). 428.91/126.44 thf(308,plain,((! [A:secrecy_chanID]: (member1967978193chanID @ A @ (insert751661162chanID @ A @ bot_bo443197316chanID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 428.91/126.44 thf(6664,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,366])). 428.91/126.44 thf(6665,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)))),inference(pattern_uni,[status(thm)],[6664:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(6672,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)))),inference(simp,[status(thm)],[6665])). 428.91/126.44 thf(6682,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[6672,363])). 428.91/126.44 thf(6688,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((p != B) | ((sup_su1712599557specID @ (subcomponents @ pq) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[6682])). 428.91/126.44 thf(6689,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[6688])). 428.91/126.44 thf(17105,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != bot_bo1785112429specID) | ((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != (sup_su1712599557specID @ (subcomponents @ pq) @ D)))),inference(paramod_ordered,[status(thm)],[16898,6689])). 428.91/126.44 thf(17106,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ B) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[17105:[bind(A, $thf(subcomponents @ pq)),bind(B, $thf(F)),bind(C, $thf(G)),bind(D, $thf(insert1671894227specID @ F @ G))]])). 428.91/126.44 thf(17275,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ B) != bot_bo1785112429specID))),inference(simp,[status(thm)],[17106])). 428.91/126.44 thf(143,axiom,((inStream = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (ins @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_inStream__def)). 428.91/126.44 thf(730,plain,(((inStream) = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (ins @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 428.91/126.44 thf(5,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: (member1967978193chanID @ A @ (insert751661162chanID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insertI1)). 428.91/126.44 thf(276,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: (member1967978193chanID @ A @ (insert751661162chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 428.91/126.44 thf(147,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((insert1671894227specID @ A @ (insert1671894227specID @ A @ B)) = (insert1671894227specID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_insert__absorb2)). 428.91/126.44 thf(741,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((insert1671894227specID @ A @ (insert1671894227specID @ A @ B)) = (insert1671894227specID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 428.91/126.44 thf(6678,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (sup_su1712599557specID @ C @ D)) | ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[6672,366])). 428.91/126.44 thf(6679,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ (subcomponents @ pq) @ B) @ A)))),inference(pattern_uni,[status(thm)],[6678:[bind(A, $thf(F)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ (subcomponents @ pq) @ F)),bind(D, $thf(D))]])). 428.91/126.44 thf(6690,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ (subcomponents @ pq) @ B) @ A)))),inference(simp,[status(thm)],[6679])). 428.91/126.44 thf(13403,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ (subcomponents @ pq) @ B) @ A)) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[6690,363])). 428.91/126.44 thf(13432,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : ((p != C) | ((sup_su1712599557specID @ (sup_su1712599557specID @ (subcomponents @ pq) @ B) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[13403])). 428.91/126.44 thf(13462,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (sup_su1712599557specID @ (subcomponents @ pq) @ B) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[13432])). 428.91/126.44 thf(62,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Un__empty)). 428.91/126.44 thf(449,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 428.91/126.44 thf(248,axiom,((correctCompositionKS @ pq)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cCompKS)). 428.91/126.44 thf(1142,plain,((correctCompositionKS @ pq)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 428.91/126.44 thf(166,axiom,((is_sin1501507247specID = (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_is__singleton__the__elem)). 428.91/126.44 thf(798,plain,(((is_sin1501507247specID) = (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 428.91/126.44 thf(799,plain,(((is_sin1501507247specID) = (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[798])). 428.91/126.44 thf(114,axiom,((is_sin1501507247specID = (^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_is__singleton__def)). 428.91/126.44 thf(616,plain,(((is_sin1501507247specID) = (^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 428.91/126.44 thf(617,plain,(((is_sin1501507247specID) = (^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[616])). 428.91/126.44 thf(1268,plain,(((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) = (^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID)))) | ((is_sin1501507247specID) != (is_sin1501507247specID))),inference(paramod_ordered,[status(thm)],[799,617])). 428.91/126.44 thf(1269,plain,(((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) = (^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(pattern_uni,[status(thm)],[1268:[]])). 428.91/126.44 thf(59,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_sup__bot_Oeq__neutr__iff)). 428.91/126.44 thf(440,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 428.91/126.44 thf(124,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: (((((correc990227761ionOut @ E) => ((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ E)) & (member1967978193chanID @ F @ B) & (out_ex985543062Single @ A @ F @ C))) => (~ (eoutM @ E @ B @ C)))) <= ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID)))) <= (~ (eoutM @ D @ B @ C))) <= (eoutM @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_TBtheorem5b__notP1)). 428.91/126.44 thf(655,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: (((correc990227761ionOut @ E) => ((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ E)) & (member1967978193chanID @ F @ B) & (out_ex985543062Single @ A @ F @ C))) => (~ (eoutM @ E @ B @ C)))) | ~ ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) | (eoutM @ D @ B @ C) | ~ (eoutM @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 428.91/126.44 thf(80,axiom,((eout = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (out @ A)) & (exprChannel @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_eout__def)). 428.91/126.44 thf(511,plain,(((eout) = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (out @ A)) & (exprChannel @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 428.91/126.44 thf(34,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => (? [C:set_Secrecy_specID]: (~ (member740727610specID @ A @ C) & (B = (insert1671894227specID @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mk__disjoint__insert)). 428.91/126.44 thf(367,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => (? [C:set_Secrecy_specID]: (~ (member740727610specID @ A @ C) & (B = (insert1671894227specID @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 428.91/126.44 thf(368,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | (~ (member740727610specID @ A @ (sk4 @ B @ A))))),inference(cnf,[status(esa)],[367])). 428.91/126.44 thf(8770,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ B @ (sk4 @ C @ B))) | ((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[8744,368])). 428.91/126.44 thf(8771,plain,(! [A:secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ p))))),inference(pattern_uni,[status(thm)],[8770:[bind(A, $thf(D)),bind(B, $thf(p)),bind(C, $thf(insert1671894227specID @ D @ (subcomponents @ pq)))]])). 428.91/126.44 thf(8789,plain,(! [A:secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ p))))),inference(simp,[status(thm)],[8771])). 428.91/126.44 thf(8899,plain,(! [A:secrecy_specID] : (((member740727610specID @ p @ (sk4 @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ p)) != (member740727610specID @ p @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[1923,8789])). 428.91/126.44 thf(8912,plain,(! [A:secrecy_specID] : ((p != p) | ((sk4 @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[8899])). 428.91/126.44 thf(8928,plain,(! [A:secrecy_specID] : (((sk4 @ (insert1671894227specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[8912])). 428.91/126.44 thf(220,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) <= (member_Secrecy_KS @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_UnI1)). 428.91/126.44 thf(1041,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) | ~ (member_Secrecy_KS @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 428.91/126.44 thf(182,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((((eout @ D @ B) <= (? [E:secrecy_chanID]: (((member1967978193chanID @ E @ (out @ A)) | (member1967978193chanID @ E @ (out @ C))) & ~ (member1967978193chanID @ E @ (loc @ D)) & (exprChannel @ E @ B)))) <= (correc990227761ionOut @ D)) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID)))) <= ((eout @ C @ B) | (eout @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_TBtheorem5a__PQ)). 428.91/126.44 thf(861,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((eout @ D @ B) | ~ (? [E:secrecy_chanID]: (((member1967978193chanID @ E @ (out @ A)) | (member1967978193chanID @ E @ (out @ C))) & ~ (member1967978193chanID @ E @ (loc @ D)) & (exprChannel @ E @ B))) | ~ (correc990227761ionOut @ D) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) | ~ ((eout @ C @ B) | (eout @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 428.91/126.44 thf(5463,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) = B) | ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) != (sup_su1301156759ecy_KS @ B @ B)))),inference(paramod_ordered,[status(thm)],[718,1823])). 428.91/126.44 thf(5464,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) = bot_bo1943466239ecy_KS)),inference(pattern_uni,[status(thm)],[5463:[bind(A, $thf(bot_bo1943466239ecy_KS)),bind(B, $thf(bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(5748,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (($false)))) = bot_bo1943466239ecy_KS)),inference(rewrite,[status(thm)],[5464,1000])). 428.91/126.44 thf(1776,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != bot_bo1943466239ecy_KS) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,1773])). 428.91/126.44 thf(1777,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[1776:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),bind(B, $thf(B))]])). 428.91/126.44 thf(1781,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1777])). 428.91/126.44 thf(1797,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A))))))))) != bot_bo1943466239ecy_KS) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,1781])). 428.91/126.44 thf(1798,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[1797:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(1806,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1798])). 428.91/126.44 thf(5772,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,1806])). 428.91/126.44 thf(5814,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))) != (^ [B:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5772])). 428.91/126.44 thf(40,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_sup__bot_Oneutr__eq__iff)). 428.91/126.44 thf(385,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 428.91/126.44 thf(5783,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,1781])). 428.91/126.44 thf(5800,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))) != (^ [B:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5783])). 428.91/126.44 thf(6026,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk62 @ A) @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(func_ext,[status(esa)],[5800])). 428.91/126.44 thf(13285,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((member_Secrecy_KS @ (sk62 @ B) @ A) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,6026])). 428.91/126.44 thf(13286,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk62 @ A) @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(pattern_uni,[status(thm)],[13285:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(13317,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk62 @ A) @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(simp,[status(thm)],[13286])). 428.91/126.44 thf(88,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_sup__eq__bot__iff)). 428.91/126.44 thf(533,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 428.91/126.44 thf(47,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) => ((A != B) => (member740727610specID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insertE)). 428.91/126.44 thf(404,plain,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) => ((~ (A = B)) => (member740727610specID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 428.91/126.44 thf(405,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (insert1671894227specID @ B @ C))) | (A = B) | (member740727610specID @ A @ C))),inference(cnf,[status(esa)],[404])). 428.91/126.44 thf(406,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((A = B) | (~ (member740727610specID @ A @ (insert1671894227specID @ B @ C))) | (member740727610specID @ A @ C))),inference(lifteq,[status(thm)],[405])). 428.91/126.44 thf(1217,plain,(((member_Secrecy_KS @ m @ (specKeysSecrets @ pq)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ p)))),inference(paramod_ordered,[status(thm)],[269,1206])). 428.91/126.44 thf(1219,plain,((m != m) | ((specKeysSecrets @ pq) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[1217])). 428.91/126.44 thf(1221,plain,(((specKeysSecrets @ pq) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[1219])). 428.91/126.44 thf(1240,plain,((pq != p)),inference(simp,[status(thm)],[1221])). 428.91/126.44 thf(9312,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (insert1671894227specID @ B @ C))) | (member740727610specID @ A @ C) | (B != p) | (A != pq))),inference(paramod_ordered,[status(thm)],[406,1240])). 428.91/126.44 thf(9313,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ pq @ (insert1671894227specID @ A @ B))) | (member740727610specID @ pq @ B) | (A != p))),inference(pattern_uni,[status(thm)],[9312:[bind(A, $thf(pq))]])). 428.91/126.44 thf(9458,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ pq @ (insert1671894227specID @ p @ A))) | (member740727610specID @ pq @ A))),inference(simp,[status(thm)],[9313])). 428.91/126.44 thf(9723,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (member740727610specID @ pq @ A) | ((insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)) != (insert1671894227specID @ p @ A)))),inference(paramod_ordered,[status(thm)],[1081,9458])). 428.91/126.44 thf(9724,plain,((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (member740727610specID @ pq @ (insert1671894227specID @ q @ bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[9723:[bind(A, $thf(insert1671894227specID @ q @ bot_bo1785112429specID))]])). 428.91/126.44 thf(9772,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (A = B) | (member740727610specID @ A @ C) | ((member740727610specID @ pq @ (insert1671894227specID @ q @ bot_bo1785112429specID)) != (member740727610specID @ A @ (insert1671894227specID @ B @ C))))),inference(paramod_ordered,[status(thm)],[9724,406])). 428.91/126.44 thf(9773,plain,((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (q = pq) | (member740727610specID @ pq @ bot_bo1785112429specID)),inference(pattern_uni,[status(thm)],[9772:[bind(A, $thf(pq)),bind(B, $thf(q)),bind(C, $thf(bot_bo1785112429specID))]])). 428.91/126.44 thf(9929,plain,((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (q = pq) | ($false)),inference(rewrite,[status(thm)],[9773,363])). 428.91/126.44 thf(9930,plain,((~ (member740727610specID @ pq @ (subcomponents @ pq))) | (q = pq)),inference(simp,[status(thm)],[9929])). 428.91/126.44 thf(1216,plain,(((member_Secrecy_KS @ m @ (specKeysSecrets @ q)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ pq)))),inference(paramod_ordered,[status(thm)],[269,1179])). 428.91/126.44 thf(1218,plain,((m != m) | ((specKeysSecrets @ q) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[1216])). 428.91/126.44 thf(1220,plain,(((specKeysSecrets @ q) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[1218])). 428.91/126.44 thf(1222,plain,((q != pq)),inference(simp,[status(thm)],[1220])). 428.91/126.44 thf(9931,plain,((~ (member740727610specID @ pq @ (subcomponents @ pq)))),inference(simplifyReflect,[status(thm)],[9930,1222])). 428.91/126.44 thf(9938,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ B @ (insert1671894227specID @ B @ A)) != (member740727610specID @ pq @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[540,9931])). 428.91/126.44 thf(9957,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((B != pq) | ((insert1671894227specID @ B @ A) != (subcomponents @ pq)))),inference(simp,[status(thm)],[9938])). 428.91/126.44 thf(9969,plain,(! [A:set_Secrecy_specID] : (((insert1671894227specID @ pq @ A) != (subcomponents @ pq)))),inference(simp,[status(thm)],[9957])). 428.91/126.44 thf(10163,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) != (subcomponents @ pq)) | ((insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C)) != (insert1671894227specID @ pq @ D)))),inference(paramod_ordered,[status(thm)],[396,9969])). 428.91/126.44 thf(10164,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ pq @ A) @ B) != (subcomponents @ pq)))),inference(pattern_uni,[status(thm)],[10163:[bind(A, $thf(pq)),bind(B, $thf(E)),bind(C, $thf(F)),bind(D, $thf(sup_su1712599557specID @ E @ F))]])). 428.91/126.44 thf(10174,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ pq @ A) @ B) != (subcomponents @ pq)))),inference(simp,[status(thm)],[10164])). 428.91/126.44 thf(10753,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : ((A != (subcomponents @ pq)) | ((sup_su1712599557specID @ bot_bo1785112429specID @ A) != (sup_su1712599557specID @ (insert1671894227specID @ pq @ B) @ C)))),inference(paramod_ordered,[status(thm)],[379,10174])). 428.91/126.44 thf(10768,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((insert1671894227specID @ pq @ A) != bot_bo1785112429specID) | (B != (subcomponents @ pq)))),inference(simp,[status(thm)],[10753])). 428.91/126.44 thf(10772,plain,(! [A:set_Secrecy_specID] : (((insert1671894227specID @ pq @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[10768])). 428.91/126.44 thf(93,axiom,((! [A:set_Secrecy_specID]: ((! [B:secrecy_specID]: ~ (member740727610specID @ B @ A)) = (A = bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_all__not__in__conv)). 428.91/126.44 thf(550,plain,((! [A:set_Secrecy_specID]: ((! [B:secrecy_specID]: ~ (member740727610specID @ B @ A)) = (A = bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 428.91/126.44 thf(12106,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)))) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,12089])). 428.91/126.44 thf(12107,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))),inference(pattern_uni,[status(thm)],[12106:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(12120,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[12107])). 428.91/126.44 thf(12126,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(rewrite,[status(thm)],[12120,1000])). 428.91/126.44 thf(49,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) = ((member740727610specID @ A @ C) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_insert__iff)). 428.91/126.44 thf(410,plain,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) = ((member740727610specID @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 428.91/126.44 thf(411,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : (((member740727610specID @ A @ (insert1671894227specID @ B @ C)) = ((member740727610specID @ A @ C) | (A = B))))),inference(cnf,[status(esa)],[410])). 428.91/126.44 thf(412,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : (((member740727610specID @ A @ (insert1671894227specID @ B @ C)) = ((member740727610specID @ A @ C) | (A = B))))),inference(lifteq,[status(thm)],[411])). 428.91/126.44 thf(55,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => (~ (! [C:set_Secrecy_specID]: ((member740727610specID @ A @ C) <= (B = (insert1671894227specID @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Set_Oset__insert)). 428.91/126.44 thf(425,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((member740727610specID @ A @ B) => (~ (! [C:set_Secrecy_specID]: ((member740727610specID @ A @ C) | ~ (B = (insert1671894227specID @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 428.91/126.44 thf(426,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | (~ (member740727610specID @ A @ (sk5 @ B @ A))))),inference(cnf,[status(esa)],[425])). 428.91/126.44 thf(10944,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (sk5 @ B @ A))) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,426])). 428.91/126.44 thf(10945,plain,((~ (member740727610specID @ p @ (sk5 @ (subcomponents @ pq) @ p)))),inference(pattern_uni,[status(thm)],[10944:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(10994,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ ((member740727610specID @ A @ C) | (A = B))) | ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) != (member740727610specID @ p @ (sk5 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[412,10945])). 428.91/126.44 thf(11010,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ ((member740727610specID @ A @ C) | (A = B))) | (A != p) | ((insert1671894227specID @ B @ C) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[10994])). 428.91/126.44 thf(11017,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ B @ C) != (sk5 @ (subcomponents @ pq) @ p)) | (A != p) | (~ (A = B)))),inference(cnf,[status(esa)],[11010])). 428.91/126.44 thf(11019,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((A != B) | ((insert1671894227specID @ B @ C) != (sk5 @ (subcomponents @ pq) @ p)) | (A != p))),inference(lifteq,[status(thm)],[11017])). 428.91/126.44 thf(11020,plain,(! [A:set_Secrecy_specID] : (((insert1671894227specID @ p @ A) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[11019])). 428.91/126.44 thf(69,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (sup_su370684444chanID @ A @ B)) = (sup_su370684444chanID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Un__left__absorb)). 428.91/126.44 thf(470,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (sup_su370684444chanID @ A @ B)) = (sup_su370684444chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 428.91/126.44 thf(471,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (sup_su370684444chanID @ A @ B)) = (sup_su370684444chanID @ A @ B)))),inference(cnf,[status(esa)],[470])). 428.91/126.44 thf(472,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (sup_su370684444chanID @ A @ B)) = (sup_su370684444chanID @ A @ B)))),inference(lifteq,[status(thm)],[471])). 428.91/126.44 thf(1979,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1054,1206])). 428.91/126.44 thf(1984,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((B != m) | ((insert_Secrecy_KS @ B @ A) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[1979])). 428.91/126.44 thf(1986,plain,(! [A:set_Secrecy_KS] : (((insert_Secrecy_KS @ m @ A) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[1984])). 428.91/126.44 thf(2152,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (specKeysSecrets @ p)) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,1986])). 428.91/126.44 thf(2153,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A)))) != (specKeysSecrets @ p)))),inference(pattern_uni,[status(thm)],[2152:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(2154,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A)))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[2153])). 428.91/126.44 thf(2163,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (specKeysSecrets @ p)) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1152,2154])). 428.91/126.44 thf(2164,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))))) != (specKeysSecrets @ p)))),inference(pattern_uni,[status(thm)],[2163:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))),bind(B, $thf(B))]])). 428.91/126.44 thf(2168,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[2164])). 428.91/126.44 thf(50,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) <= (member740727610specID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_UnI2)). 428.91/126.44 thf(413,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | ~ (member740727610specID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 428.91/126.44 thf(414,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: (! [C:set_Secrecy_specID]: (member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | ~ (member740727610specID @ A @ B)))),inference(miniscope,[status(thm)],[413])). 428.91/126.44 thf(415,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | (~ (member740727610specID @ A @ B)))),inference(cnf,[status(esa)],[414])). 428.91/126.44 thf(10246,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,415])). 428.91/126.44 thf(10247,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))))),inference(pattern_uni,[status(thm)],[10246:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(10261,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))))),inference(simp,[status(thm)],[10247])). 428.91/126.44 thf(10301,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ B @ (sk4 @ C @ B))) | ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[10261,368])). 428.91/126.44 thf(10302,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p))))),inference(pattern_uni,[status(thm)],[10301:[bind(A, $thf(D)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ D @ (subcomponents @ pq)))]])). 428.91/126.44 thf(10337,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p))))),inference(simp,[status(thm)],[10302])). 428.91/126.44 thf(10576,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p)) != (member740727610specID @ p @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[1923,10337])). 428.91/126.44 thf(10580,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sk4 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[10576])). 428.91/126.44 thf(10594,plain,(! [A:set_Secrecy_specID] : (((sk4 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[10580])). 428.91/126.44 thf(128,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sup__bot__right)). 428.91/126.44 thf(670,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 428.91/126.44 thf(2655,plain,(! [A:secrecy_KS] : (((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ m @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1712,1179])). 428.91/126.44 thf(2667,plain,(! [A:secrecy_KS] : ((A != m) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[2655])). 428.91/126.44 thf(2673,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ q))),inference(simp,[status(thm)],[2667])). 428.91/126.44 thf(5405,plain,(! [A:set_Secrecy_KS] : ((A != (specKeysSecrets @ q)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1823,2673])). 428.91/126.44 thf(5593,plain,(((^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) != (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ q) @ (specKeysSecrets @ q)))))),inference(simp,[status(thm)],[5405])). 428.91/126.44 thf(6241,plain,(((^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) != (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ q))))),inference(rewrite,[status(thm)],[5593,805])). 428.91/126.44 thf(149,axiom,((! [A:secrecy_specID]: (is_sin1501507247specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_is__singletonI)). 428.91/126.44 thf(746,plain,((! [A:secrecy_specID]: (is_sin1501507247specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 428.91/126.44 thf(747,plain,(! [A:secrecy_specID] : ((is_sin1501507247specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(cnf,[status(esa)],[746])). 428.91/126.44 thf(190,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((~ (eout @ D @ B)) <= (? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (loc @ D)) & (out_ex985543062Single @ A @ E @ B)))) <= (correc990227761ionOut @ D))) <= (~ (eout @ C @ B))) <= (eout @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_TBtheorem5a__notP1)). 428.91/126.44 thf(913,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (~ (eout @ D @ B) | ~ (? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (loc @ D)) & (out_ex985543062Single @ A @ E @ B))) | ~ (correc990227761ionOut @ D))) | (eout @ C @ B) | ~ (eout @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 428.91/126.44 thf(211,axiom,((bot_bot_Secrecy_KS_o = (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bot__empty__eq)). 428.91/126.44 thf(1001,plain,(((bot_bot_Secrecy_KS_o) = (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 428.91/126.44 thf(1924,plain,(! [C:secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ B @ (insert1671894227specID @ B @ A)) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[540,363])). 428.91/126.44 thf(1925,plain,(! [C:secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((B != C) | ((insert1671894227specID @ B @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[1924])). 428.91/126.44 thf(1926,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((insert1671894227specID @ B @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[1925])). 428.91/126.44 thf(8287,plain,(! [E:secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) != bot_bo1785112429specID) | ((insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C)) != (insert1671894227specID @ E @ D)))),inference(paramod_ordered,[status(thm)],[396,1926])). 428.91/126.44 thf(8288,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[8287:[bind(A, $thf(A)),bind(B, $thf(F)),bind(C, $thf(G)),bind(D, $thf(sup_su1712599557specID @ F @ G)),bind(E, $thf(A))]])). 428.91/126.44 thf(8329,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) != bot_bo1785112429specID))),inference(simp,[status(thm)],[8288])). 428.91/126.44 thf(19339,plain,(! [F:set_Secrecy_specID,E:set_Secrecy_specID,D:secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ (insert1671894227specID @ D @ E) @ F)))),inference(paramod_ordered,[status(thm)],[16898,8329])). 428.91/126.44 thf(19340,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[19339:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(B)),bind(E, $thf(A)),bind(F, $thf(C))]])). 428.91/126.44 thf(19954,plain,(! [F:set_Secrecy_specID,E:secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != bot_bo1785112429specID) | ((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != (sup_su1712599557specID @ D @ (insert1671894227specID @ E @ F))))),inference(paramod_ordered,[status(thm)],[16898,19340])). 428.91/126.44 thf(19955,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[19954:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(B)),bind(F, $thf(C))]])). 428.91/126.44 thf(6848,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (sk4 @ B @ A))) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,368])). 428.91/126.44 thf(6849,plain,((~ (member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p)))),inference(pattern_uni,[status(thm)],[6848:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(6897,plain,(((member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p)) != (member740727610specID @ p @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[1923,6849])). 428.91/126.44 thf(6900,plain,((p != p) | ((sk4 @ (subcomponents @ pq) @ p) != (subcomponents @ pq))),inference(simp,[status(thm)],[6897])). 428.91/126.44 thf(6909,plain,(((sk4 @ (subcomponents @ pq) @ p) != (subcomponents @ pq))),inference(simp,[status(thm)],[6900])). 428.91/126.44 thf(6243,plain,(((member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q)))),inference(func_ext,[status(esa)],[6241])). 428.91/126.44 thf(6268,plain,((member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))),inference(bool_ext,[status(thm)],[6243])). 428.91/126.44 thf(14,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C) = (insert751661162chanID @ A @ (sup_su370684444chanID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Un__insert__left)). 428.91/126.44 thf(305,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C) = (insert751661162chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 428.91/126.44 thf(306,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C) = (insert751661162chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(cnf,[status(esa)],[305])). 428.91/126.44 thf(307,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (sup_su370684444chanID @ B @ C)) = (sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C)))),inference(lifteq,[status(thm)],[306])). 428.91/126.44 thf(4,axiom,((! [A:set_Secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (sup_su370684444chanID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Un__insert__right)). 428.91/126.44 thf(273,plain,((! [A:set_Secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (sup_su370684444chanID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 428.91/126.44 thf(274,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) = (insert751661162chanID @ B @ (sup_su370684444chanID @ A @ C))))),inference(cnf,[status(esa)],[273])). 428.91/126.44 thf(275,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((insert751661162chanID @ B @ (sup_su370684444chanID @ A @ C)) = (sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C))))),inference(lifteq,[status(thm)],[274])). 428.91/126.44 thf(2227,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ B @ (insert751661162chanID @ A @ C)) = (sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C)))),inference(rewrite,[status(thm)],[307,275])). 428.91/126.44 thf(10996,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ p @ (sk5 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[6672,10945])). 428.91/126.44 thf(11015,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[10996])). 428.91/126.44 thf(11024,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[11015])). 428.91/126.44 thf(30,axiom,((! [A:set_Secrecy_specID]: ((? [B:secrecy_specID]: (member740727610specID @ B @ A)) = (A != bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_ex__in__conv)). 428.91/126.44 thf(356,plain,((! [A:set_Secrecy_specID]: ((? [B:secrecy_specID]: (member740727610specID @ B @ A)) = (~ (A = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 428.91/126.44 thf(357,plain,(! [A:set_Secrecy_specID] : (((? [B:secrecy_specID]: (member740727610specID @ B @ A)) = (~ (A = bot_bo1785112429specID))))),inference(cnf,[status(esa)],[356])). 428.91/126.44 thf(358,plain,(! [A:set_Secrecy_specID] : (((? [B:secrecy_specID]: (member740727610specID @ B @ A)) = (~ (A = bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[357])). 428.91/126.44 thf(7856,plain,(! [A:set_Secrecy_specID] : (((? [B:secrecy_specID]: (member740727610specID @ B @ A)) = (~ (bot_bo1785112429specID = A))))),inference(rewrite,[status(thm)],[358,7833])). 428.91/126.44 thf(19,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: (((insert751661162chanID @ A @ B) = B) <= (member1967978193chanID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__absorb)). 428.91/126.44 thf(320,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: (((insert751661162chanID @ A @ B) = B) | ~ (member1967978193chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 428.91/126.44 thf(5399,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : ((A != (specKeysSecrets @ p)) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1823,2154])). 428.91/126.44 thf(5633,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ p) @ (specKeysSecrets @ p))))))),inference(simp,[status(thm)],[5399])). 428.91/126.44 thf(5645,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ p) @ (specKeysSecrets @ p))))))),inference(simp,[status(thm)],[5633])). 428.91/126.44 thf(9614,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ p)))))),inference(rewrite,[status(thm)],[5645,805])). 428.91/126.44 thf(9615,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (B)) != (^ [B:secrecy_KS]: (B))) | ((^ [B:secrecy_KS]: (insert_Secrecy_KS @ m @ A)) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(simp,[status(thm)],[9614])). 428.91/126.44 thf(9626,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (insert_Secrecy_KS @ m @ A)) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(simp,[status(thm)],[9615])). 428.91/126.44 thf(9632,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))) != (^ [C:secrecy_KS]: (specKeysSecrets @ p))) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,9626])). 428.91/126.44 thf(9633,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(pattern_uni,[status(thm)],[9632:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(9634,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(simp,[status(thm)],[9633])). 428.91/126.44 thf(9650,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))) != (^ [C:secrecy_KS]: (specKeysSecrets @ p))) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1152,9634])). 428.91/126.44 thf(9651,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(pattern_uni,[status(thm)],[9650:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))),bind(B, $thf(B))]])). 428.91/126.44 thf(9657,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ p))))),inference(simp,[status(thm)],[9651])). 428.91/126.44 thf(57,axiom,((! [A:set_Secrecy_chanID,B:secrecy_chanID]: ((A = bot_bo443197316chanID) => (~ (member1967978193chanID @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equals0D)). 428.91/126.44 thf(432,plain,((! [A:set_Secrecy_chanID,B:secrecy_chanID]: ((A = bot_bo443197316chanID) => (~ (member1967978193chanID @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 428.91/126.44 thf(433,plain,((! [A:set_Secrecy_chanID]: ((A = bot_bo443197316chanID) => (~ (? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)))))),inference(miniscope,[status(thm)],[432])). 428.91/126.44 thf(434,plain,(! [B:secrecy_chanID,A:set_Secrecy_chanID] : ((~ (A = bot_bo443197316chanID)) | (~ (member1967978193chanID @ B @ A)))),inference(cnf,[status(esa)],[433])). 428.91/126.44 thf(435,plain,(! [B:secrecy_chanID,A:set_Secrecy_chanID] : ((A != bot_bo443197316chanID) | (~ (member1967978193chanID @ B @ A)))),inference(lifteq,[status(thm)],[434])). 428.91/126.44 thf(436,plain,(! [A:secrecy_chanID] : ((~ (member1967978193chanID @ A @ bot_bo443197316chanID)))),inference(simp,[status(thm)],[435])). 428.91/126.44 thf(9621,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))))) != (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (specKeysSecrets @ p)))) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,9614])). 428.91/126.44 thf(9622,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A)))))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ p)))))),inference(pattern_uni,[status(thm)],[9621:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(9625,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A)))))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ p)))))),inference(simp,[status(thm)],[9622])). 428.91/126.44 thf(450,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : ((((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(cnf,[status(esa)],[449])). 428.91/126.44 thf(451,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : ((((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(lifteq,[status(thm)],[450])). 428.91/126.44 thf(61,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Un__absorb)). 428.91/126.44 thf(446,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 428.91/126.44 thf(447,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ A) = A))),inference(cnf,[status(esa)],[446])). 428.91/126.44 thf(448,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ A) = A))),inference(lifteq,[status(thm)],[447])). 428.91/126.44 thf(386,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(cnf,[status(esa)],[385])). 428.91/126.44 thf(387,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(lifteq,[status(thm)],[386])). 428.91/126.44 thf(7965,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((bot_bo443197316chanID = A) = ((C = bot_bo443197316chanID) & (B = bot_bo443197316chanID))) | ((sup_su370684444chanID @ A @ A) != (sup_su370684444chanID @ B @ C)))),inference(paramod_ordered,[status(thm)],[448,387])). 428.91/126.44 thf(7966,plain,(! [A:set_Secrecy_chanID] : ((((A = bot_bo443197316chanID) & (A = bot_bo443197316chanID)) = (bot_bo443197316chanID = A)))),inference(pattern_uni,[status(thm)],[7965:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(A))]])). 428.91/126.44 thf(8130,plain,(! [A:set_Secrecy_chanID] : (((A = bot_bo443197316chanID) = (bot_bo443197316chanID = A)))),inference(simp,[status(thm)],[7966])). 428.91/126.44 thf(12212,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((bot_bo443197316chanID = B) & (bot_bo443197316chanID = A))))),inference(rewrite,[status(thm)],[451,8130])). 428.91/126.44 thf(1980,plain,(! [C:secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : (((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)) != (member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1054,1000])). 428.91/126.44 thf(1985,plain,(! [C:secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : ((B != C) | ((insert_Secrecy_KS @ B @ A) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1980])). 428.91/126.44 thf(1987,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((insert_Secrecy_KS @ B @ A) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1985])). 428.91/126.44 thf(2158,plain,(! [C:secrecy_KS,B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))) != bot_bo1943466239ecy_KS) | (A != (insert_Secrecy_KS @ C @ B)))),inference(paramod_ordered,[status(thm)],[1152,1987])). 428.91/126.44 thf(2159,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B)))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[2158:[bind(A, $thf(insert_Secrecy_KS @ D @ E)),bind(B, $thf(E)),bind(C, $thf(D))]])). 428.91/126.44 thf(2160,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B)))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[2159])). 428.91/126.44 thf(5520,plain,(! [C:set_Secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : ((A != bot_bo1943466239ecy_KS) | ((collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))))),inference(paramod_ordered,[status(thm)],[1823,2160])). 428.91/126.44 thf(5624,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B))) != (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[5520])). 428.91/126.44 thf(5742,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B))) != (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[5624])). 428.91/126.44 thf(12994,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B))) != (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))))),inference(rewrite,[status(thm)],[5742,718])). 428.91/126.44 thf(12995,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (C)) != (^ [C:secrecy_KS]: (C))) | ((^ [C:secrecy_KS]: (insert_Secrecy_KS @ A @ B)) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[12994])). 428.91/126.44 thf(13003,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (insert_Secrecy_KS @ A @ B)) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[12995])). 428.91/126.44 thf(13012,plain,(! [C:set_Secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : (((^ [D:secrecy_KS]: (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A)))) != (^ [D:secrecy_KS]: (bot_bo1943466239ecy_KS))) | (A != (insert_Secrecy_KS @ B @ C)))),inference(paramod_ordered,[status(thm)],[1152,13003])). 428.91/126.44 thf(13013,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[13012:[bind(A, $thf(insert_Secrecy_KS @ D @ E)),bind(B, $thf(D)),bind(C, $thf(E))]])). 428.91/126.44 thf(13016,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[13013])). 428.91/126.44 thf(13241,plain,(! [C:set_Secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : (((^ [D:secrecy_KS]: (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A)))) != (^ [D:secrecy_KS]: (bot_bo1943466239ecy_KS))) | (A != (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))))),inference(paramod_ordered,[status(thm)],[1152,13016])). 428.91/126.44 thf(13242,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ B)))))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[13241:[bind(A, $thf(collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))),bind(B, $thf(B)),bind(C, $thf(C))]])). 428.91/126.44 thf(13251,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ B)))))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[13242])). 428.91/126.44 thf(176,axiom,((! [A:secrecy_Secrets]: ((secrec1016742679ession @ (secrecy_sKS @ A)) = (secrecy_sE @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_KS2Expression_Osimps_I2_J)). 428.91/126.44 thf(841,plain,((! [A:secrecy_Secrets]: ((secrec1016742679ession @ (secrecy_sKS @ A)) = (secrecy_sE @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 428.91/126.44 thf(1265,plain,(! [A:set_Secrecy_specID] : (((is_sin1501507247specID @ A) = (? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID)))))),inference(func_ext,[status(esa)],[617])). 428.91/126.44 thf(223,axiom,((! [A:secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: (((A != B) => (member_Secrecy_KS @ A @ C)) <= (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_insertE)). 428.91/126.44 thf(1055,plain,((! [A:secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: (((~ (A = B)) => (member_Secrecy_KS @ A @ C)) | ~ (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 428.91/126.44 thf(100,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_sup__bot_Oleft__neutral)). 428.91/126.44 thf(570,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 428.91/126.44 thf(140,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: (((((correctCompositionIn @ E) => (~ (ineM @ E @ B @ C))) <= ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID)))) <= (~ (ineM @ D @ B @ C))) <= (~ (ineM @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_TBtheorem3b)). 428.91/126.44 thf(719,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: (((correctCompositionIn @ E) => (~ (ineM @ E @ B @ C))) | ~ ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) | (ineM @ D @ B @ C) | (ineM @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 428.91/126.44 thf(175,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: (((sup_su1712599557specID @ A @ B) = (insert1671894227specID @ C @ bot_bo1785112429specID)) = (((B = (insert1671894227specID @ C @ bot_bo1785112429specID)) & (A = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((B = bot_bo1785112429specID) & (A = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((B = (insert1671894227specID @ C @ bot_bo1785112429specID)) & (A = bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Un__singleton__iff)). 428.91/126.44 thf(838,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID]: (((sup_su1712599557specID @ A @ B) = (insert1671894227specID @ C @ bot_bo1785112429specID)) = (((B = (insert1671894227specID @ C @ bot_bo1785112429specID)) & (A = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((B = bot_bo1785112429specID) & (A = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((B = (insert1671894227specID @ C @ bot_bo1785112429specID)) & (A = bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 428.91/126.44 thf(66,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) <= ((~ (member740727610specID @ A @ B)) => (member740727610specID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_UnCI)). 428.91/126.44 thf(460,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | ~ ((~ (member740727610specID @ A @ B)) => (member740727610specID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 428.91/126.44 thf(2332,plain,(! [C:set_Secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : ((A != bot_bo1943466239ecy_KS) | ((collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))) != (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))))),inference(paramod_ordered,[status(thm)],[1152,2160])). 428.91/126.44 thf(2333,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((insert_Secrecy_KS @ A @ B) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[2332:[bind(A, $thf(insert_Secrecy_KS @ D @ E)),bind(B, $thf(D)),bind(C, $thf(E))]])). 428.91/126.44 thf(2339,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((insert_Secrecy_KS @ A @ B) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[2333])). 428.91/126.44 thf(161,axiom,((! [A:secrecy_specID,B:secrecy_Keys]: ((~ (knowle945212990e_know @ A @ (secrecy_kKS @ B))) => (~ (ine @ A @ (secrecy_kE @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_not__know__k__not__ine)). 428.91/126.44 thf(785,plain,((! [A:secrecy_specID,B:secrecy_Keys]: ((~ (knowle945212990e_know @ A @ (secrecy_kKS @ B))) => (~ (ine @ A @ (secrecy_kE @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 428.91/126.44 thf(191,axiom,((! [A:secrecy_Keys]: ((secrec1016742679ession @ (secrecy_kKS @ A)) = (secrecy_kE @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_KS2Expression_Osimps_I1_J)). 428.91/126.44 thf(917,plain,((! [A:secrecy_Keys]: ((secrec1016742679ession @ (secrecy_kKS @ A)) = (secrecy_kE @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 428.91/126.44 thf(152,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((correc990227761ionOut @ D) => (((loc @ D) = bot_bo443197316chanID) => (eout @ D @ B))) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID)))) <= ((eout @ A @ B) | (eout @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_TBtheorem5a__empty)). 428.91/126.44 thf(751,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((correc990227761ionOut @ D) => (((loc @ D) = bot_bo443197316chanID) => (eout @ D @ B))) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) | ~ ((eout @ A @ B) | (eout @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 428.91/126.44 thf(244,axiom,((! [A:set_Secrecy_KS,B:secrecy_KS]: ((~ (member_Secrecy_KS @ B @ A)) <= (A = bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_equals0D)). 428.91/126.44 thf(1132,plain,((! [A:set_Secrecy_KS,B:secrecy_KS]: (~ (member_Secrecy_KS @ B @ A) | ~ (A = bot_bo1943466239ecy_KS)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 428.91/126.44 thf(10308,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (sup_su1712599557specID @ D @ C)) | ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[10261,415])). 428.91/126.44 thf(10309,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ B @ (subcomponents @ pq)))))),inference(pattern_uni,[status(thm)],[10308:[bind(A, $thf(E)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ E @ (subcomponents @ pq))),bind(D, $thf(D))]])). 428.91/126.44 thf(10322,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ B @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[10309])). 428.91/126.44 thf(15226,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ B @ (subcomponents @ pq)))) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[10322,363])). 428.91/126.44 thf(15243,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : ((p != C) | ((sup_su1712599557specID @ A @ (sup_su1712599557specID @ B @ (subcomponents @ pq))) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15226])). 428.91/126.44 thf(15264,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (sup_su1712599557specID @ B @ (subcomponents @ pq))) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15243])). 428.91/126.44 thf(119,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((eoutM @ A @ B @ C) => ((((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (out @ E)) & ~ (member1967978193chanID @ F @ (loc @ D)) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C))) => (eoutM @ D @ B @ C)) <= (correc990227761ionOut @ D)) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ E @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_TBtheore54b__P)). 428.91/126.44 thf(638,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((eoutM @ A @ B @ C) => (((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (out @ E)) & ~ (member1967978193chanID @ F @ (loc @ D)) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C))) => (eoutM @ D @ B @ C)) | ~ (correc990227761ionOut @ D) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ E @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 428.91/126.44 thf(250,axiom,((! [A:set_Secrecy_KS]: ((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) = (A = bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_all__not__in__conv)). 428.91/126.44 thf(1147,plain,((! [A:set_Secrecy_KS]: ((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) = (A = bot_bo1943466239ecy_KS)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 428.91/126.44 thf(204,axiom,((notSpe1586871396tsExpr = (^ [A:secrecy_specID,B:list_S529945141ession]: (! [C:secrecy_Keys]: ((~ (member_Secrecy_KS @ (secrecy_kKS @ C) @ (specKeysSecrets @ A))) <= (mem_Se1967555118ession @ (secrecy_kE @ C) @ B)) & ! [C:secrecy_Secrets]: ((~ (member_Secrecy_KS @ (secrecy_sKS @ C) @ (specKeysSecrets @ A))) <= (mem_Se1967555118ession @ (secrecy_sE @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_notSpecKeysSecretsExpr__def)). 428.91/126.44 thf(969,plain,(((notSpe1586871396tsExpr) = (^ [A:secrecy_specID,B:list_S529945141ession]: (! [C:secrecy_Keys]: (~ (member_Secrecy_KS @ (secrecy_kKS @ C) @ (specKeysSecrets @ A)) | ~ (mem_Se1967555118ession @ (secrecy_kE @ C) @ B)) & ! [C:secrecy_Secrets]: (~ (member_Secrecy_KS @ (secrecy_sKS @ C) @ (specKeysSecrets @ A)) | ~ (mem_Se1967555118ession @ (secrecy_sE @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 428.91/126.44 thf(7,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (? [C:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ C) & (B = (insert751661162chanID @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mk__disjoint__insert)). 428.91/126.44 thf(283,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (? [C:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ C) & (B = (insert751661162chanID @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 428.91/126.44 thf(284,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((~ (member1967978193chanID @ A @ B)) | (~ (member1967978193chanID @ A @ (sk1 @ B @ A))))),inference(cnf,[status(esa)],[283])). 428.91/126.44 thf(26,axiom,((! [A:set_Secrecy_specID]: ((A = bot_bo1785112429specID) <= (! [B:secrecy_specID]: ~ (member740727610specID @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_equals0I)). 428.91/126.44 thf(343,plain,((! [A:set_Secrecy_specID]: ((A = bot_bo1785112429specID) | ~ (! [B:secrecy_specID]: ~ (member740727610specID @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 428.91/126.44 thf(344,plain,((! [A:set_Secrecy_specID]: ((A = bot_bo1785112429specID) | ~ (~ (? [B:secrecy_specID]: (member740727610specID @ B @ A)))))),inference(miniscope,[status(thm)],[343])). 428.91/126.44 thf(345,plain,(! [A:set_Secrecy_specID] : ((A = bot_bo1785112429specID) | (member740727610specID @ (sk3 @ A) @ A))),inference(cnf,[status(esa)],[344])). 428.91/126.44 thf(346,plain,(! [A:set_Secrecy_specID] : ((A = bot_bo1785112429specID) | (member740727610specID @ (sk3 @ A) @ A))),inference(lifteq,[status(thm)],[345])). 428.91/126.44 thf(157,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: ((insert1671894227specID @ A @ B) != bot_bo1785112429specID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insert__not__empty)). 428.91/126.44 thf(772,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: ~ ((insert1671894227specID @ A @ B) = bot_bo1785112429specID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 428.91/126.44 thf(773,plain,((~ (? [A:secrecy_specID,B:set_Secrecy_specID]: ((insert1671894227specID @ A @ B) = bot_bo1785112429specID)))),inference(miniscope,[status(thm)],[772])). 428.91/126.44 thf(774,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ ((insert1671894227specID @ A @ B) = bot_bo1785112429specID)))),inference(cnf,[status(esa)],[773])). 428.91/126.44 thf(775,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ B) != bot_bo1785112429specID))),inference(lifteq,[status(thm)],[774])). 428.91/126.44 thf(1363,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((subcomponents @ pq) != bot_bo1785112429specID) | ((insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)) != (insert1671894227specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1081,775])). 428.91/126.44 thf(1364,plain,(((subcomponents @ pq) != bot_bo1785112429specID)),inference(pattern_uni,[status(thm)],[1363:[bind(A, $thf(p)),bind(B, $thf(insert1671894227specID @ q @ bot_bo1785112429specID))]])). 428.91/126.44 thf(2733,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ A) @ A) | (A != (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[346,1364])). 428.91/126.44 thf(2734,plain,((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[2733:[bind(A, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(9937,plain,(((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ pq @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[2734,9931])). 428.91/126.44 thf(9967,plain,(((sk3 @ (subcomponents @ pq)) != pq) | ((subcomponents @ pq) != (subcomponents @ pq))),inference(simp,[status(thm)],[9937])). 428.91/126.44 thf(9973,plain,(((sk3 @ (subcomponents @ pq)) != pq)),inference(simp,[status(thm)],[9967])). 428.91/126.44 thf(17,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (~ (! [C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ C) <= (B = (insert751661162chanID @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Set_Oset__insert)). 428.91/126.44 thf(313,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (~ (! [C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ C) | ~ (B = (insert751661162chanID @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 428.91/126.44 thf(315,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((~ (member1967978193chanID @ A @ B)) | (B = (insert751661162chanID @ A @ (sk2 @ B @ A))))),inference(cnf,[status(esa)],[313])). 428.91/126.44 thf(316,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (sk2 @ B @ A)) = B) | (~ (member1967978193chanID @ A @ B)))),inference(lifteq,[status(thm)],[315])). 428.91/126.44 thf(17661,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ B) = B) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,523])). 428.91/126.44 thf(17662,plain,(((insert1671894227specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[17661:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(10462,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | (sk63 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS)),inference(simp,[status(thm)],[10439])). 428.91/126.44 thf(10527,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | (sk63 != m)),inference(simp,[status(thm)],[10462])). 428.91/126.44 thf(5756,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,1773])). 428.91/126.44 thf(5807,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5756])). 428.91/126.44 thf(5868,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk60 @ A) @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(func_ext,[status(esa)],[5807])). 428.91/126.44 thf(10480,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1712,10439])). 428.91/126.44 thf(10494,plain,(! [A:secrecy_KS] : ((sk63 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS) | (A != sk63) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[10480])). 428.91/126.44 thf(10534,plain,((sk63 != m) | ((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[10494])). 428.91/126.44 thf(237,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) = ((member_Secrecy_KS @ A @ C) | (member_Secrecy_KS @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_Un__iff)). 428.91/126.44 thf(1100,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) = ((member_Secrecy_KS @ A @ C) | (member_Secrecy_KS @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 428.91/126.44 thf(369,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | (B = (insert1671894227specID @ A @ (sk4 @ B @ A))))),inference(cnf,[status(esa)],[367])). 428.91/126.44 thf(370,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk4 @ B @ A)) = B) | (~ (member740727610specID @ A @ B)))),inference(lifteq,[status(thm)],[369])). 428.91/126.44 thf(7031,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk4 @ B @ A)) = B) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,370])). 428.91/126.44 thf(7032,plain,(((insert1671894227specID @ p @ (sk4 @ (subcomponents @ pq) @ p)) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[7031:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(193,axiom,((! [A:secrecy_KS]: ((! [B:secrecy_Keys]: (A != (secrecy_kKS @ B))) => (~ (! [B:secrecy_Secrets]: (A != (secrecy_sKS @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_KS_Oexhaust)). 428.91/126.44 thf(924,plain,((! [A:secrecy_KS]: ((! [B:secrecy_Keys]: ~ (A = (secrecy_kKS @ B))) => (~ (! [B:secrecy_Secrets]: ~ (A = (secrecy_sKS @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 428.91/126.44 thf(74,axiom,((! [A:set_Secrecy_specID]: (((! [B:secrecy_specID,C:secrecy_specID]: (((member740727610specID @ C @ A) => (B = C)) <= (member740727610specID @ B @ A))) => (is_sin1501507247specID @ A)) <= (A != bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_is__singletonI_H)). 428.91/126.44 thf(487,plain,((! [A:set_Secrecy_specID]: (((! [B:secrecy_specID,C:secrecy_specID]: (((member740727610specID @ C @ A) => (B = C)) | ~ (member740727610specID @ B @ A))) => (is_sin1501507247specID @ A)) | (A = bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 428.91/126.44 thf(488,plain,((! [A:set_Secrecy_specID]: (((! [B:secrecy_specID]: (! [C:secrecy_specID]: ((member740727610specID @ C @ A) => (B = C)) | ~ (member740727610specID @ B @ A))) => (is_sin1501507247specID @ A)) | (A = bot_bo1785112429specID)))),inference(miniscope,[status(thm)],[487])). 428.91/126.44 thf(489,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk7 @ A) @ A) | (is_sin1501507247specID @ A) | (A = bot_bo1785112429specID))),inference(cnf,[status(esa)],[488])). 428.91/126.44 thf(492,plain,(! [A:set_Secrecy_specID] : ((A = bot_bo1785112429specID) | (member740727610specID @ (sk7 @ A) @ A) | (is_sin1501507247specID @ A))),inference(lifteq,[status(thm)],[489])). 428.91/126.44 thf(1704,plain,(! [A:secrecy_KS] : (((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1138,1206])). 428.91/126.44 thf(1710,plain,(! [A:secrecy_KS] : ((A != m) | ((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[1704])). 428.91/126.44 thf(1714,plain,(((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ p))),inference(simp,[status(thm)],[1710])). 428.91/126.44 thf(60,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_sup__bot_Oeq__neutr__iff)). 428.91/126.44 thf(443,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 428.91/126.44 thf(1904,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A))))))))) != bot_bo1943466239ecy_KS) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,1806])). 428.91/126.44 thf(1905,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))))))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[1904:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),bind(B, $thf(B))]])). 428.91/126.44 thf(1911,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))))))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[1905])). 428.91/126.44 thf(240,axiom,((! [A:set_Secrecy_KS]: ((A != bot_bo1943466239ecy_KS) => ((! [B:secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ B @ A) => ((B = C) <= (member_Secrecy_KS @ C @ A)))) => (is_sin1442426433ecy_KS @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_is__singletonI_H)). 428.91/126.44 thf(1109,plain,((! [A:set_Secrecy_KS]: ((~ (A = bot_bo1943466239ecy_KS)) => ((! [B:secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ B @ A) => ((B = C) | ~ (member_Secrecy_KS @ C @ A)))) => (is_sin1442426433ecy_KS @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 428.91/126.44 thf(36,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C)) = (sup_su370684444chanID @ B @ (sup_su370684444chanID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Un__left__commute)). 428.91/126.44 thf(374,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C)) = (sup_su370684444chanID @ B @ (sup_su370684444chanID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 428.91/126.44 thf(375,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C)) = (sup_su370684444chanID @ B @ (sup_su370684444chanID @ A @ C))))),inference(cnf,[status(esa)],[374])). 428.91/126.44 thf(376,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C)) = (sup_su370684444chanID @ B @ (sup_su370684444chanID @ A @ C))))),inference(lifteq,[status(thm)],[375])). 428.91/126.44 thf(121,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_sup__bot_Oright__neutral)). 428.91/126.44 thf(646,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 428.91/126.44 thf(551,plain,(! [A:set_Secrecy_specID] : (((! [B:secrecy_specID]: ~ (member740727610specID @ B @ A)) = (A = bot_bo1785112429specID)))),inference(cnf,[status(esa)],[550])). 428.91/126.44 thf(552,plain,(! [A:set_Secrecy_specID] : (((! [B:secrecy_specID]: ~ (member740727610specID @ B @ A)) = (A = bot_bo1785112429specID)))),inference(lifteq,[status(thm)],[551])). 428.91/126.44 thf(2539,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((~ (! [C:secrecy_specID]: ~ (member740727610specID @ C @ A))) = (? [C:secrecy_specID]: (member740727610specID @ C @ B))) | ((A = bot_bo1785112429specID) != (B = bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[552,358])). 428.91/126.44 thf(2540,plain,(! [A:set_Secrecy_specID] : (((~ (! [B:secrecy_specID]: ~ (member740727610specID @ B @ A))) = (? [B:secrecy_specID]: (member740727610specID @ B @ A))))),inference(pattern_uni,[status(thm)],[2539:[bind(A, $thf(A)),bind(B, $thf(A))]])). 428.91/126.44 thf(169,axiom,((! [A:secrecy_chanID,B:secrecy_Secrets,C:secrecy_specID,D:secrecy_specID]: ((((~ (ine @ D @ (secrecy_sE @ B))) => (~ (member1967978193chanID @ A @ (ins @ C)) & ~ (member1967978193chanID @ A @ (ins @ D)))) <= (~ (ine @ C @ (secrecy_sE @ B)))) <= (exprChannel @ A @ (secrecy_sE @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_LocalSecretsComposition__exprChannel__s)). 428.91/126.44 thf(806,plain,((! [A:secrecy_chanID,B:secrecy_Secrets,C:secrecy_specID,D:secrecy_specID]: (((~ (ine @ D @ (secrecy_sE @ B))) => (~ (member1967978193chanID @ A @ (ins @ C)) & ~ (member1967978193chanID @ A @ (ins @ D)))) | (ine @ C @ (secrecy_sE @ B)) | ~ (exprChannel @ A @ (secrecy_sE @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 428.91/126.44 thf(29,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ (sup_su370684444chanID @ A @ B) @ C) = (sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Un__assoc)). 428.91/126.44 thf(353,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((sup_su370684444chanID @ (sup_su370684444chanID @ A @ B) @ C) = (sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 428.91/126.44 thf(203,axiom,((! [A:secrecy_KS,B:secrecy_KS]: ((A = B) <= (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_singletonD)). 428.91/126.44 thf(966,plain,((! [A:secrecy_KS,B:secrecy_KS]: ((A = B) | ~ (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 428.91/126.44 thf(16933,plain,(! [E:set_Secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != (subcomponents @ pq)) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ (insert1671894227specID @ pq @ D) @ E)))),inference(paramod_ordered,[status(thm)],[16898,10174])). 428.91/126.44 thf(16934,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ pq @ B)) != (subcomponents @ pq)))),inference(pattern_uni,[status(thm)],[16933:[bind(A, $thf(A)),bind(B, $thf(pq)),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(C))]])). 428.91/126.44 thf(17210,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ pq @ B)) != (subcomponents @ pq)))),inference(simp,[status(thm)],[16934])). 428.91/126.44 thf(10933,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ B @ (sk5 @ C @ B))) | ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[10261,426])). 428.91/126.44 thf(10934,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p))))),inference(pattern_uni,[status(thm)],[10933:[bind(A, $thf(D)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ D @ (subcomponents @ pq)))]])). 428.91/126.44 thf(10986,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p))))),inference(simp,[status(thm)],[10934])). 428.91/126.44 thf(11497,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p)) != (member740727610specID @ p @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[1923,10986])). 428.91/126.44 thf(11506,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sk5 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[11497])). 428.91/126.44 thf(11523,plain,(! [A:set_Secrecy_specID] : (((sk5 @ (sup_su1712599557specID @ A @ (subcomponents @ pq)) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[11506])). 428.91/126.44 thf(118,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((correctCompositionIn @ A) => (((member1967978193chanID @ D @ (ins @ B)) | (member1967978193chanID @ D @ (ins @ C))) <= (member1967978193chanID @ D @ (ins @ A)))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_correctCompositionIn__prop1)). 428.91/126.44 thf(634,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((correctCompositionIn @ A) => ((member1967978193chanID @ D @ (ins @ B)) | (member1967978193chanID @ D @ (ins @ C)) | ~ (member1967978193chanID @ D @ (ins @ A)))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 428.91/126.44 thf(185,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID,G:set_Secrecy_chanID]: ((((out_exprChannelSet @ B @ D @ E) => (((((~ (eoutM @ A @ G @ E)) <= (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ (loc @ A)) <= (member1967978193chanID @ H @ F)))) <= (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ D) => (member1967978193chanID @ H @ (loc @ A))))) <= (G = (sup_su370684444chanID @ D @ F))) <= (out_exprChannelSet @ C @ F @ E))) <= (correc990227761ionOut @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_TBtheorem5b__notPQ)). 428.91/126.44 thf(877,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID,G:set_Secrecy_chanID]: (((out_exprChannelSet @ B @ D @ E) => (~ (eoutM @ A @ G @ E) | ~ (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ (loc @ A)) | ~ (member1967978193chanID @ H @ F))) | ~ (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ D) => (member1967978193chanID @ H @ (loc @ A)))) | ~ (G = (sup_su370684444chanID @ D @ F)) | ~ (out_exprChannelSet @ C @ F @ E))) | ~ (correc990227761ionOut @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 428.91/126.44 thf(10,axiom,((! [A:secrecy_chanID,B:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_singleton__iff)). 428.91/126.44 thf(293,plain,((! [A:secrecy_chanID,B:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 428.91/126.44 thf(6840,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ B @ (sk4 @ C @ B))) | ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[6672,368])). 428.91/126.44 thf(6841,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p))))),inference(pattern_uni,[status(thm)],[6840:[bind(A, $thf(E)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ (subcomponents @ pq) @ E))]])). 428.91/126.44 thf(6881,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p))))),inference(simp,[status(thm)],[6841])). 428.91/126.44 thf(7177,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sk4 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p)) != (member740727610specID @ p @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[1923,6881])). 428.91/126.44 thf(7183,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sk4 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[7177])). 428.91/126.44 thf(7194,plain,(! [A:set_Secrecy_specID] : (((sk4 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[7183])). 428.91/126.44 thf(1978,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1054,1179])). 428.91/126.44 thf(1983,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((B != m) | ((insert_Secrecy_KS @ B @ A) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[1978])). 428.91/126.44 thf(1989,plain,(! [A:set_Secrecy_KS] : (((insert_Secrecy_KS @ m @ A) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[1983])). 428.91/126.44 thf(2155,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (specKeysSecrets @ q)) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,1989])). 428.91/126.44 thf(2156,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A)))) != (specKeysSecrets @ q)))),inference(pattern_uni,[status(thm)],[2155:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(2157,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A)))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[2156])). 428.91/126.44 thf(5431,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : ((A != (specKeysSecrets @ q)) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1823,2157])). 428.91/126.44 thf(5635,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ q) @ (specKeysSecrets @ q))))))),inference(simp,[status(thm)],[5431])). 428.91/126.44 thf(5648,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ q) @ (specKeysSecrets @ q))))))),inference(simp,[status(thm)],[5635])). 428.91/126.44 thf(9905,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ A))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ q)))))),inference(rewrite,[status(thm)],[5648,805])). 428.91/126.44 thf(9906,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (B)) != (^ [B:secrecy_KS]: (B))) | ((^ [B:secrecy_KS]: (insert_Secrecy_KS @ m @ A)) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(simp,[status(thm)],[9905])). 428.91/126.44 thf(9914,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (insert_Secrecy_KS @ m @ A)) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(simp,[status(thm)],[9906])). 428.91/126.44 thf(208,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: ((((((exprChannel @ E @ (secrecy_kE @ D)) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => ((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ A)) & (exprChannel @ F @ (secrecy_kE @ D)))) <= (correctCompositionIn @ A)))) <= (member1967978193chanID @ E @ (ins @ C))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A)))) <= (correctCompositionKS @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_correctCompositionKS__exprChannel__k__Qex)). 428.91/126.44 thf(988,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((exprChannel @ E @ (secrecy_kE @ D)) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => (? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ A)) & (exprChannel @ F @ (secrecy_kE @ D))) | ~ (correctCompositionIn @ A)))) | ~ (member1967978193chanID @ E @ (ins @ C)) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A)) | ~ (correctCompositionKS @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 428.91/126.44 thf(78,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Un__iff)). 428.91/126.44 thf(505,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 428.91/126.44 thf(506,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))))),inference(cnf,[status(esa)],[505])). 428.91/126.44 thf(507,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))))),inference(lifteq,[status(thm)],[506])). 428.91/126.44 thf(16,axiom,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_insert__iff)). 428.91/126.44 thf(310,plain,((! [A:secrecy_chanID,B:secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 428.91/126.44 thf(311,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((member1967978193chanID @ A @ (insert751661162chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (A = B))))),inference(cnf,[status(esa)],[310])). 428.91/126.44 thf(312,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((member1967978193chanID @ A @ (insert751661162chanID @ B @ C)) = ((member1967978193chanID @ A @ C) | (A = B))))),inference(lifteq,[status(thm)],[311])). 428.91/126.44 thf(427,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | (B = (insert1671894227specID @ A @ (sk5 @ B @ A))))),inference(cnf,[status(esa)],[425])). 428.91/126.44 thf(428,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk5 @ B @ A)) = B) | (~ (member740727610specID @ A @ B)))),inference(lifteq,[status(thm)],[427])). 428.91/126.44 thf(11241,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk5 @ B @ A)) = B) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,428])). 428.91/126.44 thf(11242,plain,(((insert1671894227specID @ (sk3 @ (subcomponents @ pq)) @ (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[11241:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(44,axiom,((out_ex985543062Single = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((member1967978193chanID @ B @ (out @ A)) & ! [D:secrecy_chanID,E:nat]: ((~ (exprChannel @ D @ C)) <= ((member1967978193chanID @ D @ (out @ A)) & (D != B))) & (exprChannel @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_out__exprChannelSingle__def)). 428.91/126.44 thf(397,plain,(((out_ex985543062Single) = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((member1967978193chanID @ B @ (out @ A)) & ! [D:secrecy_chanID]: (~ (exprChannel @ D @ C) | ~ ((member1967978193chanID @ D @ (out @ A)) & ~ (D = B))) & (exprChannel @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 428.91/126.44 thf(131,axiom,((sup_su1301156759ecy_KS = (^ [A:set_Secrecy_KS,B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Un__commute)). 428.91/126.44 thf(678,plain,(((sup_su1301156759ecy_KS) = (^ [A:set_Secrecy_KS,B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 428.91/126.44 thf(679,plain,(((sup_su1301156759ecy_KS) = (^ [A:set_Secrecy_KS,B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ A)))),inference(lifteq,[status(thm)],[678])). 428.91/126.44 thf(1213,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ A) = (^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ A))))),inference(func_ext,[status(esa)],[679])). 428.91/126.44 thf(151,axiom,((insert_Secrecy_KS = (^ [A:secrecy_KS]: (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_insert__is__Un)). 428.91/126.44 thf(749,plain,(((insert_Secrecy_KS) = (^ [A:secrecy_KS]: (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 428.91/126.44 thf(750,plain,(((insert_Secrecy_KS) = (^ [A:secrecy_KS]: (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))),inference(lifteq,[status(thm)],[749])). 428.91/126.44 thf(1263,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ A) = (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))),inference(func_ext,[status(esa)],[750])). 428.91/126.44 thf(1935,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((^ [C:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ C @ A)) = (insert_Secrecy_KS @ B)) | ((sup_su1301156759ecy_KS @ A) != (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),inference(paramod_ordered,[status(thm)],[1213,1263])). 428.91/126.44 thf(1936,plain,(! [A:secrecy_KS] : (((^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) = (insert_Secrecy_KS @ A)))),inference(pattern_uni,[status(thm)],[1935:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(1943,plain,(! [A:secrecy_KS] : (((^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) = (insert_Secrecy_KS @ A)))),inference(simp,[status(thm)],[1936])). 428.91/126.44 thf(265,axiom,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B)) => (((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ B) => ((((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ D))) => (ine @ D @ (secrecy_kE @ A))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ C)))) <= (~ (ine @ C @ (secrecy_kE @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_LocalSecretsComposition__ine2__k)). 428.91/126.44 thf(1201,plain,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B)) => (((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ B) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ D))) => (ine @ D @ (secrecy_kE @ A))) | (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ C)) | (ine @ C @ (secrecy_kE @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 428.91/126.44 thf(9912,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))))) != (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (specKeysSecrets @ q)))) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,9905])). 428.91/126.44 thf(9913,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A)))))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ q)))))),inference(pattern_uni,[status(thm)],[9912:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(9917,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A)))))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ q)))))),inference(simp,[status(thm)],[9913])). 428.91/126.44 thf(192,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((subcomponents @ A) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correc990227761ionOut @ A) => ((eout @ C @ B) | (eout @ D @ B)))) <= (eout @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_TBtheorem2a)). 428.91/126.44 thf(920,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((subcomponents @ A) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correc990227761ionOut @ A) => ((eout @ C @ B) | (eout @ D @ B)))) | ~ (eout @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 428.91/126.44 thf(38,axiom,((eoutM = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (out @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_eoutM__def)). 428.91/126.44 thf(380,plain,(((eoutM) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (out @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 428.91/126.44 thf(164,axiom,((! [A:secrecy_specID,B:secrecy_specID]: ((A = B) <= (member740727610specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_singletonD)). 428.91/126.44 thf(793,plain,((! [A:secrecy_specID,B:secrecy_specID]: ((A = B) | ~ (member740727610specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 428.91/126.44 thf(6281,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))),inference(paramod_ordered,[status(thm)],[1712,6243])). 428.91/126.44 thf(6290,plain,(! [A:secrecy_KS] : ((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | (A != sk65) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))),inference(simp,[status(thm)],[6281])). 428.91/126.44 thf(6296,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS)))) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[6290])). 428.91/126.44 thf(252,axiom,((! [A:secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ C)) = ((member_Secrecy_KS @ A @ C) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_insert__iff)). 428.91/126.44 thf(1153,plain,((! [A:secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ C)) = ((member_Secrecy_KS @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 428.91/126.44 thf(381,plain,(((eoutM) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (out @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),inference(lifteq,[status(thm)],[380])). 428.91/126.44 thf(13050,plain,(! [A:set_Secrecy_KS] : ((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | (A != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,6296])). 428.91/126.44 thf(13051,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[13050:[bind(A, $thf(insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(5612,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[5373])). 428.91/126.44 thf(5730,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[5612])). 428.91/126.44 thf(6298,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),inference(rewrite,[status(thm)],[5730,718])). 428.91/126.44 thf(6299,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (B)) != (^ [B:secrecy_KS]: (B))) | ((^ [B:secrecy_KS]: (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[6298])). 428.91/126.44 thf(6316,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[6299])). 428.91/126.44 thf(6328,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,6316])). 428.91/126.44 thf(6329,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[6328:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(6334,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[6329])). 428.91/126.44 thf(6518,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A))))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,6334])). 428.91/126.44 thf(6519,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[6518:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(6531,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[6519])). 428.91/126.44 thf(6560,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (collect_Secrecy_KS @ (^ [F:secrecy_KS]: (member_Secrecy_KS @ F @ A)))))))))) != (^ [C:secrecy_KS]: (bot_bo1943466239ecy_KS))) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,6531])). 428.91/126.44 thf(6561,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[6560:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(6571,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))))) != (^ [B:secrecy_KS]: (bot_bo1943466239ecy_KS))))),inference(simp,[status(thm)],[6561])). 428.91/126.44 thf(228,axiom,((! [A:secrecy_KS,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ A @ (localSecrets @ B)) => ((member_Secrecy_KS @ A @ (localSecrets @ C)) <= ((subcomponents @ C) = (insert1671894227specID @ B @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_LocalSecretsComposition1)). 428.91/126.44 thf(1067,plain,((! [A:secrecy_KS,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ A @ (localSecrets @ B)) => ((member_Secrecy_KS @ A @ (localSecrets @ C)) | ~ ((subcomponents @ C) = (insert1671894227specID @ B @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 428.91/126.44 thf(63,axiom,((! [A:secrecy_chanID]: ~ (member1967978193chanID @ A @ bot_bo443197316chanID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_empty__iff)). 428.91/126.44 thf(452,plain,((! [A:secrecy_chanID]: ~ (member1967978193chanID @ A @ bot_bo443197316chanID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 428.91/126.44 thf(512,plain,(((eout) = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (out @ A)) & (exprChannel @ C @ B))))),inference(lifteq,[status(thm)],[511])). 428.91/126.44 thf(196,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((ine @ D @ B) <= ((loc @ D) = bot_bo443197316chanID)) <= (correctCompositionIn @ D))) <= ((ine @ A @ B) | (ine @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_TBtheorem4a__empty)). 428.91/126.44 thf(942,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((ine @ D @ B) | ~ ((loc @ D) = bot_bo443197316chanID) | ~ (correctCompositionIn @ D))) | ~ ((ine @ A @ B) | (ine @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 428.91/126.44 thf(491,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk8 @ A) @ A) | (is_sin1501507247specID @ A) | (A = bot_bo1785112429specID))),inference(cnf,[status(esa)],[488])). 428.91/126.44 thf(494,plain,(! [A:set_Secrecy_specID] : ((A = bot_bo1785112429specID) | (member740727610specID @ (sk8 @ A) @ A) | (is_sin1501507247specID @ A))),inference(lifteq,[status(thm)],[491])). 428.91/126.44 thf(15835,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk8 @ A) @ A) | (is_sin1501507247specID @ A) | (A != (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[494,1364])). 428.91/126.44 thf(15836,plain,((member740727610specID @ (sk8 @ (subcomponents @ pq)) @ (subcomponents @ pq)) | (is_sin1501507247specID @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[15835:[bind(A, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(16352,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((member740727610specID @ (sk8 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ pq @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[15836,9931])). 428.91/126.44 thf(16391,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((sk8 @ (subcomponents @ pq)) != pq) | ((subcomponents @ pq) != (subcomponents @ pq))),inference(simp,[status(thm)],[16352])). 428.91/126.44 thf(16401,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((sk8 @ (subcomponents @ pq)) != pq)),inference(simp,[status(thm)],[16391])). 428.91/126.44 thf(87,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: (((((insert1671894227specID @ A @ B) = (insert1671894227specID @ A @ C)) = (B = C)) <= (~ (member740727610specID @ A @ C))) <= (~ (member740727610specID @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__ident)). 428.91/126.44 thf(529,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ A @ C)) = (B = C)) | (member740727610specID @ A @ C) | (member740727610specID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 428.91/126.44 thf(170,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID,G:set_Secrecy_chanID]: ((((ine_exprChannelSet @ B @ D @ E) => ((ine_exprChannelSet @ C @ F @ E) => ((! [H:secrecy_chanID]: ((member1967978193chanID @ H @ D) => (member1967978193chanID @ H @ (loc @ A)))) => ((~ (ineM @ A @ G @ E)) <= (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ F) => (member1967978193chanID @ H @ (loc @ A)))))))) <= (correctCompositionIn @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_TBtheorem4b__notPQ)). 428.91/126.44 thf(810,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID,G:set_Secrecy_chanID]: (((ine_exprChannelSet @ B @ D @ E) => ((ine_exprChannelSet @ C @ F @ E) => ((! [H:secrecy_chanID]: ((member1967978193chanID @ H @ D) => (member1967978193chanID @ H @ (loc @ A)))) => (~ (ineM @ A @ G @ E) | ~ (! [H:secrecy_chanID]: ((member1967978193chanID @ H @ F) => (member1967978193chanID @ H @ (loc @ A)))))))) | ~ (correctCompositionIn @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 428.91/126.44 thf(1330,plain,(! [E:set_Secrecy_chanID,D:secrecy_chanID,C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) != bot_bo443197316chanID) | ((insert751661162chanID @ B @ (sup_su370684444chanID @ A @ C)) != (insert751661162chanID @ D @ E)))),inference(paramod_ordered,[status(thm)],[275,326])). 428.91/126.44 thf(1331,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ B @ (insert751661162chanID @ A @ C)) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[1330:[bind(A, $thf(F)),bind(B, $thf(B)),bind(C, $thf(G)),bind(D, $thf(B)),bind(E, $thf(sup_su370684444chanID @ F @ G))]])). 428.91/126.44 thf(1336,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ B @ (insert751661162chanID @ A @ C)) != bot_bo443197316chanID))),inference(simp,[status(thm)],[1331])). 428.91/126.44 thf(2251,plain,(! [F:set_Secrecy_chanID,E:set_Secrecy_chanID,D:secrecy_chanID,C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C) != bot_bo443197316chanID) | ((sup_su370684444chanID @ B @ (insert751661162chanID @ A @ C)) != (sup_su370684444chanID @ E @ (insert751661162chanID @ D @ F))))),inference(paramod_ordered,[status(thm)],[2227,1336])). 428.91/126.44 thf(2252,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ (insert751661162chanID @ A @ B) @ C) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[2251:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(B)),bind(F, $thf(C))]])). 428.91/126.44 thf(16841,plain,(! [E:set_Secrecy_chanID,D:set_Secrecy_chanID,C:secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ B) != bot_bo443197316chanID) | ((sup_su370684444chanID @ A @ (sup_su370684444chanID @ A @ B)) != (sup_su370684444chanID @ (insert751661162chanID @ C @ D) @ E)))),inference(paramod_ordered,[status(thm)],[472,2252])). 428.91/126.44 thf(16842,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ (insert751661162chanID @ B @ C) @ A) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[16841:[bind(A, $thf(insert751661162chanID @ J @ K)),bind(B, $thf(I)),bind(C, $thf(J)),bind(D, $thf(K)),bind(E, $thf(sup_su370684444chanID @ (insert751661162chanID @ J @ K) @ I))]])). 428.91/126.44 thf(16882,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ (insert751661162chanID @ B @ C) @ A) != bot_bo443197316chanID))),inference(simp,[status(thm)],[16842])). 428.91/126.44 thf(189,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_sup__eq__bot__iff)). 428.91/126.44 thf(910,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 428.91/126.44 thf(200,axiom,((! [A:secrecy_specID]: ((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_the__elem__eq)). 428.91/126.44 thf(957,plain,((! [A:secrecy_specID]: ((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 428.91/126.44 thf(77,axiom,((! [A:set_Secrecy_chanID]: ((? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)) = (A != bot_bo443197316chanID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ex__in__conv)). 428.91/126.44 thf(502,plain,((! [A:set_Secrecy_chanID]: ((? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)) = (~ (A = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 428.91/126.44 thf(503,plain,(! [A:set_Secrecy_chanID] : (((? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)) = (~ (A = bot_bo443197316chanID))))),inference(cnf,[status(esa)],[502])). 428.91/126.44 thf(504,plain,(! [A:set_Secrecy_chanID] : (((? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)) = (~ (A = bot_bo443197316chanID))))),inference(lifteq,[status(thm)],[503])). 428.91/126.44 thf(8168,plain,(! [A:set_Secrecy_chanID] : (((? [B:secrecy_chanID]: (member1967978193chanID @ B @ A)) = (~ (bot_bo443197316chanID = A))))),inference(rewrite,[status(thm)],[504,8130])). 428.91/126.44 thf(198,axiom,((ineM = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (ins @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_ineM__def)). 428.91/126.44 thf(951,plain,(((ineM) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (ins @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 428.91/126.44 thf(952,plain,(((ineM) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (ins @ A)) & (member1967978193chanID @ D @ B) & (exprChannel @ D @ C))))),inference(lifteq,[status(thm)],[951])). 428.91/126.44 thf(13,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = (insert751661162chanID @ C @ bot_bo443197316chanID)) = (((B = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (A = (insert751661162chanID @ C @ bot_bo443197316chanID))) | ((A = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (B = bot_bo443197316chanID)) | ((B = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (A = bot_bo443197316chanID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Un__singleton__iff)). 428.91/126.44 thf(302,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = (insert751661162chanID @ C @ bot_bo443197316chanID)) = (((B = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (A = (insert751661162chanID @ C @ bot_bo443197316chanID))) | ((A = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (B = bot_bo443197316chanID)) | ((B = (insert751661162chanID @ C @ bot_bo443197316chanID)) & (A = bot_bo443197316chanID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 428.91/126.44 thf(258,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys]: ((((~ (ine @ B @ (secrecy_kE @ D))) => ((((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ C)))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ B)))) <= (~ (ine @ C @ (secrecy_kE @ D))))) <= (correc965049635ionLoc @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_LocalSecretsComposition__neg1__k)). 428.91/126.44 thf(1174,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys]: (((~ (ine @ B @ (secrecy_kE @ D))) => (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A)) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ C)) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ B)) | (ine @ C @ (secrecy_kE @ D)))) | ~ (correc965049635ionLoc @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 428.91/126.44 thf(109,axiom,((ine = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (ins @ A)) & (exprChannel @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_ine__def)). 428.91/126.44 thf(598,plain,(((ine) = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (ins @ A)) & (exprChannel @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 428.91/126.44 thf(54,axiom,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((ine_ex1303305700Single @ A @ B @ C) <= (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_ine__exprChannelSet__Single)). 428.91/126.44 thf(423,plain,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((ine_ex1303305700Single @ A @ B @ C) | ~ (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 428.91/126.44 thf(424,plain,(! [C:secrecy_Expression,B:secrecy_chanID,A:secrecy_specID] : ((ine_ex1303305700Single @ A @ B @ C) | (~ (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)))),inference(cnf,[status(esa)],[423])). 428.91/126.44 thf(48,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:set_Secrecy_chanID]: ((~ (eoutM @ A @ C @ B)) <= (~ (eout @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_not__eout__eoutM)). 428.91/126.44 thf(407,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:set_Secrecy_chanID]: (~ (eoutM @ A @ C @ B) | (eout @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 428.91/126.44 thf(56,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sup__bot__right)). 428.91/126.44 thf(429,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 428.91/126.44 thf(142,axiom,((! [A:secrecy_Keys,B:secrecy_Secrets]: ((secrecy_kE @ A) != (secrecy_sE @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Expression_Odistinct_I1_J)). 428.91/126.44 thf(726,plain,((! [A:secrecy_Keys,B:secrecy_Secrets]: ~ ((secrecy_kE @ A) = (secrecy_sE @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 428.91/126.44 thf(727,plain,((~ (? [A:secrecy_Keys,B:secrecy_Secrets]: ((secrecy_kE @ A) = (secrecy_sE @ B))))),inference(miniscope,[status(thm)],[726])). 428.91/126.44 thf(728,plain,(! [B:secrecy_Secrets,A:secrecy_Keys] : ((~ ((secrecy_kE @ A) = (secrecy_sE @ B))))),inference(cnf,[status(esa)],[727])). 428.91/126.44 thf(729,plain,(! [B:secrecy_Secrets,A:secrecy_Keys] : (((secrecy_kE @ A) != (secrecy_sE @ B)))),inference(lifteq,[status(thm)],[728])). 428.91/126.44 thf(16899,plain,(! [E:secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ (insert1671894227specID @ E @ (subcomponents @ pq)) @ D)))),inference(paramod_ordered,[status(thm)],[16898,14922])). 428.91/126.44 thf(16900,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ (insert1671894227specID @ A @ B)) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[16899:[bind(A, $thf(subcomponents @ pq)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(C)),bind(E, $thf(B))]])). 428.91/126.44 thf(17179,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ (insert1671894227specID @ A @ B)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[16900])). 428.91/126.44 thf(17372,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq)) != bot_bo1785112429specID) | ((insert1671894227specID @ p @ (sk4 @ (subcomponents @ pq) @ p)) != (insert1671894227specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[7032,17179])). 428.91/126.44 thf(17373,plain,(((sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq)) != bot_bo1785112429specID)),inference(pattern_uni,[status(thm)],[17372:[bind(A, $thf(p)),bind(B, $thf(sk4 @ (subcomponents @ pq) @ p))]])). 428.91/126.44 thf(17450,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ A) @ A) | (A != (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[346,17373])). 428.91/126.44 thf(17451,plain,((member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq)))),inference(pattern_uni,[status(thm)],[17450:[bind(A, $thf(sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq)))]])). 428.91/126.44 thf(86,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) = ((member740727610specID @ A @ C) | (member740727610specID @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Un__iff)). 428.91/126.44 thf(526,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) = ((member740727610specID @ A @ C) | (member740727610specID @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 428.91/126.44 thf(527,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) = ((member740727610specID @ A @ C) | (member740727610specID @ A @ B))))),inference(cnf,[status(esa)],[526])). 428.91/126.44 thf(528,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) = ((member740727610specID @ A @ C) | (member740727610specID @ A @ B))))),inference(lifteq,[status(thm)],[527])). 428.91/126.44 thf(18700,plain,(((member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq)) | (member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq)))),inference(rewrite,[status(thm)],[17451,528])). 428.91/126.44 thf(18701,plain,((member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq))),inference(simp,[status(thm)],[18700])). 428.91/126.44 thf(18704,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ B) = B) | ((member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[18701,523])). 428.91/126.44 thf(18705,plain,(((insert1671894227specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq)) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[18704:[bind(A, $thf(sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq)))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(14340,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk7 @ A) @ A) | (is_sin1501507247specID @ A) | ((^ [B:set_Secrecy_specID]: (B = (insert1671894227specID @ (the_el827131246specID @ B) @ bot_bo1785112429specID))) = (is_sin1501507247specID)) | (A != bot_bo1785112429specID))),inference(paramod_ordered,[status(thm)],[492,799])). 428.91/126.44 thf(14341,plain,((member740727610specID @ (sk7 @ bot_bo1785112429specID) @ bot_bo1785112429specID) | (is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) = (is_sin1501507247specID))),inference(pattern_uni,[status(thm)],[14340:[bind(A, $thf(bot_bo1785112429specID))]])). 428.91/126.44 thf(17466,plain,(($false) | (is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) = (is_sin1501507247specID))),inference(rewrite,[status(thm)],[14341,363])). 428.91/126.44 thf(17467,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) = (is_sin1501507247specID))),inference(simp,[status(thm)],[17466])). 428.91/126.44 thf(235,axiom,((! [A:set_Secrecy_KS]: ((? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A)) = (A != bot_bo1943466239ecy_KS)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_ex__in__conv)). 428.91/126.44 thf(1091,plain,((! [A:set_Secrecy_KS]: ((? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A)) = (~ (A = bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 428.91/126.44 thf(171,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((ine @ C @ B) | (ine @ A @ B)) => (((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((ine @ D @ B) <= (? [E:secrecy_chanID]: ((exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ D)) & ((member1967978193chanID @ E @ (ins @ C)) | (member1967978193chanID @ E @ (ins @ A)))))) <= (correctCompositionIn @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_TBtheorem4a__PQ)). 428.91/126.44 thf(820,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((ine @ C @ B) | (ine @ A @ B)) => (((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((ine @ D @ B) | ~ (? [E:secrecy_chanID]: ((exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ D)) & ((member1967978193chanID @ E @ (ins @ C)) | (member1967978193chanID @ E @ (ins @ A))))) | ~ (correctCompositionIn @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 428.91/126.44 thf(2336,plain,(! [C:set_Secrecy_KS,B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))) != bot_bo1943466239ecy_KS) | (A != (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))))),inference(paramod_ordered,[status(thm)],[1152,2160])). 428.91/126.44 thf(2337,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B))))))) != bot_bo1943466239ecy_KS))),inference(pattern_uni,[status(thm)],[2336:[bind(A, $thf(collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ C))))),bind(B, $thf(B)),bind(C, $thf(C))]])). 428.91/126.44 thf(2338,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B))))))) != bot_bo1943466239ecy_KS))),inference(simp,[status(thm)],[2337])). 428.91/126.44 thf(5769,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B))))))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,2338])). 428.91/126.44 thf(5815,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ A @ B)))))) != (^ [C:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5769])). 428.91/126.44 thf(2172,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (specKeysSecrets @ q)) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1152,2157])). 428.91/126.44 thf(2173,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))))) != (specKeysSecrets @ q)))),inference(pattern_uni,[status(thm)],[2172:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))),bind(B, $thf(B))]])). 428.91/126.44 thf(2177,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[2173])). 428.91/126.44 thf(2416,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ A))))))))) != (specKeysSecrets @ q)) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,2177])). 428.91/126.44 thf(2417,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))))) != (specKeysSecrets @ q)))),inference(pattern_uni,[status(thm)],[2416:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(2418,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[2417])). 428.91/126.44 thf(2977,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))))) != (specKeysSecrets @ q)) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ B)))))))))),inference(paramod_ordered,[status(thm)],[1152,2418])). 428.91/126.44 thf(2978,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ m @ A))))))))))))) != (specKeysSecrets @ q)))),inference(pattern_uni,[status(thm)],[2977:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ B)))))))),bind(B, $thf(B))]])). 428.91/126.44 thf(2986,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ m @ A))))))))))))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[2978])). 428.91/126.44 thf(2634,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((? [C:secrecy_specID]: (B = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((is_sin1501507247specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) != (is_sin1501507247specID @ B)))),inference(paramod_ordered,[status(thm)],[747,1265])). 428.91/126.44 thf(2635,plain,(! [A:secrecy_specID] : ((? [B:secrecy_specID]: ((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(pattern_uni,[status(thm)],[2634:[bind(A, $thf(C)),bind(B, $thf(insert1671894227specID @ C @ bot_bo1785112429specID))]])). 428.91/126.44 thf(2652,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID)))),inference(cnf,[status(esa)],[2635])). 428.91/126.44 thf(2653,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID) = (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(lifteq,[status(thm)],[2652])). 428.91/126.44 thf(2654,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID) = (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(simp,[status(thm)],[2653])). 428.91/126.44 thf(3123,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ C @ (insert1671894227specID @ A @ bot_bo1785112429specID)) | ((insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID) != (insert1671894227specID @ C @ B)))),inference(paramod_ordered,[status(thm)],[2654,540])). 428.91/126.44 thf(3124,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk50 @ A) @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(pattern_uni,[status(thm)],[3123:[bind(A, $thf(D)),bind(B, $thf(bot_bo1785112429specID)),bind(C, $thf(sk50 @ D))]])). 428.91/126.44 thf(3152,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk50 @ A) @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(simp,[status(thm)],[3124])). 428.91/126.44 thf(3157,plain,(! [B:secrecy_specID,A:secrecy_specID] : ((member740727610specID @ (sk50 @ B) @ (insert1671894227specID @ A @ bot_bo1785112429specID)) | ((insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID) != (insert1671894227specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[2654,3152])). 428.91/126.44 thf(3158,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk50 @ (sk50 @ A)) @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(pattern_uni,[status(thm)],[3157:[bind(A, $thf(C)),bind(B, $thf(sk50 @ C))]])). 428.91/126.44 thf(3170,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk50 @ (sk50 @ A)) @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(simp,[status(thm)],[3158])). 428.91/126.44 thf(958,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = A))),inference(cnf,[status(esa)],[957])). 428.91/126.44 thf(959,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = A))),inference(lifteq,[status(thm)],[958])). 428.91/126.44 thf(3127,plain,(! [B:secrecy_specID,A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = B) | ((insert1671894227specID @ (sk50 @ A) @ bot_bo1785112429specID) != (insert1671894227specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[2654,959])). 428.91/126.44 thf(3128,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = (sk50 @ A)))),inference(pattern_uni,[status(thm)],[3127:[bind(A, $thf(C)),bind(B, $thf(sk50 @ C))]])). 428.91/126.44 thf(3154,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = (sk50 @ A)))),inference(simp,[status(thm)],[3128])). 428.91/126.44 thf(3174,plain,(! [A:secrecy_specID] : (((sk50 @ A) = A))),inference(rewrite,[status(thm)],[3154,959])). 428.91/126.44 thf(4040,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk50 @ A) @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(rewrite,[status(thm)],[3170,3174])). 428.91/126.44 thf(9933,plain,(! [A:secrecy_specID] : (((member740727610specID @ (sk50 @ A) @ (insert1671894227specID @ A @ bot_bo1785112429specID)) != (member740727610specID @ pq @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[4040,9931])). 428.91/126.44 thf(9956,plain,(! [A:secrecy_specID] : (((sk50 @ A) != pq) | ((insert1671894227specID @ A @ bot_bo1785112429specID) != (subcomponents @ pq)))),inference(simp,[status(thm)],[9933])). 428.91/126.44 thf(13971,plain,(! [A:secrecy_specID] : ((A != pq) | ((insert1671894227specID @ A @ bot_bo1785112429specID) != (subcomponents @ pq)))),inference(rewrite,[status(thm)],[9956,3174])). 428.91/126.44 thf(90,axiom,((! [A:set_Secrecy_chanID]: ((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) = (A = bot_bo443197316chanID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_all__not__in__conv)). 428.91/126.44 thf(541,plain,((! [A:set_Secrecy_chanID]: ((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) = (A = bot_bo443197316chanID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 428.91/126.44 thf(542,plain,(! [A:set_Secrecy_chanID] : (((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) = (A = bot_bo443197316chanID)))),inference(cnf,[status(esa)],[541])). 428.91/126.44 thf(543,plain,(! [A:set_Secrecy_chanID] : (((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) = (A = bot_bo443197316chanID)))),inference(lifteq,[status(thm)],[542])). 428.91/126.44 thf(2444,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((~ (! [C:secrecy_chanID]: ~ (member1967978193chanID @ C @ A))) = (? [C:secrecy_chanID]: (member1967978193chanID @ C @ B))) | ((A = bot_bo443197316chanID) != (B = bot_bo443197316chanID)))),inference(paramod_ordered,[status(thm)],[543,504])). 428.91/126.44 thf(2445,plain,(! [A:set_Secrecy_chanID] : (((~ (! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A))) = (? [B:secrecy_chanID]: (member1967978193chanID @ B @ A))))),inference(pattern_uni,[status(thm)],[2444:[bind(A, $thf(A)),bind(B, $thf(A))]])). 428.91/126.44 thf(490,plain,(! [A:set_Secrecy_specID] : ((~ ((sk7 @ A) = (sk8 @ A))) | (is_sin1501507247specID @ A) | (A = bot_bo1785112429specID))),inference(cnf,[status(esa)],[488])). 428.91/126.44 thf(493,plain,(! [A:set_Secrecy_specID] : (((sk8 @ A) != (sk7 @ A)) | (A = bot_bo1785112429specID) | (is_sin1501507247specID @ A))),inference(lifteq,[status(thm)],[490])). 428.91/126.44 thf(218,axiom,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B)) => (((correc965049635ionLoc @ B) => ((~ (ine @ C @ (secrecy_sE @ A))) => (((ine @ D @ (secrecy_sE @ A)) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ D)))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ C)))))) <= ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_LocalSecretsComposition__ine2__s)). 428.91/126.44 thf(1027,plain,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B)) => (((correc965049635ionLoc @ B) => ((~ (ine @ C @ (secrecy_sE @ A))) => ((ine @ D @ (secrecy_sE @ A)) | (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ D)) | (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ C))))) | ~ ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 428.91/126.44 thf(153,axiom,(((ine @ p @ (secrecy_kE @ key)) | (ine @ q @ (secrecy_kE @ key)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_a11ext)). 428.91/126.44 thf(757,plain,(((ine @ p @ (secrecy_kE @ key)) | (ine @ q @ (secrecy_kE @ key)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 428.91/126.44 thf(6267,plain,((~ (member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | (~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q)))),inference(bool_ext,[status(thm)],[6243])). 428.91/126.44 thf(277,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((member1967978193chanID @ A @ (insert751661162chanID @ A @ B)))),inference(cnf,[status(esa)],[276])). 428.91/126.44 thf(1279,plain,(! [C:secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((member1967978193chanID @ A @ (insert751661162chanID @ A @ B)) != (member1967978193chanID @ C @ bot_bo443197316chanID)))),inference(paramod_ordered,[status(thm)],[277,436])). 428.91/126.44 thf(1280,plain,(! [C:secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : ((A != C) | ((insert751661162chanID @ A @ B) != bot_bo443197316chanID))),inference(simp,[status(thm)],[1279])). 428.91/126.44 thf(1281,plain,(! [B:secrecy_chanID,A:set_Secrecy_chanID] : (((insert751661162chanID @ B @ A) != bot_bo443197316chanID))),inference(simp,[status(thm)],[1280])). 428.91/126.44 thf(64,axiom,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C) => (out_ex985543062Single @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_out__exprChannelSet__Single)). 428.91/126.44 thf(455,plain,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C) => (out_ex985543062Single @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 428.91/126.44 thf(456,plain,(! [C:secrecy_Expression,B:secrecy_chanID,A:secrecy_specID] : ((~ (out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)) | (out_ex985543062Single @ A @ B @ C))),inference(cnf,[status(esa)],[455])). 428.91/126.44 thf(206,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ B))) => ((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ A))) <= (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ C)))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_correctCompositionKS__neg1)). 428.91/126.44 thf(974,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ B))) => (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ A)) | (member_Secrecy_KS @ D @ (specKeysSecrets @ C))))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 428.91/126.44 thf(7094,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ A) @ A) | ((insert1671894227specID @ p @ bot_bo1785112429specID) = (subcomponents @ pq)) | (A != (sk4 @ (subcomponents @ pq) @ p)))),inference(paramod_ordered,[status(thm)],[346,7032])). 428.91/126.44 thf(7095,plain,((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ p @ bot_bo1785112429specID) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[7094:[bind(A, $thf(sk4 @ (subcomponents @ pq) @ p))]])). 428.91/126.44 thf(239,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_UnI2)). 428.91/126.44 thf(1106,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 428.91/126.44 thf(178,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sup__bot__left)). 428.91/126.44 thf(847,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 428.91/126.44 thf(73,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_sup__eq__bot__iff)). 428.91/126.44 thf(484,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: (((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 428.91/126.44 thf(22,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: (((((insert751661162chanID @ A @ B) = (insert751661162chanID @ A @ C)) = (B = C)) <= (~ (member1967978193chanID @ A @ C))) <= (~ (member1967978193chanID @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__ident)). 428.91/126.44 thf(329,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((((insert751661162chanID @ A @ B) = (insert751661162chanID @ A @ C)) = (B = C)) | (member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 428.91/126.44 thf(10783,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ A @ B) @ C) != bot_bo1785112429specID) | ((insert1671894227specID @ A @ (sup_su1712599557specID @ B @ C)) != (insert1671894227specID @ pq @ D)))),inference(paramod_ordered,[status(thm)],[396,10772])). 428.91/126.44 thf(10784,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ pq @ A) @ B) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[10783:[bind(A, $thf(pq)),bind(B, $thf(E)),bind(C, $thf(F)),bind(D, $thf(sup_su1712599557specID @ E @ F))]])). 428.91/126.44 thf(10794,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ pq @ A) @ B) != bot_bo1785112429specID))),inference(simp,[status(thm)],[10784])). 428.91/126.44 thf(254,axiom,((! [A:secrecy_specID,B:secrecy_Keys]: ((knowle945212990e_know @ A @ (secrecy_kKS @ B)) = ((ine @ A @ (secrecy_kE @ B)) | (member_Secrecy_KS @ (secrecy_kKS @ B) @ (localSecrets @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_know_Osimps_I1_J)). 428.91/126.44 thf(1159,plain,((! [A:secrecy_specID,B:secrecy_Keys]: ((knowle945212990e_know @ A @ (secrecy_kKS @ B)) = ((ine @ A @ (secrecy_kE @ B)) | (member_Secrecy_KS @ (secrecy_kKS @ B) @ (localSecrets @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 428.91/126.44 thf(1002,plain,(((^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) = (bot_bot_Secrecy_KS_o))),inference(lifteq,[status(thm)],[1001])). 428.91/126.44 thf(1287,plain,(((bot_bot_Secrecy_KS_o) = (^ [A:secrecy_KS]: (($false))))),inference(rewrite,[status(thm)],[1002,1000])). 428.91/126.44 thf(1291,plain,(! [A:secrecy_KS] : ((~ (bot_bot_Secrecy_KS_o @ A)))),inference(func_ext,[status(esa)],[1287])). 428.91/126.44 thf(137,axiom,((! [A:secrecy_specID,B:secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_singleton__iff)). 428.91/126.44 thf(710,plain,((! [A:secrecy_specID,B:secrecy_specID]: ((member740727610specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 428.91/126.44 thf(83,axiom,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C) <= (out_ex985543062Single @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_out__exprChannelSingle__Set)). 428.91/126.44 thf(519,plain,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C) | ~ (out_ex985543062Single @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 428.91/126.44 thf(18,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((insert751661162chanID @ A @ (insert751661162chanID @ A @ B)) = (insert751661162chanID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_insert__absorb2)). 428.91/126.44 thf(317,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((insert751661162chanID @ A @ (insert751661162chanID @ A @ B)) = (insert751661162chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 428.91/126.44 thf(197,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((insert1671894227specID @ A @ (insert1671894227specID @ B @ C)) = (insert1671894227specID @ B @ (insert1671894227specID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insert__commute)). 428.91/126.44 thf(948,plain,((! [A:secrecy_specID,B:secrecy_specID,C:set_Secrecy_specID]: ((insert1671894227specID @ A @ (insert1671894227specID @ B @ C)) = (insert1671894227specID @ B @ (insert1671894227specID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 428.91/126.44 thf(16985,plain,(! [E:set_Secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ (insert1671894227specID @ pq @ D) @ E)))),inference(paramod_ordered,[status(thm)],[16898,10794])). 428.91/126.44 thf(16986,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ pq @ B)) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[16985:[bind(A, $thf(A)),bind(B, $thf(pq)),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(C))]])). 428.91/126.44 thf(17232,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ pq @ B)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[16986])). 428.91/126.44 thf(226,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) => ((~ (member_Secrecy_KS @ A @ B)) => (member_Secrecy_KS @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_UnE)). 428.91/126.44 thf(1064,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) => ((~ (member_Secrecy_KS @ A @ B)) => (member_Secrecy_KS @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 428.91/126.44 thf(46,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ((ineM @ A @ B @ C) => (ine @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_ineM__ine)). 428.91/126.44 thf(402,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ((ineM @ A @ B @ C) => (ine @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 428.91/126.44 thf(403,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((~ (ineM @ A @ B @ C)) | (ine @ A @ C))),inference(cnf,[status(esa)],[402])). 428.91/126.44 thf(41,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_Un__empty__right)). 428.91/126.44 thf(388,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 428.91/126.44 thf(107,axiom,((! [A:secrecy_Keys,B:secrecy_Secrets]: ((secrecy_kKS @ A) != (secrecy_sKS @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_KS_Odistinct_I1_J)). 428.91/126.44 thf(590,plain,((! [A:secrecy_Keys,B:secrecy_Secrets]: ~ ((secrecy_kKS @ A) = (secrecy_sKS @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 428.91/126.44 thf(591,plain,((~ (? [A:secrecy_Keys,B:secrecy_Secrets]: ((secrecy_kKS @ A) = (secrecy_sKS @ B))))),inference(miniscope,[status(thm)],[590])). 428.91/126.44 thf(592,plain,(! [B:secrecy_Secrets,A:secrecy_Keys] : ((~ ((secrecy_kKS @ A) = (secrecy_sKS @ B))))),inference(cnf,[status(esa)],[591])). 428.91/126.44 thf(593,plain,(! [B:secrecy_Secrets,A:secrecy_Keys] : (((secrecy_kKS @ A) != (secrecy_sKS @ B)))),inference(lifteq,[status(thm)],[592])). 428.91/126.44 thf(53,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_Un__empty__left)). 428.91/126.44 thf(420,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 428.91/126.44 thf(76,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:set_Secrecy_chanID]: ((ineM @ A @ (sup_su370684444chanID @ B @ D) @ C) <= (ineM @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_ineM__Un1)). 428.91/126.44 thf(499,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:set_Secrecy_chanID]: ((ineM @ A @ (sup_su370684444chanID @ B @ D) @ C) | ~ (ineM @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 428.91/126.44 thf(181,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((((member1967978193chanID @ D @ (out @ B)) | (member1967978193chanID @ D @ (out @ C))) <= (member1967978193chanID @ D @ (out @ A))) <= (correc990227761ionOut @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_correctCompositionOut__prop1)). 428.91/126.44 thf(857,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((member1967978193chanID @ D @ (out @ B)) | (member1967978193chanID @ D @ (out @ C)) | ~ (member1967978193chanID @ D @ (out @ A)) | ~ (correc990227761ionOut @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 428.91/126.44 thf(234,axiom,((m = (secrecy_kKS @ key))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_a1)). 428.91/126.44 thf(1089,plain,((m = (secrecy_kKS @ key))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 428.91/126.44 thf(3685,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((member_Secrecy_KS @ (sk39 @ A) @ A) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1196,1715])). 428.91/126.44 thf(3686,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk39 @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(pattern_uni,[status(thm)],[3685:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(3831,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk39 @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))),inference(simp,[status(thm)],[3686])). 428.91/126.44 thf(184,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_sup__bot_Oeq__neutr__iff)). 428.91/126.44 thf(874,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 428.91/126.44 thf(249,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ C))) <= (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ A)))) <= (correctCompositionKS @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_correctCompositionKS__negQ)). 428.91/126.44 thf(1143,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ C)) | (member_Secrecy_KS @ D @ (specKeysSecrets @ A)) | ~ (correctCompositionKS @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 428.91/126.44 thf(21,axiom,((insert751661162chanID = (^ [A:secrecy_chanID]: (sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_insert__is__Un)). 428.91/126.44 thf(327,plain,(((insert751661162chanID) = (^ [A:secrecy_chanID]: (sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 428.91/126.44 thf(328,plain,(((insert751661162chanID) = (^ [A:secrecy_chanID]: (sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID))))),inference(lifteq,[status(thm)],[327])). 428.91/126.44 thf(232,axiom,((! [A:secrecy_KS,B:(secrecy_KS > $o)]: ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_mem__Collect__eq)). 428.91/126.44 thf(1082,plain,((! [A:secrecy_KS,B:(secrecy_KS > $o)]: ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 428.91/126.44 thf(25,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID,D:set_Secrecy_chanID]: ((~ (member1967978193chanID @ A @ B)) => ((~ (member1967978193chanID @ C @ D)) => (((insert751661162chanID @ A @ B) = (insert751661162chanID @ C @ D)) = (((? [E:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ E) & (D = (insert751661162chanID @ A @ E)) & ~ (member1967978193chanID @ C @ E) & (B = (insert751661162chanID @ C @ E)))) <= (A != C)) & ((A = C) => (B = D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insert__eq__iff)). 428.91/126.44 thf(339,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID,D:set_Secrecy_chanID]: ((~ (member1967978193chanID @ A @ B)) => ((~ (member1967978193chanID @ C @ D)) => (((insert751661162chanID @ A @ B) = (insert751661162chanID @ C @ D)) = ((? [E:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ E) & (D = (insert751661162chanID @ A @ E)) & ~ (member1967978193chanID @ C @ E) & (B = (insert751661162chanID @ C @ E))) | (A = C)) & ((A = C) => (B = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 428.91/126.44 thf(2311,plain,(! [B:secrecy_KS,A:secrecy_KS] : (((^ [C:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) = (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))) | ((insert_Secrecy_KS @ A) != (insert_Secrecy_KS @ B)))),inference(paramod_ordered,[status(thm)],[1943,1263])). 428.91/126.44 thf(2312,plain,(! [A:secrecy_KS] : (((^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) = (sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))),inference(pattern_uni,[status(thm)],[2311:[bind(A, $thf(A)),bind(B, $thf(A))]])). 428.91/126.44 thf(120,axiom,((! [A:secrecy_chanID,B:secrecy_Keys,C:secrecy_specID,D:secrecy_specID]: ((((~ (ine @ D @ (secrecy_kE @ B))) => (~ (member1967978193chanID @ A @ (ins @ C)) & ~ (member1967978193chanID @ A @ (ins @ D)))) <= (~ (ine @ C @ (secrecy_kE @ B)))) <= (exprChannel @ A @ (secrecy_kE @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_LocalSecretsComposition__exprChannel__k)). 428.91/126.44 thf(642,plain,((! [A:secrecy_chanID,B:secrecy_Keys,C:secrecy_specID,D:secrecy_specID]: (((~ (ine @ D @ (secrecy_kE @ B))) => (~ (member1967978193chanID @ A @ (ins @ C)) & ~ (member1967978193chanID @ A @ (ins @ D)))) | (ine @ C @ (secrecy_kE @ B)) | ~ (exprChannel @ A @ (secrecy_kE @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 428.91/126.44 thf(11115,plain,(! [A:set_Secrecy_KS] : ((sk63 != m) | (A != (specKeysSecrets @ p)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,10534])). 428.91/126.44 thf(11116,plain,((sk63 != m) | ((insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ p))),inference(pattern_uni,[status(thm)],[11115:[bind(A, $thf(insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(187,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:set_Secrecy_chanID]: ((((subcomponents @ D) = (insert1671894227specID @ E @ (insert1671894227specID @ A @ bot_bo1785112429specID))) => ((((~ (ineM @ D @ B @ C)) <= (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ F) => (member1967978193chanID @ G @ (loc @ D))))) <= (ine_exprChannelSet @ E @ F @ C)) <= (correctCompositionIn @ D))) <= (~ (ineM @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_TBtheorem4b__notP2)). 428.91/126.44 thf(901,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:set_Secrecy_chanID]: ((((subcomponents @ D) = (insert1671894227specID @ E @ (insert1671894227specID @ A @ bot_bo1785112429specID))) => (~ (ineM @ D @ B @ C) | ~ (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ F) => (member1967978193chanID @ G @ (loc @ D)))) | ~ (ine_exprChannelSet @ E @ F @ C) | ~ (correctCompositionIn @ D))) | (ineM @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 428.91/126.44 thf(71,axiom,((! [A:set_Secrecy_specID,B:secrecy_specID]: ((~ (member740727610specID @ B @ A)) <= (A = bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_equals0D)). 428.91/126.44 thf(476,plain,((! [A:set_Secrecy_specID,B:secrecy_specID]: (~ (member740727610specID @ B @ A) | ~ (A = bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 428.91/126.44 thf(11004,plain,(((member740727610specID @ p @ (sk5 @ (subcomponents @ pq) @ p)) != (member740727610specID @ p @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[1923,10945])). 428.91/126.44 thf(11006,plain,((p != p) | ((sk5 @ (subcomponents @ pq) @ p) != (subcomponents @ pq))),inference(simp,[status(thm)],[11004])). 428.91/126.44 thf(11026,plain,(((sk5 @ (subcomponents @ pq) @ p) != (subcomponents @ pq))),inference(simp,[status(thm)],[11006])). 428.91/126.44 thf(267,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((((member_Secrecy_KS @ D @ (specKeysSecrets @ B)) | (member_Secrecy_KS @ D @ (specKeysSecrets @ C))) <= (member_Secrecy_KS @ D @ (specKeysSecrets @ A))) <= (correctCompositionKS @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_correctCompositionKS__PQ)). 428.91/126.44 thf(1207,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: ((member_Secrecy_KS @ D @ (specKeysSecrets @ B)) | (member_Secrecy_KS @ D @ (specKeysSecrets @ C)) | ~ (member_Secrecy_KS @ D @ (specKeysSecrets @ A)) | ~ (correctCompositionKS @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 428.91/126.44 thf(148,axiom,((insert1671894227specID = (^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_insert__is__Un)). 428.91/126.44 thf(744,plain,(((insert1671894227specID) = (^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 428.91/126.44 thf(745,plain,(((insert1671894227specID) = (^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[744])). 428.91/126.44 thf(14301,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk7 @ A) @ A) | (is_sin1501507247specID @ A) | ((^ [B:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ B @ bot_bo1785112429specID))) = (insert1671894227specID)) | (A != bot_bo1785112429specID))),inference(paramod_ordered,[status(thm)],[492,745])). 428.91/126.44 thf(14302,plain,((member740727610specID @ (sk7 @ bot_bo1785112429specID) @ bot_bo1785112429specID) | (is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))) = (insert1671894227specID))),inference(pattern_uni,[status(thm)],[14301:[bind(A, $thf(bot_bo1785112429specID))]])). 428.91/126.44 thf(15420,plain,(($false) | (is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))) = (insert1671894227specID))),inference(rewrite,[status(thm)],[14302,363])). 428.91/126.44 thf(15421,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:secrecy_specID]: (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))) = (insert1671894227specID))),inference(simp,[status(thm)],[15420])). 428.91/126.44 thf(92,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_UnI1)). 428.91/126.44 thf(547,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 428.91/126.44 thf(11270,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk5 @ B @ A)) = B) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,428])). 428.91/126.44 thf(11271,plain,(((insert1671894227specID @ p @ (sk5 @ (subcomponents @ pq) @ p)) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[11270:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(11386,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ A) @ A) | ((insert1671894227specID @ p @ bot_bo1785112429specID) = (subcomponents @ pq)) | (A != (sk5 @ (subcomponents @ pq) @ p)))),inference(paramod_ordered,[status(thm)],[346,11271])). 428.91/126.44 thf(11387,plain,((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ p @ bot_bo1785112429specID) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[11386:[bind(A, $thf(sk5 @ (subcomponents @ pq) @ p))]])). 428.91/126.44 thf(12755,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | ((the_el827131246specID @ (subcomponents @ pq)) = A) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[11387,959])). 428.91/126.44 thf(12756,plain,((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | ((the_el827131246specID @ (subcomponents @ pq)) = p)),inference(pattern_uni,[status(thm)],[12755:[bind(A, $thf(p))]])). 428.91/126.44 thf(146,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: ((bot_bo1943466239ecy_KS = (sup_su1301156759ecy_KS @ A @ B)) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_sup__bot_Oneutr__eq__iff)). 428.91/126.44 thf(738,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: ((bot_bo1943466239ecy_KS = (sup_su1301156759ecy_KS @ A @ B)) = ((A = bot_bo1943466239ecy_KS) & (B = bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 428.91/126.44 thf(10223,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ C @ B)) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,415])). 428.91/126.44 thf(10224,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ A @ (subcomponents @ pq))))),inference(pattern_uni,[status(thm)],[10223:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(10281,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ A @ (subcomponents @ pq))))),inference(simp,[status(thm)],[10224])). 428.91/126.44 thf(6834,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (sk4 @ B @ A))) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,368])). 428.91/126.44 thf(6835,plain,((~ (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(pattern_uni,[status(thm)],[6834:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(10366,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[10281,6835])). 428.91/126.44 thf(10384,plain,(! [A:set_Secrecy_specID] : (((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[10366])). 428.91/126.44 thf(10401,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[10384])). 428.91/126.44 thf(159,axiom,((! [A:secrecy_specID]: (member740727610specID @ A @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_singletonI)). 428.91/126.44 thf(779,plain,((! [A:secrecy_specID]: (member740727610specID @ A @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 428.91/126.44 thf(6653,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (sup_su1712599557specID @ B @ C)) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,366])). 428.91/126.44 thf(6654,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)))),inference(pattern_uni,[status(thm)],[6653:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(6676,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)))),inference(simp,[status(thm)],[6654])). 428.91/126.44 thf(10927,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ (sk5 @ B @ A))) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,426])). 428.91/126.44 thf(10928,plain,((~ (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(pattern_uni,[status(thm)],[10927:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(11055,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[6676,10928])). 428.91/126.44 thf(11081,plain,(! [A:set_Secrecy_specID] : (((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[11055])). 428.91/126.44 thf(11093,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[11081])). 428.91/126.44 thf(35,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:(secrecy_chanID > $o)]: ((! [D:secrecy_chanID]: ((member1967978193chanID @ D @ (sup_su370684444chanID @ A @ B)) => (C @ D))) = (! [D:secrecy_chanID]: ((C @ D) <= (member1967978193chanID @ D @ A)) & ! [D:secrecy_chanID]: ((C @ D) <= (member1967978193chanID @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ball__Un)). 428.91/126.44 thf(371,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:(secrecy_chanID > $o)]: ((! [D:secrecy_chanID]: ((member1967978193chanID @ D @ (sup_su370684444chanID @ A @ B)) => (C @ D))) = (! [D:secrecy_chanID]: ((C @ D) | ~ (member1967978193chanID @ D @ A)) & ! [D:secrecy_chanID]: ((C @ D) | ~ (member1967978193chanID @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 428.91/126.44 thf(65,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:set_Secrecy_chanID]: ((~ (ine @ A @ B)) => (~ (ineM @ A @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_not__ine__ineM)). 428.91/126.44 thf(457,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:set_Secrecy_chanID]: ((~ (ine @ A @ B)) => (~ (ineM @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 428.91/126.44 thf(7120,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[6676,6835])). 428.91/126.44 thf(7144,plain,(! [A:set_Secrecy_specID] : (((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[7120])). 428.91/126.44 thf(7150,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[7144])). 428.91/126.44 thf(1241,plain,(! [A:secrecy_chanID] : (((insert751661162chanID @ A) = (sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID))))),inference(func_ext,[status(esa)],[328])). 428.91/126.44 thf(1874,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A) = (^ [C:set_Secrecy_chanID]: (sup_su370684444chanID @ C @ B))) | ((sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID)) != (sup_su370684444chanID @ B)))),inference(paramod_ordered,[status(thm)],[1241,1211])). 428.91/126.44 thf(1875,plain,(! [A:secrecy_chanID] : (((insert751661162chanID @ A) = (^ [B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ (insert751661162chanID @ A @ bot_bo443197316chanID)))))),inference(pattern_uni,[status(thm)],[1874:[bind(A, $thf(C)),bind(B, $thf(insert751661162chanID @ C @ bot_bo443197316chanID))]])). 428.91/126.44 thf(1891,plain,(! [A:secrecy_chanID] : (((insert751661162chanID @ A) = (^ [B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ (insert751661162chanID @ A @ bot_bo443197316chanID)))))),inference(simp,[status(thm)],[1875])). 428.91/126.44 thf(2202,plain,(! [B:secrecy_chanID,A:secrecy_chanID] : (((^ [C:set_Secrecy_chanID]: (sup_su370684444chanID @ C @ (insert751661162chanID @ A @ bot_bo443197316chanID))) = (sup_su370684444chanID @ (insert751661162chanID @ B @ bot_bo443197316chanID))) | ((insert751661162chanID @ A) != (insert751661162chanID @ B)))),inference(paramod_ordered,[status(thm)],[1891,1241])). 428.91/126.44 thf(2203,plain,(! [A:secrecy_chanID] : (((^ [B:set_Secrecy_chanID]: (sup_su370684444chanID @ B @ (insert751661162chanID @ A @ bot_bo443197316chanID))) = (sup_su370684444chanID @ (insert751661162chanID @ A @ bot_bo443197316chanID))))),inference(pattern_uni,[status(thm)],[2202:[bind(A, $thf(A)),bind(B, $thf(A))]])). 428.91/126.44 thf(10288,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (sup_su1712599557specID @ C @ D)) | ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[10261,366])). 428.91/126.44 thf(10289,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ B @ (subcomponents @ pq)) @ A)))),inference(pattern_uni,[status(thm)],[10288:[bind(A, $thf(E)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ E @ (subcomponents @ pq))),bind(D, $thf(D))]])). 428.91/126.44 thf(10335,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ B @ (subcomponents @ pq)) @ A)))),inference(simp,[status(thm)],[10289])). 428.91/126.44 thf(15355,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (sup_su1712599557specID @ B @ (subcomponents @ pq)) @ A)) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[10335,363])). 428.91/126.44 thf(15373,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : ((p != C) | ((sup_su1712599557specID @ (sup_su1712599557specID @ B @ (subcomponents @ pq)) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15355])). 428.91/126.44 thf(15395,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (sup_su1712599557specID @ B @ (subcomponents @ pq)) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15373])). 428.91/126.44 thf(79,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_bot__eq__sup__iff)). 428.91/126.44 thf(508,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID]: ((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((B = bot_bo443197316chanID) & (A = bot_bo443197316chanID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 428.91/126.44 thf(257,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys]: (((correc965049635ionLoc @ A) => ((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ B))) => (((~ (ine @ B @ (secrecy_kE @ D))) => ((~ (ine @ C @ (secrecy_kE @ D))) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C))))))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ C))))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_LocalSecretsComposition__neg__k)). 428.91/126.44 thf(1170,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys]: (((correc965049635ionLoc @ A) => ((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ B))) => (((~ (ine @ B @ (secrecy_kE @ D))) => ((~ (ine @ C @ (secrecy_kE @ D))) => (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A)) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C)))))) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ C)))))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 428.91/126.44 thf(398,plain,(((out_ex985543062Single) = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((member1967978193chanID @ B @ (out @ A)) & ! [D:secrecy_chanID]: (~ (exprChannel @ D @ C) | ~ ((member1967978193chanID @ D @ (out @ A)) & ~ (D = B))) & (exprChannel @ B @ C))))),inference(lifteq,[status(thm)],[397])). 428.91/126.44 thf(13483,plain,(! [A:secrecy_KS] : (((insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((member_Secrecy_KS @ A @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) != (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1712,13051])). 428.91/126.44 thf(13504,plain,(! [A:secrecy_KS] : ((sk65 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS) | (A != sk65) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[13483])). 428.91/126.44 thf(13523,plain,((sk65 != m) | ((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS)))) != (specKeysSecrets @ q))),inference(simp,[status(thm)],[13504])). 428.91/126.44 thf(13878,plain,(! [A:set_Secrecy_KS] : ((sk65 != m) | (A != (specKeysSecrets @ q)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,13523])). 428.91/126.44 thf(13879,plain,((sk65 != m) | ((insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ q))),inference(pattern_uni,[status(thm)],[13878:[bind(A, $thf(insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(199,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correctCompositionIn @ A) => ((member1967978193chanID @ D @ (ins @ A)) => ((member1967978193chanID @ D @ (ins @ C)) | (member1967978193chanID @ D @ (ins @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_correctCompositionIn__L2)). 428.91/126.44 thf(953,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correctCompositionIn @ A) => ((member1967978193chanID @ D @ (ins @ A)) => ((member1967978193chanID @ D @ (ins @ C)) | (member1967978193chanID @ D @ (ins @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 428.91/126.44 thf(155,axiom,((! [A:secrecy_Secrets,B:secrecy_Secrets]: (((secrecy_sKS @ A) = (secrecy_sKS @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_KS_Oinject_I2_J)). 428.91/126.44 thf(765,plain,((! [A:secrecy_Secrets,B:secrecy_Secrets]: (((secrecy_sKS @ A) = (secrecy_sKS @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 428.91/126.44 thf(96,axiom,((out_exprChannelSet = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (! [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) => ((member1967978193chanID @ D @ (out @ A)) & (exprChannel @ D @ C))) & ! [D:secrecy_chanID]: ((~ (member1967978193chanID @ D @ B) & (member1967978193chanID @ D @ (out @ A))) => (~ (exprChannel @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_out__exprChannelSet__def)). 428.91/126.44 thf(558,plain,(((out_exprChannelSet) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (! [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) => ((member1967978193chanID @ D @ (out @ A)) & (exprChannel @ D @ C))) & ! [D:secrecy_chanID]: ((~ (member1967978193chanID @ D @ B) & (member1967978193chanID @ D @ (out @ A))) => (~ (exprChannel @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 428.91/126.44 thf(229,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: ((((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ C)) => (((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A))) => (((exprChannel @ E @ (secrecy_sE @ D)) & (member1967978193chanID @ E @ (ins @ A))) <= (correctCompositionIn @ A))) <= (exprChannel @ E @ (secrecy_sE @ D))))) <= (correctCompositionKS @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_correctCompositionKS__exprChannel__s__Q)). 428.91/126.44 thf(1071,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ C)) => (((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A))) => (((exprChannel @ E @ (secrecy_sE @ D)) & (member1967978193chanID @ E @ (ins @ A))) | ~ (correctCompositionIn @ A))) | ~ (exprChannel @ E @ (secrecy_sE @ D))))) | ~ (correctCompositionKS @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 428.91/126.44 thf(106,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((eoutM @ A @ B @ C) => (((subcomponents @ A) = (insert1671894227specID @ D @ (insert1671894227specID @ E @ bot_bo1785112429specID))) => (((eoutM @ E @ B @ C) | (eoutM @ D @ B @ C)) <= (correc990227761ionOut @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_TBtheorem2b)). 428.91/126.44 thf(586,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((eoutM @ A @ B @ C) => (((subcomponents @ A) = (insert1671894227specID @ D @ (insert1671894227specID @ E @ bot_bo1785112429specID))) => ((eoutM @ E @ B @ C) | (eoutM @ D @ B @ C) | ~ (correc990227761ionOut @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 428.91/126.44 thf(11,axiom,((! [A:secrecy_chanID,B:secrecy_chanID]: (((insert751661162chanID @ A @ bot_bo443197316chanID) = (insert751661162chanID @ B @ bot_bo443197316chanID)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_singleton__inject)). 428.91/126.44 thf(296,plain,((! [A:secrecy_chanID,B:secrecy_chanID]: (((insert751661162chanID @ A @ bot_bo443197316chanID) = (insert751661162chanID @ B @ bot_bo443197316chanID)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 428.91/126.44 thf(297,plain,(! [B:secrecy_chanID,A:secrecy_chanID] : ((~ ((insert751661162chanID @ A @ bot_bo443197316chanID) = (insert751661162chanID @ B @ bot_bo443197316chanID))) | (A = B))),inference(cnf,[status(esa)],[296])). 428.91/126.44 thf(298,plain,(! [B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ bot_bo443197316chanID) != (insert751661162chanID @ B @ bot_bo443197316chanID)) | (A = B))),inference(lifteq,[status(thm)],[297])). 428.91/126.44 thf(115,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) = (sup_su1301156759ecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Un__left__commute)). 428.91/126.44 thf(618,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C)) = (sup_su1301156759ecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 428.91/126.44 thf(81,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_sup__bot_Oright__neutral)). 428.91/126.44 thf(513,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 428.91/126.44 thf(101,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_sup__bot__left)). 428.91/126.44 thf(573,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 428.91/126.44 thf(8703,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((member740727610specID @ A @ (insert1671894227specID @ C @ B)) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,401])). 428.91/126.44 thf(8704,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (insert1671894227specID @ A @ (subcomponents @ pq))))),inference(pattern_uni,[status(thm)],[8703:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq)),bind(C, $thf(C))]])). 428.91/126.44 thf(8735,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (insert1671894227specID @ A @ (subcomponents @ pq))))),inference(simp,[status(thm)],[8704])). 428.91/126.44 thf(8839,plain,(! [A:secrecy_specID] : (((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (insert1671894227specID @ A @ (subcomponents @ pq))) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[8735,6835])). 428.91/126.44 thf(8860,plain,(! [A:secrecy_specID] : (((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((insert1671894227specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[8839])). 428.91/126.44 thf(8874,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[8860])). 428.91/126.44 thf(14399,plain,(! [A:set_Secrecy_specID] : ((member740727610specID @ (sk7 @ A) @ A) | (is_sin1501507247specID @ A) | (A != (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[492,1364])). 428.91/126.44 thf(14400,plain,((member740727610specID @ (sk7 @ (subcomponents @ pq)) @ (subcomponents @ pq)) | (is_sin1501507247specID @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[14399:[bind(A, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(15101,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((member740727610specID @ (sk7 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ pq @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[14400,9931])). 428.91/126.44 thf(15133,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((sk7 @ (subcomponents @ pq)) != pq) | ((subcomponents @ pq) != (subcomponents @ pq))),inference(simp,[status(thm)],[15101])). 428.91/126.44 thf(15147,plain,((is_sin1501507247specID @ (subcomponents @ pq)) | ((sk7 @ (subcomponents @ pq)) != pq)),inference(simp,[status(thm)],[15133])). 428.91/126.44 thf(5781,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B)))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,2160])). 428.91/126.44 thf(5808,plain,(! [B:set_Secrecy_KS,A:secrecy_KS] : (((^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ B))) != (^ [C:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5781])). 428.91/126.44 thf(238,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => ((insert_Secrecy_KS @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__absorb)). 428.91/126.44 thf(1103,plain,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => ((insert_Secrecy_KS @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 428.91/126.44 thf(3666,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | ((member_Secrecy_KS @ (sk39 @ A) @ A) != (member_Secrecy_KS @ m @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1196,1206])). 428.91/126.44 thf(3808,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | ((sk39 @ A) != m) | (A != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[3666])). 428.91/126.44 thf(3871,plain,(((specKeysSecrets @ p) = bot_bo1943466239ecy_KS) | ((sk39 @ (specKeysSecrets @ p)) != m)),inference(simp,[status(thm)],[3808])). 428.91/126.44 thf(10230,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ B @ (sup_su1712599557specID @ D @ C)) | ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[6672,415])). 428.91/126.44 thf(10231,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ (subcomponents @ pq) @ B))))),inference(pattern_uni,[status(thm)],[10230:[bind(A, $thf(F)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ (subcomponents @ pq) @ F)),bind(D, $thf(D))]])). 428.91/126.44 thf(10283,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ (subcomponents @ pq) @ B))))),inference(simp,[status(thm)],[10231])). 428.91/126.44 thf(15023,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ A @ (sup_su1712599557specID @ (subcomponents @ pq) @ B))) != (member740727610specID @ C @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[10283,363])). 428.91/126.44 thf(15044,plain,(! [C:secrecy_specID,B:set_Secrecy_specID,A:set_Secrecy_specID] : ((p != C) | ((sup_su1712599557specID @ A @ (sup_su1712599557specID @ (subcomponents @ pq) @ B)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15023])). 428.91/126.44 thf(15057,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (sup_su1712599557specID @ (subcomponents @ pq) @ B)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[15044])). 428.91/126.44 thf(7009,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ (sk4 @ B @ A)) = B) | ((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[2734,370])). 428.91/126.44 thf(7010,plain,(((insert1671894227specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[7009:[bind(A, $thf(sk3 @ (subcomponents @ pq))),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(10299,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[10261,363])). 428.91/126.44 thf(10315,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((p != B) | ((sup_su1712599557specID @ A @ (subcomponents @ pq)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[10299])). 428.91/126.44 thf(10332,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (subcomponents @ pq)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[10315])). 428.91/126.44 thf(17098,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ D @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[16898,10332])). 428.91/126.44 thf(17099,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ B @ (insert1671894227specID @ A @ (subcomponents @ pq))) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[17098:[bind(A, $thf(F)),bind(B, $thf(E)),bind(C, $thf(subcomponents @ pq)),bind(D, $thf(insert1671894227specID @ E @ F))]])). 428.91/126.44 thf(17273,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((sup_su1712599557specID @ B @ (insert1671894227specID @ A @ (subcomponents @ pq))) != bot_bo1785112429specID))),inference(simp,[status(thm)],[17099])). 428.91/126.44 thf(18105,plain,(! [E:set_Secrecy_specID,D:secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != bot_bo1785112429specID) | ((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != (sup_su1712599557specID @ E @ (insert1671894227specID @ D @ (subcomponents @ pq)))))),inference(paramod_ordered,[status(thm)],[16898,17273])). 428.91/126.44 thf(18106,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ (subcomponents @ pq)) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[18105:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(subcomponents @ pq)),bind(D, $thf(B)),bind(E, $thf(A))]])). 428.91/126.44 thf(18552,plain,(! [E:secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ C)) != bot_bo1785112429specID) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ A) @ C) != (sup_su1712599557specID @ (insert1671894227specID @ E @ D) @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[16898,18106])). 428.91/126.44 thf(18553,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (insert1671894227specID @ B @ (subcomponents @ pq))) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[18552:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(subcomponents @ pq)),bind(D, $thf(A)),bind(E, $thf(B))]])). 428.91/126.44 thf(144,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:secrecy_chanID]: ((~ (ineM @ A @ B @ C)) => ((~ (ineM @ D @ B @ C)) => (((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correctCompositionIn @ E) => (((member1967978193chanID @ F @ (ins @ E)) => (~ (exprChannel @ F @ C))) <= (member1967978193chanID @ F @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_TBlemma3b)). 428.91/126.44 thf(732,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:secrecy_chanID]: ((~ (ineM @ A @ B @ C)) => ((~ (ineM @ D @ B @ C)) => (((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correctCompositionIn @ E) => (((member1967978193chanID @ F @ (ins @ E)) => (~ (exprChannel @ F @ C))) | ~ (member1967978193chanID @ F @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 428.91/126.44 thf(13972,plain,(((insert1671894227specID @ pq @ bot_bo1785112429specID) != (subcomponents @ pq))),inference(simp,[status(thm)],[13971])). 428.91/126.44 thf(285,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((~ (member1967978193chanID @ A @ B)) | (B = (insert751661162chanID @ A @ (sk1 @ B @ A))))),inference(cnf,[status(esa)],[283])). 428.91/126.44 thf(286,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (sk1 @ B @ A)) = B) | (~ (member1967978193chanID @ A @ B)))),inference(lifteq,[status(thm)],[285])). 428.91/126.44 thf(103,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID]: (member740727610specID @ A @ (insert1671894227specID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insertI1)). 428.91/126.44 thf(579,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: (member740727610specID @ A @ (insert1671894227specID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 428.91/126.44 thf(213,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ D @ (specKeysSecrets @ B))) <= (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ A))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_correctCompositionKS__negP)). 428.91/126.44 thf(1007,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((correctCompositionKS @ A) => (~ (member_Secrecy_KS @ D @ (specKeysSecrets @ B)) | (member_Secrecy_KS @ D @ (specKeysSecrets @ A)))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 428.91/126.44 thf(134,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:set_Secrecy_chanID]: ((~ (eoutM @ A @ B @ C)) => (((correc990227761ionOut @ D) => ((out_exprChannelSet @ E @ F @ C) => ((! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ D)) <= (member1967978193chanID @ G @ F))) => (~ (eoutM @ D @ B @ C))))) <= ((subcomponents @ D) = (insert1671894227specID @ E @ (insert1671894227specID @ A @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_TBtheorem5b__notP2)). 428.91/126.44 thf(694,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID,F:set_Secrecy_chanID]: ((~ (eoutM @ A @ B @ C)) => (((correc990227761ionOut @ D) => ((out_exprChannelSet @ E @ F @ C) => ((! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ D)) | ~ (member1967978193chanID @ G @ F))) => (~ (eoutM @ D @ B @ C))))) | ~ ((subcomponents @ D) = (insert1671894227specID @ E @ (insert1671894227specID @ A @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 428.91/126.44 thf(9923,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))) != (^ [C:secrecy_KS]: (specKeysSecrets @ q))) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,9914])). 428.91/126.44 thf(9924,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(pattern_uni,[status(thm)],[9923:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(9927,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ A))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(simp,[status(thm)],[9924])). 428.91/126.44 thf(10193,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((^ [C:secrecy_KS]: (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))) != (^ [C:secrecy_KS]: (specKeysSecrets @ q))) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1152,9927])). 428.91/126.44 thf(10194,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(pattern_uni,[status(thm)],[10193:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))),bind(B, $thf(B))]])). 428.91/126.44 thf(10200,plain,(! [A:set_Secrecy_KS] : (((^ [B:secrecy_KS]: (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))) != (^ [B:secrecy_KS]: (specKeysSecrets @ q))))),inference(simp,[status(thm)],[10194])). 428.91/126.44 thf(842,plain,(! [A:secrecy_Secrets] : (((secrec1016742679ession @ (secrecy_sKS @ A)) = (secrecy_sE @ A)))),inference(cnf,[status(esa)],[841])). 428.91/126.44 thf(843,plain,(! [A:secrecy_Secrets] : (((secrec1016742679ession @ (secrecy_sKS @ A)) = (secrecy_sE @ A)))),inference(lifteq,[status(thm)],[842])). 428.91/126.44 thf(162,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: (((insert1671894227specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID)) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) = (((B = C) & (A = D)) | ((B = D) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_doubleton__eq__iff)). 428.91/126.44 thf(787,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: (((insert1671894227specID @ A @ (insert1671894227specID @ B @ bot_bo1785112429specID)) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))) = (((B = C) & (A = D)) | ((B = D) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 428.91/126.44 thf(11188,plain,(! [D:set_Secrecy_specID,C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((~ (member740727610specID @ A @ B)) | ((sup_su1712599557specID @ B @ D) != bot_bo1785112429specID) | ((insert1671894227specID @ A @ (sk4 @ B @ A)) != (insert1671894227specID @ pq @ C)))),inference(paramod_ordered,[status(thm)],[370,10794])). 428.91/126.44 thf(11189,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ pq @ B)) | ((sup_su1712599557specID @ B @ A) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[11188:[bind(A, $thf(pq)),bind(B, $thf(E)),bind(C, $thf(sk4 @ E @ pq)),bind(D, $thf(D))]])). 428.91/126.44 thf(11201,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ pq @ B)) | ((sup_su1712599557specID @ B @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[11189])). 428.91/126.44 thf(224,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:(secrecy_KS > $o)]: ((? [D:secrecy_KS]: ((member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ A @ B)) & (C @ D))) = (? [D:secrecy_KS]: ((member_Secrecy_KS @ D @ A) & (C @ D)) | ? [D:secrecy_KS]: ((C @ D) & (member_Secrecy_KS @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_bex__Un)). 428.91/126.44 thf(1058,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:(secrecy_KS > $o)]: ((? [D:secrecy_KS]: ((member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ A @ B)) & (C @ D))) = (? [D:secrecy_KS]: ((member_Secrecy_KS @ D @ A) & (C @ D)) | ? [D:secrecy_KS]: ((C @ D) & (member_Secrecy_KS @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 428.91/126.44 thf(5592,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ (specKeysSecrets @ q) @ (specKeysSecrets @ q))))))),inference(simp,[status(thm)],[5405])). 428.91/126.44 thf(7908,plain,(((collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ q)))))),inference(rewrite,[status(thm)],[5592,805])). 428.91/126.44 thf(7923,plain,(! [A:set_Secrecy_KS] : ((A != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (specKeysSecrets @ q))))) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,7908])). 428.91/126.44 thf(7924,plain,(((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (collect_Secrecy_KS @ (^ [A:secrecy_KS]: (member_Secrecy_KS @ A @ (specKeysSecrets @ q)))))),inference(pattern_uni,[status(thm)],[7923:[bind(A, $thf(insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(68,axiom,((! [A:set_Secrecy_chanID]: ((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) => (A = bot_bo443197316chanID)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_equals0I)). 428.91/126.44 thf(466,plain,((! [A:set_Secrecy_chanID]: ((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) => (A = bot_bo443197316chanID)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 428.91/126.44 thf(1090,plain,(((secrecy_kKS @ key) = m)),inference(lifteq,[status(thm)],[1089])). 428.91/126.44 thf(918,plain,(! [A:secrecy_Keys] : (((secrec1016742679ession @ (secrecy_kKS @ A)) = (secrecy_kE @ A)))),inference(cnf,[status(esa)],[917])). 428.91/126.44 thf(919,plain,(! [A:secrecy_Keys] : (((secrec1016742679ession @ (secrecy_kKS @ A)) = (secrecy_kE @ A)))),inference(lifteq,[status(thm)],[918])). 428.91/126.44 thf(136,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID,E:set_Secrecy_chanID]: ((~ (eout @ A @ B)) => (((subcomponents @ C) = (insert1671894227specID @ D @ (insert1671894227specID @ A @ bot_bo1785112429specID))) => ((correc990227761ionOut @ C) => (((! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ C)) <= (member1967978193chanID @ F @ E))) => (~ (eout @ C @ B))) <= (out_exprChannelSet @ D @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_TBtheorem5a__notP2)). 428.91/126.44 thf(704,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID,E:set_Secrecy_chanID]: ((~ (eout @ A @ B)) => (((subcomponents @ C) = (insert1671894227specID @ D @ (insert1671894227specID @ A @ bot_bo1785112429specID))) => ((correc990227761ionOut @ C) => (((! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ C)) | ~ (member1967978193chanID @ F @ E))) => (~ (eout @ C @ B))) | ~ (out_exprChannelSet @ D @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 428.91/126.44 thf(28,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Un__empty)). 428.91/126.44 thf(350,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: (((sup_su1712599557specID @ A @ B) = bot_bo1785112429specID) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 428.91/126.44 thf(42,axiom,((! [A:secrecy_specID]: ~ (member740727610specID @ A @ bot_bo1785112429specID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_emptyE)). 428.91/126.44 thf(391,plain,((! [A:secrecy_specID]: ~ (member740727610specID @ A @ bot_bo1785112429specID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 428.91/126.44 thf(246,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insertI1)). 428.91/126.44 thf(1139,plain,((! [A:secrecy_KS,B:set_Secrecy_KS]: (member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 428.91/126.44 thf(138,axiom,((! [A:secrecy_Secrets,B:secrecy_Secrets]: (((secrecy_sE @ A) = (secrecy_sE @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Expression_Oinject_I2_J)). 428.91/126.44 thf(713,plain,((! [A:secrecy_Secrets,B:secrecy_Secrets]: (((secrecy_sE @ A) = (secrecy_sE @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 428.91/126.44 thf(75,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (((~ (ine @ A @ C)) <= (B = bot_bo443197316chanID)) <= (ine_exprChannelSet @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ine__empty__exprChannelSet)). 428.91/126.44 thf(495,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (~ (ine @ A @ C) | ~ (B = bot_bo443197316chanID) | ~ (ine_exprChannelSet @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 428.91/126.44 thf(496,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((~ (ine @ A @ C)) | (~ (B = bot_bo443197316chanID)) | (~ (ine_exprChannelSet @ A @ B @ C)))),inference(cnf,[status(esa)],[495])). 428.91/126.44 thf(497,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((B != bot_bo443197316chanID) | (~ (ine @ A @ C)) | (~ (ine_exprChannelSet @ A @ B @ C)))),inference(lifteq,[status(thm)],[496])). 428.91/126.44 thf(498,plain,(! [B:secrecy_Expression,A:secrecy_specID] : ((~ (ine @ A @ B)) | (~ (ine_exprChannelSet @ A @ bot_bo443197316chanID @ B)))),inference(simp,[status(thm)],[497])). 428.91/126.44 thf(241,axiom,((! [A:secrecy_KS]: ~ (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_empty__iff)). 428.91/126.44 thf(1117,plain,((! [A:secrecy_KS]: ~ (member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 428.91/126.44 thf(99,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_Un__empty__right)). 428.91/126.44 thf(567,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 428.91/126.44 thf(145,axiom,((ine_ex1303305700Single = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((exprChannel @ B @ C) & ! [D:secrecy_chanID,E:nat]: (((D != B) & (member1967978193chanID @ D @ (ins @ A))) => (~ (exprChannel @ D @ C))) & (member1967978193chanID @ B @ (ins @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ine__exprChannelSingle__def)). 428.91/126.44 thf(736,plain,(((ine_ex1303305700Single) = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((exprChannel @ B @ C) & ! [D:secrecy_chanID]: ((~ (D = B) & (member1967978193chanID @ D @ (ins @ A))) => (~ (exprChannel @ D @ C))) & (member1967978193chanID @ B @ (ins @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 428.91/126.44 thf(737,plain,(((ine_ex1303305700Single) = (^ [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((exprChannel @ B @ C) & ! [D:secrecy_chanID]: ((~ (D = B) & (member1967978193chanID @ D @ (ins @ A))) => (~ (exprChannel @ D @ C))) & (member1967978193chanID @ B @ (ins @ A)))))),inference(lifteq,[status(thm)],[736])). 428.91/126.44 thf(122,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_Secrets]: ((ord_le1802272080chanID @ (out @ A) @ (ins @ B)) => ((~ (eout @ A @ (secrecy_sE @ C))) <= (~ (knowle945212990e_know @ B @ (secrecy_sKS @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_adv__not__know2)). 428.91/126.44 thf(649,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_Secrets]: ((ord_le1802272080chanID @ (out @ A) @ (ins @ B)) => (~ (eout @ A @ (secrecy_sE @ C)) | (knowle945212990e_know @ B @ (secrecy_sKS @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 428.91/126.44 thf(6279,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((member_Secrecy_KS @ (sk39 @ (specKeysSecrets @ pq)) @ (specKeysSecrets @ pq)) != (member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[3615,6243])). 428.91/126.44 thf(6289,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((sk39 @ (specKeysSecrets @ pq)) != sk65) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[6279])). 428.91/126.44 thf(214,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets]: (((correc965049635ionLoc @ A) => ((correctCompositionKS @ A) => (((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ C))) => ((~ (ine @ B @ (secrecy_sE @ D))) => ((~ (ine @ C @ (secrecy_sE @ D))) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C)))))))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ B)))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_LocalSecretsComposition__neg__s)). 428.91/126.44 thf(1011,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets]: (((correc965049635ionLoc @ A) => ((correctCompositionKS @ A) => (((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ C))) => ((~ (ine @ B @ (secrecy_sE @ D))) => ((~ (ine @ C @ (secrecy_sE @ D))) => (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A)) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (sup_su1301156759ecy_KS @ (localSecrets @ B) @ (localSecrets @ C))))))) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ B))))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 428.91/126.44 thf(52,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ((eout @ A @ C) <= (eoutM @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_eoutM__eout)). 428.91/126.44 thf(418,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: ((eout @ A @ C) | ~ (eoutM @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 428.91/126.44 thf(419,plain,(! [C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((eout @ A @ C) | (~ (eoutM @ A @ B @ C)))),inference(cnf,[status(esa)],[418])). 428.91/126.44 thf(19505,plain,(! [A:set_Secrecy_KS] : ((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | (A != (specKeysSecrets @ p)) | ((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,6387])). 428.91/126.44 thf(19506,plain,((~ (member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS))) | ((insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ p))),inference(pattern_uni,[status(thm)],[19505:[bind(A, $thf(insert_Secrecy_KS @ sk63 @ bot_bo1943466239ecy_KS))]])). 428.91/126.44 thf(11058,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[10281,10928])). 428.91/126.44 thf(11080,plain,(! [A:set_Secrecy_specID] : (((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[11058])). 428.91/126.44 thf(11092,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[11080])). 428.91/126.44 thf(599,plain,(((ine) = (^ [A:secrecy_specID,B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (ins @ A)) & (exprChannel @ C @ B))))),inference(lifteq,[status(thm)],[598])). 428.91/126.44 thf(5530,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((A != bot_bo1943466239ecy_KS) | ((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (sup_su1301156759ecy_KS @ A @ A)))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))))))),inference(paramod_ordered,[status(thm)],[1823,1781])). 428.91/126.44 thf(5604,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))),inference(simp,[status(thm)],[5530])). 428.91/126.44 thf(5725,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ bot_bo1943466239ecy_KS))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))),inference(simp,[status(thm)],[5604])). 428.91/126.44 thf(11979,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))) != (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),inference(rewrite,[status(thm)],[5725,718])). 428.91/126.44 thf(117,axiom,((! [A:secrecy_specID]: ((correc965049635ionLoc @ A) => (((loc @ A) = bot_bo443197316chanID) <= ((subcomponents @ A) = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subcomponents__loc)). 428.91/126.44 thf(631,plain,((! [A:secrecy_specID]: ((correc965049635ionLoc @ A) => (((loc @ A) = bot_bo443197316chanID) | ~ ((subcomponents @ A) = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 428.91/126.44 thf(108,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: ((((~ (member1967978193chanID @ D @ (loc @ A))) => ((member1967978193chanID @ D @ (ins @ A)) <= (member1967978193chanID @ D @ (ins @ B)))) <= (correctCompositionIn @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_correctCompositionIn__L1)). 428.91/126.44 thf(594,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID]: (((~ (member1967978193chanID @ D @ (loc @ A))) => ((member1967978193chanID @ D @ (ins @ A)) | ~ (member1967978193chanID @ D @ (ins @ B)))) | ~ (correctCompositionIn @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 428.91/126.44 thf(116,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correctCompositionIn @ E) => ((ineM @ E @ B @ C) <= (? [F:secrecy_chanID]: (((member1967978193chanID @ F @ (ins @ A)) | (member1967978193chanID @ F @ (ins @ D))) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C) & ~ (member1967978193chanID @ F @ (loc @ E))))))) <= ((ineM @ A @ B @ C) | (ineM @ D @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_TBtheorem4b__PQ)). 428.91/126.44 thf(621,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => ((correctCompositionIn @ E) => ((ineM @ E @ B @ C) | ~ (? [F:secrecy_chanID]: (((member1967978193chanID @ F @ (ins @ A)) | (member1967978193chanID @ F @ (ins @ D))) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C) & ~ (member1967978193chanID @ F @ (loc @ E))))))) | ~ ((ineM @ A @ B @ C) | (ineM @ D @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 428.91/126.44 thf(1148,plain,(! [A:set_Secrecy_KS] : (((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) = (A = bot_bo1943466239ecy_KS)))),inference(cnf,[status(esa)],[1147])). 428.91/126.44 thf(1149,plain,(! [A:set_Secrecy_KS] : (((! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A)) = (A = bot_bo1943466239ecy_KS)))),inference(lifteq,[status(thm)],[1148])). 428.91/126.44 thf(10824,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | ((the_el827131246specID @ (subcomponents @ pq)) = A) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[7095,959])). 428.91/126.44 thf(10825,plain,((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | ((the_el827131246specID @ (subcomponents @ pq)) = p)),inference(pattern_uni,[status(thm)],[10824:[bind(A, $thf(p))]])). 428.91/126.44 thf(10930,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((~ (member740727610specID @ B @ (sk5 @ C @ B))) | ((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ B @ C)))),inference(paramod_ordered,[status(thm)],[6672,426])). 428.91/126.44 thf(10931,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p))))),inference(pattern_uni,[status(thm)],[10930:[bind(A, $thf(E)),bind(B, $thf(p)),bind(C, $thf(sup_su1712599557specID @ (subcomponents @ pq) @ E))]])). 428.91/126.44 thf(10985,plain,(! [A:set_Secrecy_specID] : ((~ (member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p))))),inference(simp,[status(thm)],[10931])). 428.91/126.44 thf(11060,plain,(((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[2734,10928])). 428.91/126.44 thf(11084,plain,(((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))) != (subcomponents @ pq))),inference(simp,[status(thm)],[11060])). 428.91/126.44 thf(11095,plain,(((sk5 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))) != (subcomponents @ pq))),inference(simp,[status(thm)],[11084])). 428.91/126.44 thf(255,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (~ (! [C:set_Secrecy_KS]: ((B = (insert_Secrecy_KS @ A @ C)) => (member_Secrecy_KS @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Set_Oset__insert)). 428.91/126.44 thf(1162,plain,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (~ (! [C:set_Secrecy_KS]: ((B = (insert_Secrecy_KS @ A @ C)) => (member_Secrecy_KS @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 428.91/126.44 thf(135,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((ine @ A @ B) => (((correctCompositionIn @ C) => ((? [E:secrecy_chanID]: ((exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ C)) & (member1967978193chanID @ E @ (ins @ A)))) => (ine @ C @ B))) <= ((subcomponents @ C) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_TBtheorem4a__P)). 428.91/126.44 thf(700,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((ine @ A @ B) => (((correctCompositionIn @ C) => ((? [E:secrecy_chanID]: ((exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ C)) & (member1967978193chanID @ E @ (ins @ A)))) => (ine @ C @ B))) | ~ ((subcomponents @ C) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 428.91/126.44 thf(520,plain,(! [C:secrecy_Expression,B:secrecy_chanID,A:secrecy_specID] : ((out_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C) | (~ (out_ex985543062Single @ A @ B @ C)))),inference(cnf,[status(esa)],[519])). 428.91/126.44 thf(195,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((((ine_exprChannelSet @ C @ F @ E) => (((~ (ine @ A @ E)) <= (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ A)) <= (member1967978193chanID @ G @ F)))) <= (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ D) => (member1967978193chanID @ G @ (loc @ A)))))) <= (ine_exprChannelSet @ B @ D @ E)) <= (correctCompositionIn @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_TBtheorem4a__notPQ)). 428.91/126.44 thf(932,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((ine_exprChannelSet @ C @ F @ E) => (~ (ine @ A @ E) | ~ (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ A)) | ~ (member1967978193chanID @ G @ F))) | ~ (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ D) => (member1967978193chanID @ G @ (loc @ A)))))) | ~ (ine_exprChannelSet @ B @ D @ E) | ~ (correctCompositionIn @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 428.91/126.44 thf(225,axiom,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_chanID]: (((exprChannel @ C @ (secrecy_kE @ A)) => ((~ (member1967978193chanID @ C @ (loc @ B))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (specKeysSecrets @ B))))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_LocalSecretsComposition__neg__loc__k)). 428.91/126.44 thf(1061,plain,((! [A:secrecy_Keys,B:secrecy_specID,C:secrecy_chanID]: (((exprChannel @ C @ (secrecy_kE @ A)) => (~ (member1967978193chanID @ C @ (loc @ B)) | (member_Secrecy_KS @ (secrecy_kKS @ A) @ (specKeysSecrets @ B)))) | (member_Secrecy_KS @ (secrecy_kKS @ A) @ (localSecrets @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 428.91/126.44 thf(221,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => ((((exprChannel @ E @ (secrecy_sE @ D)) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A))) => ((? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_sE @ D)) & (member1967978193chanID @ F @ (ins @ A)))) <= (correctCompositionIn @ A)))) <= (member1967978193chanID @ E @ (ins @ B))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_correctCompositionKS__exprChannel__s__Pex)). 428.91/126.44 thf(1044,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => (((exprChannel @ E @ (secrecy_sE @ D)) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A))) => (? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_sE @ D)) & (member1967978193chanID @ F @ (ins @ A))) | ~ (correctCompositionIn @ A)))) | ~ (member1967978193chanID @ E @ (ins @ B)) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A)))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 428.91/126.44 thf(215,axiom,((! [A:secrecy_KS,B:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_singleton__iff)). 428.91/126.44 thf(1015,plain,((! [A:secrecy_KS,B:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 428.91/126.44 thf(98,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID,D:set_Secrecy_specID]: ((~ (member740727610specID @ A @ B)) => ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ C @ D)) = (((B = D) <= (A = C)) & ((A != C) => (? [E:set_Secrecy_specID]: ((B = (insert1671894227specID @ C @ E)) & (D = (insert1671894227specID @ A @ E)) & ~ (member740727610specID @ A @ E) & ~ (member740727610specID @ C @ E)))))) <= (~ (member740727610specID @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insert__eq__iff)). 428.91/126.44 thf(563,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:secrecy_specID,D:set_Secrecy_specID]: ((~ (member740727610specID @ A @ B)) => ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ C @ D)) = (((B = D) | ~ (A = C)) & ((~ (A = C)) => (? [E:set_Secrecy_specID]: ((B = (insert1671894227specID @ C @ E)) & (D = (insert1671894227specID @ A @ E)) & ~ (member740727610specID @ A @ E) & ~ (member740727610specID @ C @ E)))))) | (member740727610specID @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 428.91/126.44 thf(12,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (insert751661162chanID @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insertI2)). 428.91/126.44 thf(299,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (insert751661162chanID @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 428.91/126.44 thf(430,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),inference(cnf,[status(esa)],[429])). 428.91/126.44 thf(431,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),inference(lifteq,[status(thm)],[430])). 428.91/126.44 thf(156,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => (((subcomponents @ A) = (insert1671894227specID @ D @ (insert1671894227specID @ E @ bot_bo1785112429specID))) => ((correctCompositionIn @ A) => ((ineM @ E @ B @ C) | (ineM @ D @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_TBtheorem1b)). 428.91/126.44 thf(768,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => (((subcomponents @ A) = (insert1671894227specID @ D @ (insert1671894227specID @ E @ bot_bo1785112429specID))) => ((correctCompositionIn @ A) => ((ineM @ E @ B @ C) | (ineM @ D @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 428.91/126.44 thf(227,axiom,((correctCompositionIn @ pq)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cCompI)). 428.91/126.44 thf(1066,plain,((correctCompositionIn @ pq)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 428.91/126.44 thf(6,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ C @ B)) <= ((A = C) <= (~ (member1967978193chanID @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_insertCI)). 428.91/126.44 thf(278,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ C @ B)) | ~ ((A = C) | (member1967978193chanID @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 428.91/126.44 thf(2632,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((? [C:secrecy_specID]: (A = (insert1671894227specID @ C @ bot_bo1785112429specID))) | ((is_sin1501507247specID @ A) != (is_sin1501507247specID @ (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(paramod_ordered,[status(thm)],[1265,747])). 428.91/126.44 thf(2633,plain,(! [A:secrecy_specID] : ((? [B:secrecy_specID]: ((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(pattern_uni,[status(thm)],[2632:[bind(A, $thf(insert1671894227specID @ C @ bot_bo1785112429specID)),bind(B, $thf(C))]])). 428.91/126.44 thf(2649,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ (sk49 @ A) @ bot_bo1785112429specID)))),inference(cnf,[status(esa)],[2633])). 428.91/126.44 thf(2650,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ (sk49 @ A) @ bot_bo1785112429specID) = (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(lifteq,[status(thm)],[2649])). 428.91/126.44 thf(2651,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ (sk49 @ A) @ bot_bo1785112429specID) = (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(simp,[status(thm)],[2650])). 428.91/126.44 thf(2920,plain,(! [B:secrecy_specID,A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = B) | ((insert1671894227specID @ (sk49 @ A) @ bot_bo1785112429specID) != (insert1671894227specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[2651,959])). 428.91/126.44 thf(2921,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = (sk49 @ A)))),inference(pattern_uni,[status(thm)],[2920:[bind(A, $thf(C)),bind(B, $thf(sk49 @ C))]])). 428.91/126.44 thf(2943,plain,(! [A:secrecy_specID] : (((the_el827131246specID @ (insert1671894227specID @ A @ bot_bo1785112429specID)) = (sk49 @ A)))),inference(simp,[status(thm)],[2921])). 428.91/126.44 thf(2967,plain,(! [A:secrecy_specID] : (((sk49 @ A) = A))),inference(rewrite,[status(thm)],[2943,959])). 428.91/126.44 thf(70,axiom,((! [A:secrecy_chanID]: ~ (member1967978193chanID @ A @ bot_bo443197316chanID))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_emptyE)). 428.91/126.44 thf(473,plain,((! [A:secrecy_chanID]: ~ (member1967978193chanID @ A @ bot_bo443197316chanID))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 428.91/126.44 thf(132,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => ((((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ E)) & ~ (member1967978193chanID @ F @ (loc @ D)) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C))) => (ineM @ D @ B @ C)) <= (correctCompositionIn @ D)) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ E @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_TBtheorem4b__P)). 428.91/126.44 thf(680,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => (((? [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ E)) & ~ (member1967978193chanID @ F @ (loc @ D)) & (member1967978193chanID @ F @ B) & (exprChannel @ F @ C))) => (ineM @ D @ B @ C)) | ~ (correctCompositionIn @ D) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ E @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 428.91/126.44 thf(126,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((~ (ine @ A @ B)) => ((~ (ine @ C @ B)) => (((~ (ine @ D @ B)) <= (correctCompositionIn @ D)) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_TBtheorem3a)). 428.91/126.44 thf(663,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((~ (ine @ A @ B)) => ((~ (ine @ C @ B)) => (~ (ine @ D @ B) | ~ (correctCompositionIn @ D) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 428.91/126.44 thf(17471,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))) = (is_sin1501507247specID)) | ((^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))) != (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))))),inference(paramod_ordered,[status(thm)],[1269,17467])). 428.91/126.44 thf(17472,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))) = (is_sin1501507247specID))),inference(pattern_uni,[status(thm)],[17471:[]])). 428.91/126.44 thf(340,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: ((~ (member1967978193chanID @ A @ B)) => (! [C:secrecy_chanID,D:set_Secrecy_chanID]: ((~ (member1967978193chanID @ C @ D)) => (((insert751661162chanID @ A @ B) = (insert751661162chanID @ C @ D)) = ((? [E:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ E) & (D = (insert751661162chanID @ A @ E)) & ~ (member1967978193chanID @ C @ E) & (B = (insert751661162chanID @ C @ E))) | (A = C)) & ((A = C) => (B = D))))))))),inference(miniscope,[status(thm)],[339])). 428.91/126.44 thf(341,plain,(! [D:set_Secrecy_chanID,C:secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : ((member1967978193chanID @ A @ B) | (member1967978193chanID @ C @ D) | (((insert751661162chanID @ A @ B) = (insert751661162chanID @ C @ D)) = ((? [E:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ E) & (D = (insert751661162chanID @ A @ E)) & ~ (member1967978193chanID @ C @ E) & (B = (insert751661162chanID @ C @ E))) | (A = C)) & ((A = C) => (B = D)))))),inference(cnf,[status(esa)],[340])). 428.91/126.44 thf(342,plain,(! [D:set_Secrecy_chanID,C:secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : ((((insert751661162chanID @ A @ B) = (insert751661162chanID @ C @ D)) = ((? [E:set_Secrecy_chanID]: (~ (member1967978193chanID @ A @ E) & (D = (insert751661162chanID @ A @ E)) & ~ (member1967978193chanID @ C @ E) & (B = (insert751661162chanID @ C @ E))) | (A = C)) & ((A = C) => (B = D)))) | (member1967978193chanID @ A @ B) | (member1967978193chanID @ C @ D))),inference(lifteq,[status(thm)],[341])). 428.91/126.44 thf(216,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => ((exprChannel @ E @ (secrecy_sE @ D)) => ((((exprChannel @ E @ (secrecy_sE @ D)) & (member1967978193chanID @ E @ (ins @ A))) <= (correctCompositionIn @ A)) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A)))))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_correctCompositionKS__exprChannel__s__P)). 428.91/126.44 thf(1018,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => ((exprChannel @ E @ (secrecy_sE @ D)) => (((exprChannel @ E @ (secrecy_sE @ D)) & (member1967978193chanID @ E @ (ins @ A))) | ~ (correctCompositionIn @ A) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A))))))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 428.91/126.44 thf(354,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ (sup_su370684444chanID @ A @ B) @ C) = (sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(cnf,[status(esa)],[353])). 428.91/126.44 thf(355,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ (sup_su370684444chanID @ A @ B) @ C) = (sup_su370684444chanID @ A @ (sup_su370684444chanID @ B @ C))))),inference(lifteq,[status(thm)],[354])). 428.91/126.44 thf(256,axiom,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B)) => (((correc965049635ionLoc @ B) => ((((~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ D))) => (ine @ C @ (secrecy_sE @ A))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ C)))) <= (~ (ine @ D @ (secrecy_sE @ A))))) <= ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_LocalSecretsComposition__ine1__s)). 428.91/126.44 thf(1166,plain,((! [A:secrecy_Secrets,B:secrecy_specID,C:secrecy_specID,D:secrecy_specID]: ((member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ B)) => (((correc965049635ionLoc @ B) => (((~ (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ D))) => (ine @ C @ (secrecy_sE @ A))) | (member_Secrecy_KS @ (secrecy_sKS @ A) @ (localSecrets @ C)) | (ine @ D @ (secrecy_sE @ A)))) | ~ ((subcomponents @ B) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 428.91/126.44 thf(647,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),inference(cnf,[status(esa)],[646])). 428.91/126.44 thf(648,plain,(! [A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),inference(lifteq,[status(thm)],[647])). 428.91/126.44 thf(7125,plain,(((member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[2734,6835])). 428.91/126.44 thf(7145,plain,(((sk3 @ (subcomponents @ pq)) != (sk3 @ (subcomponents @ pq))) | ((sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))) != (subcomponents @ pq))),inference(simp,[status(thm)],[7125])). 428.91/126.44 thf(7151,plain,(((sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))) != (subcomponents @ pq))),inference(simp,[status(thm)],[7145])). 428.91/126.44 thf(17503,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))) = (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID)))) | ((is_sin1501507247specID) != (is_sin1501507247specID))),inference(paramod_ordered,[status(thm)],[617,17467])). 428.91/126.44 thf(17504,plain,((is_sin1501507247specID @ bot_bo1785112429specID) | ((^ [A:set_Secrecy_specID]: ? [B:secrecy_specID]: (A = (insert1671894227specID @ B @ bot_bo1785112429specID))) = (^ [A:set_Secrecy_specID]: (A = (insert1671894227specID @ (the_el827131246specID @ A) @ bot_bo1785112429specID))))),inference(pattern_uni,[status(thm)],[17503:[]])). 428.91/126.44 thf(441,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : ((((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),inference(cnf,[status(esa)],[440])). 428.91/126.44 thf(442,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : ((((sup_su370684444chanID @ A @ B) = bot_bo443197316chanID) = ((A = bot_bo443197316chanID) & (B = bot_bo443197316chanID))))),inference(lifteq,[status(thm)],[441])). 428.91/126.44 thf(11795,plain,(! [B:set_Secrecy_chanID,A:set_Secrecy_chanID] : (((bot_bo443197316chanID = (sup_su370684444chanID @ A @ B)) = ((bot_bo443197316chanID = A) & (bot_bo443197316chanID = B))))),inference(rewrite,[status(thm)],[442,8130])). 428.91/126.44 thf(2183,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A)))))) != (specKeysSecrets @ p)) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))))),inference(paramod_ordered,[status(thm)],[1152,2168])). 428.91/126.44 thf(2184,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))))) != (specKeysSecrets @ p)))),inference(pattern_uni,[status(thm)],[2183:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ m @ B))))),bind(B, $thf(B))]])). 428.91/126.44 thf(2191,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (insert_Secrecy_KS @ m @ A)))))))))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[2184])). 428.91/126.44 thf(2511,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (collect_Secrecy_KS @ (^ [F:secrecy_KS]: (member_Secrecy_KS @ F @ A)))))))))))) != (specKeysSecrets @ p)) | (A != (insert_Secrecy_KS @ m @ B)))),inference(paramod_ordered,[status(thm)],[1152,2191])). 428.91/126.44 thf(2512,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ m @ A))))))))))))) != (specKeysSecrets @ p)))),inference(pattern_uni,[status(thm)],[2511:[bind(A, $thf(insert_Secrecy_KS @ m @ D)),bind(B, $thf(D))]])). 428.91/126.44 thf(2513,plain,(! [A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ m @ A))))))))))))) != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[2512])). 428.91/126.44 thf(158,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)) = (((B = bot_bo1943466239ecy_KS) & (A = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))) | ((A = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)) & (B = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))) | ((A = bot_bo1943466239ecy_KS) & (B = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Un__singleton__iff)). 428.91/126.44 thf(776,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)) = (((B = bot_bo1943466239ecy_KS) & (A = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))) | ((A = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)) & (B = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))) | ((A = bot_bo1943466239ecy_KS) & (B = (insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 428.91/126.44 thf(85,axiom,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((ine_ex1303305700Single @ A @ B @ C) => (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ine__exprChannelSingle__Set)). 428.91/126.44 thf(524,plain,((! [A:secrecy_specID,B:secrecy_chanID,C:secrecy_Expression]: ((ine_ex1303305700Single @ A @ B @ C) => (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 428.91/126.44 thf(525,plain,(! [C:secrecy_Expression,B:secrecy_chanID,A:secrecy_specID] : ((~ (ine_ex1303305700Single @ A @ B @ C)) | (ine_exprChannelSet @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID) @ C))),inference(cnf,[status(esa)],[524])). 428.91/126.44 thf(212,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets]: ((((~ (ine @ B @ (secrecy_sE @ D))) => ((~ (ine @ C @ (secrecy_sE @ D))) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ B))) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ C))))))) <= (correc965049635ionLoc @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_LocalSecretsComposition__neg1__s)). 428.91/126.44 thf(1003,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets]: (((~ (ine @ B @ (secrecy_sE @ D))) => ((~ (ine @ C @ (secrecy_sE @ D))) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ B))) => (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A)) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ C)))))) | ~ (correc965049635ionLoc @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 428.91/126.44 thf(6271,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | ((member_Secrecy_KS @ sk65 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ pq)))),inference(paramod_ordered,[status(thm)],[269,6243])). 428.91/126.44 thf(6292,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | (sk65 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[6271])). 428.91/126.44 thf(6433,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | (sk65 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((member_Secrecy_KS @ (sk39 @ A) @ A) != (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1196,6292])). 428.91/126.44 thf(6445,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | (sk65 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((sk39 @ A) != sk65) | (A != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[6433])). 428.91/126.44 thf(6453,plain,(((specKeysSecrets @ q) = bot_bo1943466239ecy_KS) | (sk65 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((sk39 @ (specKeysSecrets @ q)) != sk65)),inference(simp,[status(thm)],[6445])). 428.91/126.44 thf(253,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)) <= (member_Secrecy_KS @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insertI2)). 428.91/126.44 thf(1156,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS]: ((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ C @ B)) | ~ (member_Secrecy_KS @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 428.91/126.44 thf(205,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: (((member_Secrecy_KS @ A @ C) <= (~ (member_Secrecy_KS @ A @ B))) => (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_UnCI)). 428.91/126.44 thf(971,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: (((member_Secrecy_KS @ A @ C) | (member_Secrecy_KS @ A @ B)) => (member_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 428.91/126.44 thf(3613,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | ((member_Secrecy_KS @ (sk39 @ A) @ A) != (member_Secrecy_KS @ m @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1196,1179])). 428.91/126.44 thf(3809,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | ((sk39 @ A) != m) | (A != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[3613])). 428.91/126.44 thf(3872,plain,(((specKeysSecrets @ q) = bot_bo1943466239ecy_KS) | ((sk39 @ (specKeysSecrets @ q)) != m)),inference(simp,[status(thm)],[3809])). 428.91/126.44 thf(12108,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A))) != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)))) | (A != (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))))),inference(paramod_ordered,[status(thm)],[1152,12089])). 428.91/126.44 thf(12109,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))),inference(pattern_uni,[status(thm)],[12108:[bind(A, $thf(collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS))))),bind(B, $thf(B))]])). 428.91/126.44 thf(12121,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))))),inference(simp,[status(thm)],[12109])). 428.91/126.44 thf(12648,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(rewrite,[status(thm)],[12121,1000])). 428.91/126.44 thf(780,plain,(! [A:secrecy_specID] : ((member740727610specID @ A @ (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(cnf,[status(esa)],[779])). 428.91/126.44 thf(1643,plain,(! [B:secrecy_specID,A:secrecy_specID] : (((member740727610specID @ A @ (insert1671894227specID @ A @ bot_bo1785112429specID)) != (member740727610specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[780,363])). 428.91/126.44 thf(1645,plain,(! [B:secrecy_specID,A:secrecy_specID] : ((A != B) | ((insert1671894227specID @ A @ bot_bo1785112429specID) != bot_bo1785112429specID))),inference(simp,[status(thm)],[1643])). 428.91/126.44 thf(1647,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ bot_bo1785112429specID) != bot_bo1785112429specID))),inference(simp,[status(thm)],[1645])). 428.91/126.44 thf(10294,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[10261,6849])). 428.91/126.44 thf(10316,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[10294])). 428.91/126.44 thf(10333,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[10316])). 428.91/126.44 thf(408,plain,((! [A:secrecy_specID,B:secrecy_Expression]: (~ (? [C:set_Secrecy_chanID]: (eoutM @ A @ C @ B)) | (eout @ A @ B)))),inference(miniscope,[status(thm)],[407])). 428.91/126.44 thf(409,plain,(! [C:set_Secrecy_chanID,B:secrecy_Expression,A:secrecy_specID] : ((~ (eoutM @ A @ C @ B)) | (eout @ A @ B))),inference(cnf,[status(esa)],[408])). 428.91/126.44 thf(129,axiom,((! [A:secrecy_Keys,B:secrecy_Keys]: (((secrecy_kE @ A) = (secrecy_kE @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Expression_Oinject_I1_J)). 428.91/126.44 thf(673,plain,((! [A:secrecy_Keys,B:secrecy_Keys]: (((secrecy_kE @ A) = (secrecy_kE @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 428.91/126.44 thf(12719,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | (is_sin1501507247specID @ (subcomponents @ pq)) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[11387,747])). 428.91/126.44 thf(12720,plain,((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | (is_sin1501507247specID @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[12719:[bind(A, $thf(p))]])). 428.91/126.44 thf(261,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS,D:set_Secrecy_KS]: (((~ (member_Secrecy_KS @ C @ D)) => (((insert_Secrecy_KS @ A @ B) = (insert_Secrecy_KS @ C @ D)) = (((A = C) => (B = D)) & ((A != C) => (? [E:set_Secrecy_KS]: (~ (member_Secrecy_KS @ C @ E) & ~ (member_Secrecy_KS @ A @ E) & (D = (insert_Secrecy_KS @ A @ E)) & (B = (insert_Secrecy_KS @ C @ E)))))))) <= (~ (member_Secrecy_KS @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__eq__iff)). 428.91/126.44 thf(1186,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:secrecy_KS,D:set_Secrecy_KS]: (((~ (member_Secrecy_KS @ C @ D)) => (((insert_Secrecy_KS @ A @ B) = (insert_Secrecy_KS @ C @ D)) = (((A = C) => (B = D)) & ((~ (A = C)) => (? [E:set_Secrecy_KS]: (~ (member_Secrecy_KS @ C @ E) & ~ (member_Secrecy_KS @ A @ E) & (D = (insert_Secrecy_KS @ A @ E)) & (B = (insert_Secrecy_KS @ C @ E)))))))) | (member_Secrecy_KS @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 428.91/126.44 thf(10997,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ A @ (subcomponents @ pq))) != (member740727610specID @ p @ (sk5 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[10261,10945])). 428.91/126.44 thf(11012,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[10997])). 428.91/126.44 thf(11022,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ A @ (subcomponents @ pq)) != (sk5 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[11012])). 428.91/126.44 thf(1261,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A) = (sup_su1712599557specID @ (insert1671894227specID @ A @ bot_bo1785112429specID))))),inference(func_ext,[status(esa)],[745])). 428.91/126.44 thf(10860,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ A) = (sup_su1712599557specID @ (subcomponents @ pq))) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[7095,1261])). 428.91/126.44 thf(10861,plain,((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ p) = (sup_su1712599557specID @ (subcomponents @ pq)))),inference(pattern_uni,[status(thm)],[10860:[bind(A, $thf(p))]])). 428.91/126.44 thf(731,plain,(((inStream) = (^ [A:secrecy_specID]: ((=) @ set_Secrecy_chanID @ (ins @ A))))),inference(lifteq,[status(thm)],[730])). 428.91/126.44 thf(1235,plain,(! [A:secrecy_specID] : (((inStream @ A) = ((=) @ set_Secrecy_chanID @ (ins @ A))))),inference(func_ext,[status(esa)],[731])). 428.91/126.44 thf(67,axiom,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:(secrecy_chanID > $o)]: ((? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (sup_su370684444chanID @ A @ B)) & (C @ D))) = (? [D:secrecy_chanID]: ((member1967978193chanID @ D @ A) & (C @ D)) | ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) & (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_bex__Un)). 428.91/126.44 thf(463,plain,((! [A:set_Secrecy_chanID,B:set_Secrecy_chanID,C:(secrecy_chanID > $o)]: ((? [D:secrecy_chanID]: ((member1967978193chanID @ D @ (sup_su370684444chanID @ A @ B)) & (C @ D))) = (? [D:secrecy_chanID]: ((member1967978193chanID @ D @ A) & (C @ D)) | ? [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) & (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 428.91/126.44 thf(58,axiom,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: ((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_sup__bot_Oneutr__eq__iff)). 428.91/126.44 thf(437,plain,((! [A:set_Secrecy_specID,B:set_Secrecy_specID]: ((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 428.91/126.44 thf(438,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(cnf,[status(esa)],[437])). 428.91/126.44 thf(439,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((A = bot_bo1785112429specID) & (B = bot_bo1785112429specID))))),inference(lifteq,[status(thm)],[438])). 428.91/126.44 thf(11622,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((bot_bo1785112429specID = (sup_su1712599557specID @ A @ B)) = ((bot_bo1785112429specID = A) & (bot_bo1785112429specID = B))))),inference(rewrite,[status(thm)],[439,7833])). 428.91/126.44 thf(24,axiom,((! [A:secrecy_chanID,B:secrecy_chanID,C:secrecy_chanID,D:secrecy_chanID]: (((insert751661162chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (insert751661162chanID @ C @ (insert751661162chanID @ D @ bot_bo443197316chanID))) = (((A = D) & (B = C)) | ((B = D) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_doubleton__eq__iff)). 428.91/126.44 thf(336,plain,((! [A:secrecy_chanID,B:secrecy_chanID,C:secrecy_chanID,D:secrecy_chanID]: (((insert751661162chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (insert751661162chanID @ C @ (insert751661162chanID @ D @ bot_bo443197316chanID))) = (((A = D) & (B = C)) | ((B = D) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 428.91/126.44 thf(337,plain,(! [D:secrecy_chanID,C:secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : ((((insert751661162chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (insert751661162chanID @ C @ (insert751661162chanID @ D @ bot_bo443197316chanID))) = (((A = D) & (B = C)) | ((B = D) & (A = C)))))),inference(cnf,[status(esa)],[336])). 428.91/126.44 thf(338,plain,(! [D:secrecy_chanID,C:secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : ((((insert751661162chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) = (insert751661162chanID @ C @ (insert751661162chanID @ D @ bot_bo443197316chanID))) = (((A = D) & (B = C)) | ((B = D) & (A = C)))))),inference(lifteq,[status(thm)],[337])). 428.91/126.44 thf(233,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (? [C:set_Secrecy_KS]: ((B = (insert_Secrecy_KS @ A @ C)) & ~ (member_Secrecy_KS @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mk__disjoint__insert)). 428.91/126.44 thf(1085,plain,((! [A:secrecy_KS,B:set_Secrecy_KS]: ((member_Secrecy_KS @ A @ B) => (? [C:set_Secrecy_KS]: ((B = (insert_Secrecy_KS @ A @ C)) & ~ (member_Secrecy_KS @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 428.91/126.44 thf(102,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_sup__bot_Oleft__neutral)). 428.91/126.44 thf(576,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ bot_bo1785112429specID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 428.91/126.44 thf(31,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) => ((~ (member1967978193chanID @ A @ B)) => (member1967978193chanID @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_UnE)). 428.91/126.44 thf(359,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ (sup_su370684444chanID @ B @ C)) => ((~ (member1967978193chanID @ A @ B)) => (member1967978193chanID @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 428.91/126.44 thf(318,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ A @ B)) = (insert751661162chanID @ A @ B)))),inference(cnf,[status(esa)],[317])). 428.91/126.44 thf(319,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ A @ B)) = (insert751661162chanID @ A @ B)))),inference(lifteq,[status(thm)],[318])). 428.91/126.44 thf(3029,plain,(! [E:set_Secrecy_chanID,D:set_Secrecy_chanID,C:secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : (((sup_su370684444chanID @ D @ (insert751661162chanID @ A @ B)) != bot_bo443197316chanID) | ((insert751661162chanID @ A @ (insert751661162chanID @ A @ B)) != (insert751661162chanID @ C @ E)))),inference(paramod_ordered,[status(thm)],[319,1336])). 428.91/126.44 thf(3030,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[3029:[bind(A, $thf(F)),bind(B, $thf(G)),bind(C, $thf(F)),bind(D, $thf(D)),bind(E, $thf(insert751661162chanID @ F @ G))]])). 428.91/126.44 thf(3095,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ (insert751661162chanID @ B @ C)) != bot_bo443197316chanID))),inference(simp,[status(thm)],[3030])). 428.91/126.44 thf(91,axiom,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_sup__bot_Oright__neutral)). 428.91/126.44 thf(544,plain,((! [A:set_Secrecy_specID]: ((sup_su1712599557specID @ A @ bot_bo1785112429specID) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 428.91/126.44 thf(188,axiom,((! [A:secrecy_specID,B:secrecy_specID]: ((A = B) <= ((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ B @ bot_bo1785112429specID))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_singleton__inject)). 428.91/126.44 thf(907,plain,((! [A:secrecy_specID,B:secrecy_specID]: ((A = B) | ~ ((insert1671894227specID @ A @ bot_bo1785112429specID) = (insert1671894227specID @ B @ bot_bo1785112429specID))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 428.91/126.44 thf(247,axiom,((knowle945212990e_know @ p @ m)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_assms_I3_J)). 428.91/126.44 thf(1141,plain,((knowle945212990e_know @ p @ m)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 428.91/126.44 thf(113,axiom,((! [A:secrecy_Keys,B:secrecy_Keys]: (((secrecy_kKS @ A) = (secrecy_kKS @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_KS_Oinject_I1_J)). 428.91/126.44 thf(613,plain,((! [A:secrecy_Keys,B:secrecy_Keys]: (((secrecy_kKS @ A) = (secrecy_kKS @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 428.91/126.44 thf(110,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ B) @ C) = (insert_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Un__insert__left)). 428.91/126.44 thf(600,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ (insert_Secrecy_KS @ A @ B) @ C) = (insert_Secrecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 428.91/126.44 thf(314,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : ((~ (member1967978193chanID @ A @ B)) | (~ (member1967978193chanID @ A @ (sk2 @ B @ A))))),inference(cnf,[status(esa)],[313])). 428.91/126.44 thf(6086,plain,((member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))),inference(bool_ext,[status(thm)],[6061])). 428.91/126.44 thf(236,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => ((correctCompositionIn @ A) => ((exprChannel @ E @ (secrecy_kE @ D)) & (member1967978193chanID @ E @ (ins @ A))))) <= (exprChannel @ E @ (secrecy_kE @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_correctCompositionKS__exprChannel__k__P)). 428.91/126.44 thf(1094,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => ((correctCompositionIn @ A) => ((exprChannel @ E @ (secrecy_kE @ D)) & (member1967978193chanID @ E @ (ins @ A))))) | ~ (exprChannel @ E @ (secrecy_kE @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 428.91/126.44 thf(207,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ A) => ((! [E:secrecy_Keys]: ((~ (ine @ B @ (secrecy_kE @ E)) & ~ (ine @ C @ (secrecy_kE @ E))) <= (D = (secrecy_kKS @ E)))) => ((((~ (member_Secrecy_KS @ D @ (localSecrets @ A))) <= (~ (member_Secrecy_KS @ D @ (localSecrets @ C)))) <= (~ (member_Secrecy_KS @ D @ (localSecrets @ B)))) <= (! [E:secrecy_Secrets]: ((~ (ine @ B @ (secrecy_sE @ E)) & ~ (ine @ C @ (secrecy_sE @ E))) <= (D = (secrecy_sKS @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_LocalSecretsComposition__neg1)). 428.91/126.44 thf(978,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_KS]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => ((correc965049635ionLoc @ A) => ((! [E:secrecy_Keys]: ((~ (ine @ B @ (secrecy_kE @ E)) & ~ (ine @ C @ (secrecy_kE @ E))) | ~ (D = (secrecy_kKS @ E)))) => (~ (member_Secrecy_KS @ D @ (localSecrets @ A)) | (member_Secrecy_KS @ D @ (localSecrets @ C)) | (member_Secrecy_KS @ D @ (localSecrets @ B)) | ~ (! [E:secrecy_Secrets]: ((~ (ine @ B @ (secrecy_sE @ E)) & ~ (ine @ C @ (secrecy_sE @ E))) | ~ (D = (secrecy_sKS @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 428.91/126.44 thf(1316,plain,(! [A:secrecy_specID] : (((ine @ A) = (^ [B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (ins @ A)) & (exprChannel @ C @ B)))))),inference(func_ext,[status(esa)],[599])). 428.91/126.44 thf(260,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((correctCompositionKS @ A) => (((((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => (((member1967978193chanID @ E @ (ins @ A)) & (exprChannel @ E @ (secrecy_kE @ D))) <= (correctCompositionIn @ A))) <= (exprChannel @ E @ (secrecy_kE @ D))) <= (member1967978193chanID @ E @ (ins @ C))) <= (~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_correctCompositionKS__exprChannel__k__Q)). 428.91/126.44 thf(1180,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((correctCompositionKS @ A) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => (((member1967978193chanID @ E @ (ins @ A)) & (exprChannel @ E @ (secrecy_kE @ D))) | ~ (correctCompositionIn @ A))) | ~ (exprChannel @ E @ (secrecy_kE @ D)) | ~ (member1967978193chanID @ E @ (ins @ C)) | (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A)))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 428.91/126.44 thf(150,axiom,((ine @ p @ (secrecy_kE @ key))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_a11)). 428.91/126.44 thf(748,plain,((ine @ p @ (secrecy_kE @ key))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 428.91/126.44 thf(16420,plain,(! [B:secrecy_Expression,A:secrecy_specID] : ((~ (ine_exprChannelSet @ A @ bot_bo443197316chanID @ B)) | ((ine @ p @ (secrecy_kE @ key)) != (ine @ A @ B)))),inference(paramod_ordered,[status(thm)],[748,498])). 428.91/126.44 thf(16421,plain,((~ (ine_exprChannelSet @ p @ bot_bo443197316chanID @ (secrecy_kE @ key)))),inference(pattern_uni,[status(thm)],[16420:[bind(A, $thf(p)),bind(B, $thf(secrecy_kE @ key))]])). 428.91/126.44 thf(154,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID,E:set_Secrecy_chanID]: (((((ine_exprChannelSet @ D @ E @ B) => ((~ (ine @ C @ B)) <= (! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ C)) <= (member1967978193chanID @ F @ E))))) <= (correctCompositionIn @ C)) <= ((subcomponents @ C) = (insert1671894227specID @ D @ (insert1671894227specID @ A @ bot_bo1785112429specID)))) <= (~ (ine @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_TBtheorem4a__notP2)). 428.91/126.44 thf(759,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID,E:set_Secrecy_chanID]: (((ine_exprChannelSet @ D @ E @ B) => (~ (ine @ C @ B) | ~ (! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (loc @ C)) | ~ (member1967978193chanID @ F @ E))))) | ~ (correctCompositionIn @ C) | ~ ((subcomponents @ C) = (insert1671894227specID @ D @ (insert1671894227specID @ A @ bot_bo1785112429specID))) | (ine @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 428.91/126.44 thf(243,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ C)) => ((((correctCompositionIn @ A) => (? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_sE @ D)) & (member1967978193chanID @ F @ (ins @ A))))) <= (~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A)))) <= (exprChannel @ E @ (secrecy_sE @ D)))))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_correctCompositionKS__exprChannel__s__Qex)). 428.91/126.44 thf(1126,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Secrets,E:secrecy_chanID]: (((correctCompositionKS @ A) => ((~ (member_Secrecy_KS @ (secrecy_sKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ C)) => (((correctCompositionIn @ A) => (? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_sE @ D)) & (member1967978193chanID @ F @ (ins @ A))))) | (member_Secrecy_KS @ (secrecy_sKS @ D) @ (specKeysSecrets @ A)) | ~ (exprChannel @ E @ (secrecy_sE @ D)))))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 428.91/126.44 thf(5760,plain,(! [A:secrecy_KS] : (((collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))))))))) != (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (($false))))))),inference(paramod_ordered,[status(thm)],[5748,1911])). 428.91/126.44 thf(5832,plain,(! [A:secrecy_KS] : (((^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ (collect_Secrecy_KS @ (^ [E:secrecy_KS]: (member_Secrecy_KS @ E @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))))))))) != (^ [B:secrecy_KS]: (($false)))))),inference(simp,[status(thm)],[5760])). 428.91/126.44 thf(95,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: (((member740727610specID @ A @ C) <= (~ (member740727610specID @ A @ B))) <= (member740727610specID @ A @ (sup_su1712599557specID @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_UnE)). 428.91/126.44 thf(556,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: ((member740727610specID @ A @ C) | (member740727610specID @ A @ B) | ~ (member740727610specID @ A @ (sup_su1712599557specID @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 428.91/126.44 thf(104,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (sup_su370684444chanID @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_UnI2)). 428.91/126.44 thf(581,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: ((member1967978193chanID @ A @ B) => (member1967978193chanID @ A @ (sup_su370684444chanID @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 428.91/126.44 thf(186,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID]: (((correc990227761ionOut @ A) => (((out_exprChannelSet @ C @ F @ E) => (((~ (eout @ A @ E)) <= (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ F) => (member1967978193chanID @ G @ (loc @ A))))) <= (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ A)) <= (member1967978193chanID @ G @ D))))) <= (out_exprChannelSet @ B @ D @ E))) <= ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_TBtheorem5a__notPQ)). 428.91/126.44 thf(891,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:set_Secrecy_chanID,E:secrecy_Expression,F:set_Secrecy_chanID]: (((correc990227761ionOut @ A) => (((out_exprChannelSet @ C @ F @ E) => (~ (eout @ A @ E) | ~ (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ F) => (member1967978193chanID @ G @ (loc @ A)))) | ~ (! [G:secrecy_chanID]: ((member1967978193chanID @ G @ (loc @ A)) | ~ (member1967978193chanID @ G @ D))))) | ~ (out_exprChannelSet @ B @ D @ E))) | ~ ((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 428.91/126.44 thf(177,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) = (sup_su1301156759ecy_KS @ B @ C)) = (((B = bot_bo1943466239ecy_KS) & (C = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) | ((B = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) & (C = bot_bo1943466239ecy_KS)) | ((C = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) & (B = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_singleton__Un__iff)). 428.91/126.44 thf(844,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: (((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) = (sup_su1301156759ecy_KS @ B @ C)) = (((B = bot_bo1943466239ecy_KS) & (C = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))) | ((B = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) & (C = bot_bo1943466239ecy_KS)) | ((C = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) & (B = (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 428.91/126.44 thf(202,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_Keys]: ((ord_le1802272080chanID @ (out @ A) @ (ins @ B)) => ((~ (eout @ A @ (secrecy_kE @ C))) <= (~ (knowle945212990e_know @ B @ (secrecy_kKS @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_adv__not__know1)). 428.91/126.44 thf(963,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_Keys]: ((ord_le1802272080chanID @ (out @ A) @ (ins @ B)) => (~ (eout @ A @ (secrecy_kE @ C)) | (knowle945212990e_know @ B @ (secrecy_kKS @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 428.91/126.44 thf(123,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ (sup_su1301156759ecy_KS @ A @ B) @ C) = (sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Un__assoc)). 428.91/126.44 thf(652,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ (sup_su1301156759ecy_KS @ A @ B) @ C) = (sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 428.91/126.44 thf(389,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),inference(cnf,[status(esa)],[388])). 428.91/126.44 thf(390,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ A @ bot_bo443197316chanID) = A))),inference(lifteq,[status(thm)],[389])). 428.91/126.44 thf(6891,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sup_su1712599557specID @ (subcomponents @ pq) @ A)) != (member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[6672,6849])). 428.91/126.44 thf(6902,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[6891])). 428.91/126.44 thf(6910,plain,(! [A:set_Secrecy_specID] : (((sup_su1712599557specID @ (subcomponents @ pq) @ A) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[6902])). 428.91/126.44 thf(160,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => ((~ (ineM @ D @ B @ C)) => (((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => (((~ (ineM @ E @ B @ C)) <= (? [F:secrecy_chanID]: ((ine_ex1303305700Single @ A @ F @ C) & (member1967978193chanID @ F @ B) & (member1967978193chanID @ F @ (loc @ E))))) <= (correctCompositionIn @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_TBtheorem4b__notP1)). 428.91/126.44 thf(781,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((ineM @ A @ B @ C) => ((~ (ineM @ D @ B @ C)) => (((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) => (~ (ineM @ E @ B @ C) | ~ (? [F:secrecy_chanID]: ((ine_ex1303305700Single @ A @ F @ C) & (member1967978193chanID @ F @ B) & (member1967978193chanID @ F @ (loc @ E)))) | ~ (correctCompositionIn @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 428.91/126.44 thf(1339,plain,(! [B:secrecy_Secrets,A:secrecy_Keys] : (((secrecy_sKS @ B) != m) | ((secrecy_kKS @ key) != (secrecy_kKS @ A)))),inference(paramod_ordered,[status(thm)],[1090,593])). 428.91/126.44 thf(1340,plain,(! [A:secrecy_Secrets] : (((secrecy_sKS @ A) != m))),inference(pattern_uni,[status(thm)],[1339:[bind(A, $thf(key))]])). 428.91/126.44 thf(1341,plain,(! [A:secrecy_Secrets] : (((secrecy_sKS @ A) != m))),inference(simp,[status(thm)],[1340])). 428.91/126.44 thf(8172,plain,(! [A:set_Secrecy_chanID] : (((! [B:secrecy_chanID]: ~ (member1967978193chanID @ B @ A)) = (bot_bo443197316chanID = A)))),inference(rewrite,[status(thm)],[543,8130])). 428.91/126.44 thf(1688,plain,(! [A:secrecy_Keys] : (((secrec1016742679ession @ m) = (secrecy_kE @ A)) | ((secrecy_kKS @ key) != (secrecy_kKS @ A)))),inference(paramod_ordered,[status(thm)],[1090,919])). 428.91/126.44 thf(1689,plain,(((secrec1016742679ession @ m) = (secrecy_kE @ key))),inference(pattern_uni,[status(thm)],[1688:[bind(A, $thf(key))]])). 428.91/126.44 thf(9,axiom,((! [A:secrecy_chanID,B:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_singletonD)). 428.91/126.44 thf(290,plain,((! [A:secrecy_chanID,B:secrecy_chanID]: ((member1967978193chanID @ A @ (insert751661162chanID @ B @ bot_bo443197316chanID)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 428.91/126.44 thf(2323,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((^ [C:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ C @ (collect_Secrecy_KS @ (^ [D:secrecy_KS]: (member_Secrecy_KS @ D @ A))))) = (insert_Secrecy_KS @ B)) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,1943])). 428.91/126.44 thf(2324,plain,(! [A:secrecy_KS] : (((^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))) = (insert_Secrecy_KS @ A)))),inference(pattern_uni,[status(thm)],[2323:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(2330,plain,(! [A:secrecy_KS] : (((^ [B:set_Secrecy_KS]: (sup_su1301156759ecy_KS @ B @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)))))) = (insert_Secrecy_KS @ A)))),inference(simp,[status(thm)],[2324])). 428.91/126.44 thf(230,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:(secrecy_KS > $o)]: ((! [D:secrecy_KS]: ((member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ A @ B)) => (C @ D))) = (! [D:secrecy_KS]: ((C @ D) <= (member_Secrecy_KS @ D @ B)) & ! [D:secrecy_KS]: ((member_Secrecy_KS @ D @ A) => (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ball__Un)). 428.91/126.44 thf(1077,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS,C:(secrecy_KS > $o)]: ((! [D:secrecy_KS]: ((member_Secrecy_KS @ D @ (sup_su1301156759ecy_KS @ A @ B)) => (C @ D))) = (! [D:secrecy_KS]: ((C @ D) | ~ (member_Secrecy_KS @ D @ B)) & ! [D:secrecy_KS]: ((member_Secrecy_KS @ D @ A) => (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 428.91/126.44 thf(8768,plain,(! [B:secrecy_specID,A:secrecy_specID] : (((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))) != (member740727610specID @ B @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[8744,363])). 428.91/126.44 thf(8779,plain,(! [B:secrecy_specID,A:secrecy_specID] : ((p != B) | ((insert1671894227specID @ A @ (subcomponents @ pq)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[8768])). 428.91/126.44 thf(8793,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ (subcomponents @ pq)) != bot_bo1785112429specID))),inference(simp,[status(thm)],[8779])). 428.91/126.44 thf(6089,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | ((member_Secrecy_KS @ sk63 @ (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ pq)))),inference(paramod_ordered,[status(thm)],[269,6061])). 428.91/126.44 thf(6103,plain,((~ (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))) | (sk63 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq))),inference(simp,[status(thm)],[6089])). 428.91/126.44 thf(6148,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | (sk63 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((member_Secrecy_KS @ (sk39 @ A) @ A) != (member_Secrecy_KS @ sk63 @ (specKeysSecrets @ p))))),inference(paramod_ordered,[status(thm)],[1196,6103])). 428.91/126.44 thf(6163,plain,(! [A:set_Secrecy_KS] : ((A = bot_bo1943466239ecy_KS) | (sk63 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((sk39 @ A) != sk63) | (A != (specKeysSecrets @ p)))),inference(simp,[status(thm)],[6148])). 428.91/126.44 thf(6166,plain,(((specKeysSecrets @ p) = bot_bo1943466239ecy_KS) | (sk63 != m) | ((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ pq)) | ((sk39 @ (specKeysSecrets @ p)) != sk63)),inference(simp,[status(thm)],[6163])). 428.91/126.44 thf(7387,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((member_Secrecy_KS @ (sk60 @ B) @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A)))) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,5868])). 428.91/126.44 thf(7388,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk60 @ A) @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(pattern_uni,[status(thm)],[7387:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(7406,plain,(! [A:secrecy_KS] : ((member_Secrecy_KS @ (sk60 @ A) @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))))),inference(simp,[status(thm)],[7388])). 428.91/126.44 thf(16457,plain,(! [E:set_Secrecy_specID,D:set_Secrecy_specID,C:set_Secrecy_specID,B:secrecy_specID,A:secrecy_specID] : ((~ ((member740727610specID @ A @ C) | (A = B))) | ((sup_su1712599557specID @ E @ D) != bot_bo1785112429specID) | ((member740727610specID @ A @ (insert1671894227specID @ B @ C)) != (member740727610specID @ pq @ E)))),inference(paramod_ordered,[status(thm)],[412,11201])). 428.91/126.44 thf(16458,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((~ ((member740727610specID @ pq @ C) | (pq = B))) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ C) @ A) != bot_bo1785112429specID))),inference(pattern_uni,[status(thm)],[16457:[bind(A, $thf(pq)),bind(B, $thf(F)),bind(C, $thf(G)),bind(D, $thf(D)),bind(E, $thf(insert1671894227specID @ F @ G))]])). 428.91/126.44 thf(16511,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ B @ C) @ A) != bot_bo1785112429specID) | (~ (pq = B)))),inference(cnf,[status(esa)],[16458])). 428.91/126.44 thf(16513,plain,(! [C:set_Secrecy_specID,B:secrecy_specID,A:set_Secrecy_specID] : ((pq != B) | ((sup_su1712599557specID @ (insert1671894227specID @ B @ C) @ A) != bot_bo1785112429specID))),inference(lifteq,[status(thm)],[16511])). 428.91/126.44 thf(16514,plain,(! [B:set_Secrecy_specID,A:set_Secrecy_specID] : (((sup_su1712599557specID @ (insert1671894227specID @ pq @ B) @ A) != bot_bo1785112429specID))),inference(simp,[status(thm)],[16513])). 428.91/126.44 thf(7855,plain,(! [A:set_Secrecy_specID] : (((! [B:secrecy_specID]: ~ (member740727610specID @ B @ A)) = (bot_bo1785112429specID = A)))),inference(rewrite,[status(thm)],[552,7833])). 428.91/126.44 thf(17739,plain,(! [B:set_Secrecy_specID,A:secrecy_specID] : (((insert1671894227specID @ A @ B) = B) | ((member740727610specID @ p @ (subcomponents @ pq)) != (member740727610specID @ A @ B)))),inference(paramod_ordered,[status(thm)],[1923,523])). 428.91/126.44 thf(17740,plain,(((insert1671894227specID @ p @ (subcomponents @ pq)) = (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[17739:[bind(A, $thf(p)),bind(B, $thf(subcomponents @ pq))]])). 428.91/126.44 thf(127,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_Un__empty__right)). 428.91/126.44 thf(667,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 428.91/126.44 thf(1294,plain,(! [A:secrecy_specID] : (((eout @ A) = (^ [B:secrecy_Expression]: ? [C:secrecy_chanID]: ((member1967978193chanID @ C @ (out @ A)) & (exprChannel @ C @ B)))))),inference(func_ext,[status(esa)],[512])). 428.91/126.44 thf(173,axiom,((! [A:(secrecy_KS > $o),B:secrecy_KS]: ((! [C:secrecy_Keys]: (A @ (secrecy_kKS @ C))) => ((A @ B) <= (! [C:secrecy_Secrets]: (A @ (secrecy_sKS @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_KS_Oinduct)). 428.91/126.44 thf(832,plain,((! [A:(secrecy_KS > $o),B:secrecy_KS]: ((! [C:secrecy_Keys]: (A @ (secrecy_kKS @ C))) => ((A @ B) | ~ (! [C:secrecy_Secrets]: (A @ (secrecy_sKS @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 428.91/126.44 thf(133,axiom,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: (((((eoutM @ E @ B @ C) <= (? [F:secrecy_chanID]: ((member1967978193chanID @ F @ B) & (exprChannel @ F @ C) & ~ (member1967978193chanID @ F @ (loc @ E)) & ((member1967978193chanID @ F @ (out @ A)) | (member1967978193chanID @ F @ (out @ D)))))) <= (correc990227761ionOut @ E)) <= ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID)))) <= ((eoutM @ D @ B @ C) | (eoutM @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_TBtheorem5b__PQ)). 428.91/126.44 thf(684,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression,D:secrecy_specID,E:secrecy_specID]: ((eoutM @ E @ B @ C) | ~ (? [F:secrecy_chanID]: ((member1967978193chanID @ F @ B) & (exprChannel @ F @ C) & ~ (member1967978193chanID @ F @ (loc @ E)) & ((member1967978193chanID @ F @ (out @ A)) | (member1967978193chanID @ F @ (out @ D))))) | ~ (correc990227761ionOut @ E) | ~ ((subcomponents @ E) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) | ~ ((eoutM @ D @ B @ C) | (eoutM @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 428.91/126.44 thf(7126,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ B @ (insert1671894227specID @ B @ A)) != (member740727610specID @ (sk3 @ (subcomponents @ pq)) @ (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq))))))),inference(paramod_ordered,[status(thm)],[540,6835])). 428.91/126.44 thf(7146,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((B != (sk3 @ (subcomponents @ pq))) | ((insert1671894227specID @ B @ A) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[7126])). 428.91/126.44 thf(7152,plain,(! [A:set_Secrecy_specID] : (((insert1671894227specID @ (sk3 @ (subcomponents @ pq)) @ A) != (sk4 @ (subcomponents @ pq) @ (sk3 @ (subcomponents @ pq)))))),inference(simp,[status(thm)],[7146])). 428.91/126.44 thf(167,axiom,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_sup__bot_Oleft__neutral)). 428.91/126.44 thf(800,plain,((! [A:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 428.91/126.44 thf(8,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: (((insert751661162chanID @ A @ bot_bo443197316chanID) = (sup_su370684444chanID @ B @ C)) = (((B = (insert751661162chanID @ A @ bot_bo443197316chanID)) & (C = bot_bo443197316chanID)) | ((C = (insert751661162chanID @ A @ bot_bo443197316chanID)) & (B = (insert751661162chanID @ A @ bot_bo443197316chanID))) | ((B = bot_bo443197316chanID) & (C = (insert751661162chanID @ A @ bot_bo443197316chanID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_singleton__Un__iff)). 428.91/126.44 thf(287,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:set_Secrecy_chanID]: (((insert751661162chanID @ A @ bot_bo443197316chanID) = (sup_su370684444chanID @ B @ C)) = (((B = (insert751661162chanID @ A @ bot_bo443197316chanID)) & (C = bot_bo443197316chanID)) | ((C = (insert751661162chanID @ A @ bot_bo443197316chanID)) & (B = (insert751661162chanID @ A @ bot_bo443197316chanID))) | ((B = bot_bo443197316chanID) & (C = (insert751661162chanID @ A @ bot_bo443197316chanID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 428.91/126.44 thf(12797,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ A) = (sup_su1712599557specID @ (subcomponents @ pq))) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[11387,1261])). 428.91/126.44 thf(12798,plain,((member740727610specID @ (sk3 @ (sk5 @ (subcomponents @ pq) @ p)) @ (sk5 @ (subcomponents @ pq) @ p)) | ((insert1671894227specID @ p) = (sup_su1712599557specID @ (subcomponents @ pq)))),inference(pattern_uni,[status(thm)],[12797:[bind(A, $thf(p))]])). 428.91/126.44 thf(111,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((((? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (loc @ D)) & (ine_ex1303305700Single @ A @ E @ B))) => (~ (ine @ D @ B))) <= (correctCompositionIn @ D)) <= ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID)))) <= (~ (ine @ C @ B))) <= (ine @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_TBtheorem4a__notP1)). 428.91/126.44 thf(603,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (loc @ D)) & (ine_ex1303305700Single @ A @ E @ B))) => (~ (ine @ D @ B))) | ~ (correctCompositionIn @ D) | ~ ((subcomponents @ D) = (insert1671894227specID @ A @ (insert1671894227specID @ C @ bot_bo1785112429specID))) | (ine @ C @ B) | ~ (ine @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 428.91/126.44 thf(8763,plain,(! [A:secrecy_specID] : (((member740727610specID @ p @ (insert1671894227specID @ A @ (subcomponents @ pq))) != (member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[8744,6849])). 428.91/126.44 thf(8788,plain,(! [A:secrecy_specID] : ((p != p) | ((insert1671894227specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[8763])). 428.91/126.44 thf(8801,plain,(! [A:secrecy_specID] : (((insert1671894227specID @ A @ (subcomponents @ pq)) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[8788])). 428.91/126.44 thf(13484,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((insert_Secrecy_KS @ sk65 @ bot_bo1943466239ecy_KS) != (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) | ((member_Secrecy_KS @ B @ (insert_Secrecy_KS @ B @ A)) != (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1054,13051])). 428.91/126.44 thf(13495,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : ((sk65 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS) | (B != sk65) | ((insert_Secrecy_KS @ B @ A) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[13484])). 428.91/126.44 thf(13542,plain,(! [A:set_Secrecy_KS] : ((sk65 != m) | ((insert_Secrecy_KS @ sk65 @ A) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[13495])). 428.91/126.44 thf(174,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ A @ B)) = (sup_su1301156759ecy_KS @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Un__left__absorb)). 428.91/126.44 thf(835,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (sup_su1301156759ecy_KS @ A @ B)) = (sup_su1301156759ecy_KS @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 428.91/126.44 thf(180,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_chanID]: (((exprChannel @ C @ B) => (~ (member1967978193chanID @ C @ (ins @ A)))) <= (~ (ine @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_ine__ins__neg1)). 428.91/126.44 thf(854,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_chanID]: (((exprChannel @ C @ B) => (~ (member1967978193chanID @ C @ (ins @ A)))) | (ine @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 428.91/126.44 thf(421,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),inference(cnf,[status(esa)],[420])). 428.91/126.44 thf(422,plain,(! [A:set_Secrecy_chanID] : (((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),inference(lifteq,[status(thm)],[421])). 428.91/126.44 thf(163,axiom,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((B = bot_bo1943466239ecy_KS) & (A = bot_bo1943466239ecy_KS))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Un__empty)). 428.91/126.44 thf(790,plain,((! [A:set_Secrecy_KS,B:set_Secrecy_KS]: (((sup_su1301156759ecy_KS @ A @ B) = bot_bo1943466239ecy_KS) = ((B = bot_bo1943466239ecy_KS) & (A = bot_bo1943466239ecy_KS))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 428.91/126.44 thf(264,axiom,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((~ (member_Secrecy_KS @ A @ B)) => ((((insert_Secrecy_KS @ A @ B) = (insert_Secrecy_KS @ A @ C)) = (B = C)) <= (~ (member_Secrecy_KS @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__ident)). 428.91/126.44 thf(1197,plain,((! [A:secrecy_KS,B:set_Secrecy_KS,C:set_Secrecy_KS]: ((~ (member_Secrecy_KS @ A @ B)) => ((((insert_Secrecy_KS @ A @ B) = (insert_Secrecy_KS @ A @ C)) = (B = C)) | (member_Secrecy_KS @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 428.91/126.44 thf(201,axiom,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_specID,D:secrecy_Expression]: ((((exprChannel @ A @ D) => (ineM @ C @ B @ D)) <= (member1967978193chanID @ A @ (ins @ C))) <= (member1967978193chanID @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ineM__L1)). 428.91/126.44 thf(960,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID,C:secrecy_specID,D:secrecy_Expression]: (((exprChannel @ A @ D) => (ineM @ C @ B @ D)) | ~ (member1967978193chanID @ A @ (ins @ C)) | ~ (member1967978193chanID @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 428.91/126.44 thf(194,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((ine @ A @ B) => ((((ine @ C @ B) | (ine @ D @ B)) <= (correctCompositionIn @ A)) <= ((subcomponents @ A) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_TBtheorem1a)). 428.91/126.44 thf(928,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((ine @ A @ B) => ((ine @ C @ B) | (ine @ D @ B) | ~ (correctCompositionIn @ A) | ~ ((subcomponents @ A) = (insert1671894227specID @ C @ (insert1671894227specID @ D @ bot_bo1785112429specID))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 428.91/126.44 thf(10803,plain,(! [A:secrecy_specID] : ((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | (is_sin1501507247specID @ (subcomponents @ pq)) | ((insert1671894227specID @ p @ bot_bo1785112429specID) != (insert1671894227specID @ A @ bot_bo1785112429specID)))),inference(paramod_ordered,[status(thm)],[7095,747])). 428.91/126.44 thf(10804,plain,((member740727610specID @ (sk3 @ (sk4 @ (subcomponents @ pq) @ p)) @ (sk4 @ (subcomponents @ pq) @ p)) | (is_sin1501507247specID @ (subcomponents @ pq))),inference(pattern_uni,[status(thm)],[10803:[bind(A, $thf(p))]])). 428.91/126.44 thf(1092,plain,(! [A:set_Secrecy_KS] : (((? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A)) = (~ (A = bot_bo1943466239ecy_KS))))),inference(cnf,[status(esa)],[1091])). 428.91/126.44 thf(1093,plain,(! [A:set_Secrecy_KS] : (((? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A)) = (~ (A = bot_bo1943466239ecy_KS))))),inference(lifteq,[status(thm)],[1092])). 428.91/126.44 thf(2618,plain,(! [B:set_Secrecy_KS,A:set_Secrecy_KS] : (((~ (! [C:secrecy_KS]: ~ (member_Secrecy_KS @ C @ A))) = (? [C:secrecy_KS]: (member_Secrecy_KS @ C @ B))) | ((A = bot_bo1943466239ecy_KS) != (B = bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1149,1093])). 428.91/126.44 thf(2619,plain,(! [A:set_Secrecy_KS] : (((~ (! [B:secrecy_KS]: ~ (member_Secrecy_KS @ B @ A))) = (? [B:secrecy_KS]: (member_Secrecy_KS @ B @ A))))),inference(pattern_uni,[status(thm)],[2618:[bind(A, $thf(A)),bind(B, $thf(A))]])). 428.91/126.44 thf(530,plain,((! [A:secrecy_specID,B:set_Secrecy_specID]: (! [C:set_Secrecy_specID]: ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ A @ C)) = (B = C)) | (member740727610specID @ A @ C)) | (member740727610specID @ A @ B)))),inference(miniscope,[status(thm)],[529])). 428.91/126.44 thf(531,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ A @ C)) = (B = C)) | (member740727610specID @ A @ C) | (member740727610specID @ A @ B))),inference(cnf,[status(esa)],[530])). 428.91/126.44 thf(532,plain,(! [C:set_Secrecy_specID,B:set_Secrecy_specID,A:secrecy_specID] : ((((insert1671894227specID @ A @ B) = (insert1671894227specID @ A @ C)) = (B = C)) | (member740727610specID @ A @ C) | (member740727610specID @ A @ B))),inference(lifteq,[status(thm)],[531])). 428.91/126.44 thf(165,axiom,((ine_exprChannelSet = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (! [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) => ((member1967978193chanID @ D @ (ins @ A)) & (exprChannel @ D @ C))) & ! [D:secrecy_chanID]: ((~ (exprChannel @ D @ C)) <= ((member1967978193chanID @ D @ (ins @ A)) & ~ (member1967978193chanID @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_ine__exprChannelSet__def)). 428.91/126.44 thf(796,plain,(((ine_exprChannelSet) = (^ [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (! [D:secrecy_chanID]: ((member1967978193chanID @ D @ B) => ((member1967978193chanID @ D @ (ins @ A)) & (exprChannel @ D @ C))) & ! [D:secrecy_chanID]: (~ (exprChannel @ D @ C) | ~ ((member1967978193chanID @ D @ (ins @ A)) & ~ (member1967978193chanID @ D @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 428.91/126.44 thf(330,plain,((! [A:secrecy_chanID,B:set_Secrecy_chanID]: (! [C:set_Secrecy_chanID]: ((((insert751661162chanID @ A @ B) = (insert751661162chanID @ A @ C)) = (B = C)) | (member1967978193chanID @ A @ C)) | (member1967978193chanID @ A @ B)))),inference(miniscope,[status(thm)],[329])). 428.91/126.44 thf(331,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : ((((insert751661162chanID @ A @ B) = (insert751661162chanID @ A @ C)) = (B = C)) | (member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))),inference(cnf,[status(esa)],[330])). 428.91/126.44 thf(332,plain,(! [C:set_Secrecy_chanID,B:set_Secrecy_chanID,A:secrecy_chanID] : ((((insert751661162chanID @ A @ B) = (insert751661162chanID @ A @ C)) = (B = C)) | (member1967978193chanID @ A @ C) | (member1967978193chanID @ A @ B))),inference(lifteq,[status(thm)],[331])). 428.91/126.44 thf(458,plain,((! [A:secrecy_specID,B:secrecy_Expression]: ((~ (ine @ A @ B)) => (~ (? [C:set_Secrecy_chanID]: (ineM @ A @ C @ B)))))),inference(miniscope,[status(thm)],[457])). 428.91/126.44 thf(459,plain,(! [C:set_Secrecy_chanID,B:secrecy_Expression,A:secrecy_specID] : ((ine @ A @ B) | (~ (ineM @ A @ C @ B)))),inference(cnf,[status(esa)],[458])). 428.91/126.44 thf(6890,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : (((member740727610specID @ B @ (insert1671894227specID @ B @ A)) != (member740727610specID @ p @ (sk4 @ (subcomponents @ pq) @ p))))),inference(paramod_ordered,[status(thm)],[540,6849])). 428.91/126.44 thf(6903,plain,(! [B:secrecy_specID,A:set_Secrecy_specID] : ((B != p) | ((insert1671894227specID @ B @ A) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[6890])). 428.91/126.44 thf(6911,plain,(! [A:set_Secrecy_specID] : (((insert1671894227specID @ p @ A) != (sk4 @ (subcomponents @ pq) @ p)))),inference(simp,[status(thm)],[6903])). 428.91/126.44 thf(183,axiom,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: (((insert1671894227specID @ A @ bot_bo1785112429specID) = (sup_su1712599557specID @ B @ C)) = (((C = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (B = bot_bo1785112429specID)) | ((C = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (B = (insert1671894227specID @ A @ bot_bo1785112429specID))) | ((B = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (C = bot_bo1785112429specID)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_singleton__Un__iff)). 428.91/126.44 thf(871,plain,((! [A:secrecy_specID,B:set_Secrecy_specID,C:set_Secrecy_specID]: (((insert1671894227specID @ A @ bot_bo1785112429specID) = (sup_su1712599557specID @ B @ C)) = (((C = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (B = bot_bo1785112429specID)) | ((C = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (B = (insert1671894227specID @ A @ bot_bo1785112429specID))) | ((B = (insert1671894227specID @ A @ bot_bo1785112429specID)) & (C = bot_bo1785112429specID)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 428.91/126.44 thf(242,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => ((correctCompositionIn @ A) => (? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_kE @ D)) & (member1967978193chanID @ F @ (ins @ A)))))) <= (exprChannel @ E @ (secrecy_kE @ D))))) <= (correctCompositionKS @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_correctCompositionKS__exprChannel__k__Pex)). 428.91/126.44 thf(1120,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_Keys,E:secrecy_chanID]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (localSecrets @ A))) => ((member1967978193chanID @ E @ (ins @ B)) => (((~ (member_Secrecy_KS @ (secrecy_kKS @ D) @ (specKeysSecrets @ A))) => ((correctCompositionIn @ A) => (? [F:secrecy_chanID]: ((exprChannel @ F @ (secrecy_kE @ D)) & (member1967978193chanID @ F @ (ins @ A)))))) | ~ (exprChannel @ E @ (secrecy_kE @ D))))) | ~ (correctCompositionKS @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 428.91/126.44 thf(500,plain,((! [A:secrecy_specID,B:set_Secrecy_chanID,C:secrecy_Expression]: (! [D:set_Secrecy_chanID]: (ineM @ A @ (sup_su370684444chanID @ B @ D) @ C) | ~ (ineM @ A @ B @ C)))),inference(miniscope,[status(thm)],[499])). 428.91/126.44 thf(501,plain,(! [D:set_Secrecy_chanID,C:secrecy_Expression,B:set_Secrecy_chanID,A:secrecy_specID] : ((ineM @ A @ (sup_su370684444chanID @ B @ D) @ C) | (~ (ineM @ A @ B @ C)))),inference(cnf,[status(esa)],[500])). 428.91/126.44 thf(112,axiom,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID,E:secrecy_Expression]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((member1967978193chanID @ D @ (ins @ B)) => ((exprChannel @ D @ E) => ((member1967978193chanID @ D @ (loc @ A)) <= (! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ A)) => (~ (exprChannel @ F @ E))))))) <= (correctCompositionIn @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_correctCompositionInLoc__exprChannel)). 428.91/126.44 thf(607,plain,((! [A:secrecy_specID,B:secrecy_specID,C:secrecy_specID,D:secrecy_chanID,E:secrecy_Expression]: (((subcomponents @ A) = (insert1671894227specID @ B @ (insert1671894227specID @ C @ bot_bo1785112429specID))) => (((member1967978193chanID @ D @ (ins @ B)) => ((exprChannel @ D @ E) => ((member1967978193chanID @ D @ (loc @ A)) | ~ (! [F:secrecy_chanID]: ((member1967978193chanID @ F @ (ins @ A)) => (~ (exprChannel @ F @ E))))))) | ~ (correctCompositionIn @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 428.91/126.44 thf(141,axiom,((! [A:set_Secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (insert_Secrecy_KS @ B @ C)) = (insert_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Un__insert__right)). 428.91/126.44 thf(723,plain,((! [A:set_Secrecy_KS,B:secrecy_KS,C:set_Secrecy_KS]: ((sup_su1301156759ecy_KS @ A @ (insert_Secrecy_KS @ B @ C)) = (insert_Secrecy_KS @ B @ (sup_su1301156759ecy_KS @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 428.91/126.44 thf(11448,plain,(! [A:set_Secrecy_specID] : (((member740727610specID @ p @ (sk5 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p)) != (member740727610specID @ p @ (subcomponents @ pq))))),inference(paramod_ordered,[status(thm)],[1923,10985])). 428.91/126.44 thf(11457,plain,(! [A:set_Secrecy_specID] : ((p != p) | ((sk5 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[11448])). 428.91/126.44 thf(11462,plain,(! [A:set_Secrecy_specID] : (((sk5 @ (sup_su1712599557specID @ (subcomponents @ pq) @ A) @ p) != (subcomponents @ pq)))),inference(simp,[status(thm)],[11457])). 428.91/126.44 thf(179,axiom,((! [A:set_Secrecy_specID]: ((~ (! [B:secrecy_specID]: (A != (insert1671894227specID @ B @ bot_bo1785112429specID)))) <= (is_sin1501507247specID @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_is__singletonE)). 428.91/126.44 thf(850,plain,((! [A:set_Secrecy_specID]: (~ (! [B:secrecy_specID]: ~ (A = (insert1671894227specID @ B @ bot_bo1785112429specID))) | ~ (is_sin1501507247specID @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 428.91/126.44 thf(1703,plain,(! [A:secrecy_KS] : (((member_Secrecy_KS @ A @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS)) != (member_Secrecy_KS @ m @ (specKeysSecrets @ q))))),inference(paramod_ordered,[status(thm)],[1138,1179])). 428.91/126.44 thf(1709,plain,(! [A:secrecy_KS] : ((A != m) | ((insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ q)))),inference(simp,[status(thm)],[1703])). 428.91/126.44 thf(1713,plain,(((insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS) != (specKeysSecrets @ q))),inference(simp,[status(thm)],[1709])). 428.91/126.44 thf(321,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ B) = B) | (~ (member1967978193chanID @ A @ B)))),inference(cnf,[status(esa)],[320])). 428.91/126.44 thf(322,plain,(! [B:set_Secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ B) = B) | (~ (member1967978193chanID @ A @ B)))),inference(lifteq,[status(thm)],[321])). 428.91/126.44 thf(125,axiom,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: ((((correc990227761ionOut @ C) => ((eout @ C @ B) <= (? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (out @ A)) & (exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ C)))))) <= ((subcomponents @ C) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID)))) <= (eout @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_TBtheorem45a__P)). 428.91/126.44 thf(659,plain,((! [A:secrecy_specID,B:secrecy_Expression,C:secrecy_specID,D:secrecy_specID]: (((correc990227761ionOut @ C) => ((eout @ C @ B) | ~ (? [E:secrecy_chanID]: ((member1967978193chanID @ E @ (out @ A)) & (exprChannel @ E @ B) & ~ (member1967978193chanID @ E @ (loc @ C)))))) | ~ ((subcomponents @ C) = (insert1671894227specID @ A @ (insert1671894227specID @ D @ bot_bo1785112429specID))) | ~ (eout @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 428.91/126.44 thf(6060,plain,(((^ [A:secrecy_KS]: (A)) != (^ [A:secrecy_KS]: (A))) | ((^ [A:secrecy_KS]: (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (^ [A:secrecy_KS]: (specKeysSecrets @ p)))),inference(simp,[status(thm)],[6059])). 428.91/126.44 thf(6072,plain,(((^ [A:secrecy_KS]: (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (^ [A:secrecy_KS]: (specKeysSecrets @ p)))),inference(simp,[status(thm)],[6060])). 428.91/126.44 thf(130,axiom,((! [A:secrecy_specID,B:secrecy_Secrets]: ((~ (knowle945212990e_know @ A @ (secrecy_sKS @ B))) => (~ (ine @ A @ (secrecy_sE @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_not__know__s__not__ine)). 428.91/126.44 thf(676,plain,((! [A:secrecy_specID,B:secrecy_Secrets]: ((~ (knowle945212990e_know @ A @ (secrecy_sKS @ B))) => (~ (ine @ A @ (secrecy_sE @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 428.91/126.44 thf(18724,plain,(((member740727610specID @ (sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) @ (subcomponents @ pq)) != (member740727610specID @ pq @ (subcomponents @ pq)))),inference(paramod_ordered,[status(thm)],[18701,9931])). 428.91/126.44 thf(18778,plain,(((sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) != pq) | ((subcomponents @ pq) != (subcomponents @ pq))),inference(simp,[status(thm)],[18724])). 428.91/126.44 thf(18798,plain,(((sk3 @ (sup_su1712599557specID @ (subcomponents @ pq) @ (subcomponents @ pq))) != pq)),inference(simp,[status(thm)],[18778])). 428.91/126.44 thf(467,plain,((! [A:set_Secrecy_chanID]: ((~ (? [B:secrecy_chanID]: (member1967978193chanID @ B @ A))) => (A = bot_bo443197316chanID)))),inference(miniscope,[status(thm)],[466])). 428.91/126.44 thf(468,plain,(! [A:set_Secrecy_chanID] : ((member1967978193chanID @ (sk6 @ A) @ A) | (A = bot_bo443197316chanID))),inference(cnf,[status(esa)],[467])). 428.91/126.44 thf(469,plain,(! [A:set_Secrecy_chanID] : ((A = bot_bo443197316chanID) | (member1967978193chanID @ (sk6 @ A) @ A))),inference(lifteq,[status(thm)],[468])). 428.91/126.44 thf(1939,plain,(! [B:secrecy_KS,A:set_Secrecy_KS] : (((sup_su1301156759ecy_KS @ (collect_Secrecy_KS @ (^ [C:secrecy_KS]: (member_Secrecy_KS @ C @ A)))) = (insert_Secrecy_KS @ B)) | (A != (insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS)))),inference(paramod_ordered,[status(thm)],[1152,1263])). 428.91/126.44 thf(1940,plain,(! [A:secrecy_KS] : (((sup_su1301156759ecy_KS @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) = (insert_Secrecy_KS @ A)))),inference(pattern_uni,[status(thm)],[1939:[bind(A, $thf(insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS)),bind(B, $thf(C))]])). 428.91/126.44 thf(1944,plain,(! [A:secrecy_KS] : (((sup_su1301156759ecy_KS @ (collect_Secrecy_KS @ (^ [B:secrecy_KS]: (member_Secrecy_KS @ B @ (insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS))))) = (insert_Secrecy_KS @ A)))),inference(simp,[status(thm)],[1940])). 428.91/126.44 thf(1489,plain,(! [F:set_Secrecy_chanID,E:secrecy_chanID,D:secrecy_chanID,C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) != bot_bo443197316chanID) | ((insert751661162chanID @ B @ (insert751661162chanID @ A @ C)) != (insert751661162chanID @ E @ (insert751661162chanID @ D @ F))))),inference(paramod_ordered,[status(thm)],[272,1337])). 428.91/126.44 thf(1490,plain,(! [C:set_Secrecy_chanID,B:secrecy_chanID,A:secrecy_chanID] : (((insert751661162chanID @ A @ (insert751661162chanID @ B @ C)) != bot_bo443197316chanID))),inference(pattern_uni,[status(thm)],[1489:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(B)),bind(F, $thf(C))]])). 428.91/126.44 thf(97,axiom,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_sup__bot__left)). 428.91/126.44 thf(560,plain,((! [A:set_Secrecy_chanID]: ((sup_su370684444chanID @ bot_bo443197316chanID @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 428.91/126.44 thf(6242,plain,(((^ [A:secrecy_KS]: (A)) != (^ [A:secrecy_KS]: (A))) | ((^ [A:secrecy_KS]: (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (^ [A:secrecy_KS]: (specKeysSecrets @ q)))),inference(simp,[status(thm)],[6241])). 428.91/126.44 thf(6254,plain,(((^ [A:secrecy_KS]: (insert_Secrecy_KS @ m @ bot_bo1943466239ecy_KS)) != (^ [A:secrecy_KS]: (specKeysSecrets @ q)))),inference(simp,[status(thm)],[6242])). 428.91/126.44 thf(13464,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | (sk65 != m) | (bot_bo1943466239ecy_KS != bot_bo1943466239ecy_KS)),inference(simp,[status(thm)],[13051])). 428.91/126.44 thf(13537,plain,((~ (member_Secrecy_KS @ sk65 @ (specKeysSecrets @ q))) | (sk65 != m)),inference(simp,[status(thm)],[13464])). 428.91/126.44 thf(145849,plain,(($false)),inference(e,[status(thm)],[6085,1337,6387,1024,7854,14922,347,10520,1237,1179,555,481,1823,1190,333,1031,16898,1211,523,6106,6744,994,12089,308,17275,730,1290,276,741,13462,1205,449,1142,379,1269,440,655,511,8928,269,1041,861,5814,385,1137,13317,533,10772,550,12126,11020,472,2168,10594,1222,670,6241,747,913,1196,1001,19955,6909,6268,2227,11024,7856,320,9657,436,9625,404,12212,13251,841,417,13003,1265,1055,570,719,838,10337,10174,460,2339,785,917,751,1132,15264,638,1147,969,284,416,9973,448,316,17662,10527,5868,10534,10945,1773,1100,7032,924,492,1714,443,1911,1109,376,646,2540,806,353,966,17210,11523,634,877,293,396,7194,9914,998,988,2154,507,312,11242,397,1943,428,1201,9917,920,380,678,793,6296,1153,381,13051,6571,1067,798,1206,452,512,942,16401,270,529,810,16882,2673,910,957,8168,952,8329,302,1174,598,424,407,429,275,729,18705,17467,746,1091,820,5815,2986,13971,2445,361,9626,830,493,1027,757,6267,1281,456,974,7095,1106,847,484,329,1178,10794,1159,1291,710,6728,519,317,948,17232,10986,1064,403,388,356,593,18701,420,499,857,1089,3615,3831,874,2157,1143,328,1082,339,2312,642,526,679,11116,901,476,11026,1207,590,15421,547,12756,1263,1150,12994,738,10401,1715,779,11093,371,1050,457,7150,343,2203,1241,15395,805,508,541,1170,398,13879,953,718,765,1712,1054,558,1071,586,2338,298,412,750,618,425,513,2734,573,296,8874,6026,15147,5808,1103,3871,15057,7010,18553,6243,745,584,7833,423,402,732,13972,6881,772,286,579,17273,413,1007,694,17373,10200,843,382,313,787,11201,1058,7924,466,1090,919,704,6334,350,391,1139,713,498,6061,6059,9614,1117,377,17179,567,737,649,6289,616,1806,1011,419,19506,11092,6112,736,599,11979,9931,631,19340,367,6849,323,594,621,1149,10825,2252,10985,11095,494,1080,799,1162,726,700,520,11387,9905,932,1061,521,2418,959,1044,455,1015,394,563,1000,299,505,431,1926,399,1213,768,1066,278,1364,2967,473,680,663,374,17472,8789,342,1018,355,5807,426,1166,648,7151,487,1081,749,17504,617,516,553,11795,2513,776,525,1003,6453,1156,971,327,3872,310,13523,12648,5748,1647,10333,409,2160,673,12720,1186,370,11022,502,10861,1235,951,1336,1220,10439,1987,9634,463,6298,11622,338,1085,470,576,3174,359,3095,15836,544,907,744,336,1141,613,1221,600,14400,314,446,6531,7908,1240,6086,1094,978,1316,1180,16421,759,1126,10928,5832,10332,363,556,524,581,6835,495,1781,891,368,844,963,319,6689,5800,652,390,6910,418,781,1341,748,8172,1689,290,2330,1193,1077,8793,272,6166,346,7406,16514,18106,7855,17740,667,1294,832,684,7152,536,716,800,287,410,273,12798,603,8801,432,11271,13542,835,854,1986,422,790,305,326,1989,437,1197,1891,960,9927,928,10804,268,2619,532,796,283,1093,332,1261,6316,1152,528,459,6911,871,1120,501,607,1923,723,11462,9969,850,1713,322,2672,803,13016,659,6072,8130,676,2191,364,18798,469,1944,1490,560,775,6254,2177,13537])). 428.91/126.44 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 428.91/126.44 % [INFO] Killing All external provers ... 428.91/126.49 EOF