TSTP Solution File: SWV011+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV011+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:54:34 EDT 2023
% Result : Theorem 5.06s 1.32s
% Output : Proof 6.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV011+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Aug 29 06:12:16 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.53 ________ _____
% 0.16/0.53 ___ __ \_________(_)________________________________
% 0.16/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.53
% 0.16/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.53 (2023-06-19)
% 0.16/0.53
% 0.16/0.53 (c) Philipp Rümmer, 2009-2023
% 0.16/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.53 Amanda Stjerna.
% 0.16/0.53 Free software under BSD-3-Clause.
% 0.16/0.53
% 0.16/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.53
% 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.54 Running up to 7 provers in parallel.
% 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.91/0.87 Prover 4: Preprocessing ...
% 1.91/0.87 Prover 1: Preprocessing ...
% 2.31/0.92 Prover 6: Preprocessing ...
% 2.31/0.92 Prover 3: Preprocessing ...
% 2.31/0.92 Prover 5: Preprocessing ...
% 2.31/0.92 Prover 0: Preprocessing ...
% 2.31/0.92 Prover 2: Preprocessing ...
% 3.91/1.14 Prover 2: Proving ...
% 3.91/1.15 Prover 5: Proving ...
% 3.91/1.15 Prover 6: Proving ...
% 3.91/1.15 Prover 0: Proving ...
% 3.91/1.15 Prover 3: Constructing countermodel ...
% 4.05/1.17 Prover 1: Constructing countermodel ...
% 4.05/1.18 Prover 4: Constructing countermodel ...
% 5.06/1.32 Prover 3: proved (765ms)
% 5.06/1.32
% 5.06/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.32
% 5.06/1.32 Prover 5: stopped
% 5.06/1.32 Prover 6: stopped
% 5.06/1.32 Prover 2: stopped
% 5.06/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.06/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.06/1.33 Prover 0: proved (780ms)
% 5.06/1.33
% 5.06/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.33
% 5.06/1.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.06/1.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.06/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.06/1.36 Prover 10: Preprocessing ...
% 5.06/1.36 Prover 8: Preprocessing ...
% 5.06/1.36 Prover 13: Preprocessing ...
% 5.06/1.37 Prover 11: Preprocessing ...
% 5.06/1.38 Prover 7: Preprocessing ...
% 5.62/1.44 Prover 13: Warning: ignoring some quantifiers
% 5.62/1.45 Prover 13: Constructing countermodel ...
% 5.62/1.45 Prover 10: Constructing countermodel ...
% 5.62/1.45 Prover 8: Warning: ignoring some quantifiers
% 5.62/1.45 Prover 7: Constructing countermodel ...
% 5.62/1.46 Prover 8: Constructing countermodel ...
% 5.62/1.47 Prover 11: Constructing countermodel ...
% 6.33/1.49 Prover 1: Found proof (size 34)
% 6.33/1.49 Prover 1: proved (946ms)
% 6.33/1.49 Prover 10: stopped
% 6.33/1.49 Prover 13: stopped
% 6.33/1.49 Prover 8: stopped
% 6.33/1.49 Prover 7: stopped
% 6.33/1.49 Prover 11: stopped
% 6.33/1.50 Prover 4: Found proof (size 40)
% 6.33/1.50 Prover 4: proved (948ms)
% 6.33/1.50
% 6.33/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/1.50
% 6.46/1.51 % SZS output start Proof for theBenchmark
% 6.46/1.51 Assumptions after simplification:
% 6.46/1.51 ---------------------------------
% 6.46/1.51
% 6.46/1.51 (ax1)
% 6.53/1.54 $i(an_a_nonce) & $i(a) & ? [v0: $i] : ? [v1: $i] : (generate_key(an_a_nonce)
% 6.53/1.54 = v0 & b_holds(v1) = 0 & key(v0, a) = v1 & $i(v1) & $i(v0))
% 6.53/1.54
% 6.53/1.54 (ax2)
% 6.53/1.54 $i(bt) & $i(an_a_nonce) & $i(b) & $i(a) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 6.53/1.54 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 6.53/1.54 (generate_expiration_time(an_a_nonce) = v1 & triple(a, v0, v1) = v2 &
% 6.53/1.54 generate_b_nonce(an_a_nonce) = v4 & encrypt(v4, v0) = v5 & encrypt(v2, bt) =
% 6.53/1.54 v3 & generate_key(an_a_nonce) = v0 & pair(v3, v5) = v6 & sent(a, b, v6) = v7
% 6.53/1.54 & message(v7) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 6.53/1.54 $i(v1) & $i(v0))
% 6.53/1.54
% 6.53/1.54 (ax3)
% 6.53/1.55 $i(an_a_nonce) & $i(b) & ? [v0: $i] : ? [v1: $i] : (generate_key(an_a_nonce)
% 6.53/1.55 = v0 & key(v0, b) = v1 & a_holds(v1) = 0 & $i(v1) & $i(v0))
% 6.53/1.55
% 6.53/1.55 (ax4)
% 6.53/1.55 $i(bt) & $i(an_a_nonce) & $i(b) & $i(a) & $i(t) & $i(at) & ? [v0: $i] : ?
% 6.53/1.55 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 6.53/1.55 : ? [v7: $i] : ? [v8: $i] : (quadruple(b, an_a_nonce, v0, v1) = v2 &
% 6.53/1.55 generate_expiration_time(an_a_nonce) = v1 & triple(v3, v5, v6) = v7 &
% 6.53/1.55 triple(a, v0, v1) = v4 & generate_b_nonce(an_a_nonce) = v6 & encrypt(v4, bt)
% 6.53/1.55 = v5 & encrypt(v2, at) = v3 & generate_key(an_a_nonce) = v0 & sent(t, a, v7)
% 6.53/1.55 = v8 & message(v8) = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 6.53/1.55 & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.55
% 6.53/1.55 (co1)
% 6.53/1.55 $i(b) & $i(a) & ! [v0: $i] : ! [v1: $i] : ( ~ (key(v0, b) = v1) | ~ $i(v0)
% 6.53/1.55 | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (b_holds(v3) = v4 & key(v0, a)
% 6.53/1.55 = v3 & a_holds(v1) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 6.53/1.55
% 6.53/1.55 (function-axioms)
% 6.53/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 6.53/1.56 $i] : (v1 = v0 | ~ (quadruple(v5, v4, v3, v2) = v1) | ~ (quadruple(v5, v4,
% 6.53/1.56 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 6.53/1.56 ! [v4: $i] : (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2)
% 6.53/1.56 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 6.53/1.56 $i] : (v1 = v0 | ~ (sent(v4, v3, v2) = v1) | ~ (sent(v4, v3, v2) = v0)) &
% 6.53/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.53/1.56 (encrypt(v3, v2) = v1) | ~ (encrypt(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 6.53/1.56 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pair(v3, v2) = v1) | ~
% 6.53/1.56 (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 6.53/1.56 : (v1 = v0 | ~ (key(v3, v2) = v1) | ~ (key(v3, v2) = v0)) & ! [v0:
% 6.53/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.53/1.56 ~ (b_stored(v2) = v1) | ~ (b_stored(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 6.53/1.56 : ! [v2: $i] : (v1 = v0 | ~ (generate_expiration_time(v2) = v1) | ~
% 6.53/1.56 (generate_expiration_time(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 6.53/1.56 $i] : (v1 = v0 | ~ (generate_b_nonce(v2) = v1) | ~ (generate_b_nonce(v2) =
% 6.53/1.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 6.53/1.56 (generate_key(v2) = v1) | ~ (generate_key(v2) = v0)) & ! [v0:
% 6.53/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.53/1.56 ~ (t_holds(v2) = v1) | ~ (t_holds(v2) = v0)) & ! [v0: MultipleValueBool] :
% 6.53/1.56 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (fresh_to_b(v2) = v1)
% 6.53/1.56 | ~ (fresh_to_b(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (b_holds(v2) = v1) | ~
% 6.53/1.56 (b_holds(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (a_stored(v2) = v1) | ~
% 6.53/1.56 (a_stored(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (message(v2) = v1) | ~
% 6.53/1.56 (message(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.53/1.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (party_of_protocol(v2) =
% 6.53/1.56 v1) | ~ (party_of_protocol(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 6.53/1.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (a_holds(v2) = v1) | ~
% 6.53/1.56 (a_holds(v2) = v0))
% 6.53/1.56
% 6.53/1.56 Further assumptions not needed in the proof:
% 6.53/1.56 --------------------------------------------
% 6.53/1.56 a_holds_key_at_for_t, a_is_party_of_protocol, a_sent_message_i_to_b,
% 6.53/1.56 a_stored_message_i, ax5, ax6, b_hold_key_bt_for_t, b_is_party_of_protocol,
% 6.53/1.56 nonce_a_is_fresh_to_b, t_holds_key_at_for_a, t_holds_key_bt_for_b,
% 6.53/1.56 t_is_party_of_protocol
% 6.53/1.56
% 6.53/1.56 Those formulas are unsatisfiable:
% 6.53/1.56 ---------------------------------
% 6.53/1.56
% 6.53/1.56 Begin of proof
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (ax1) implies:
% 6.53/1.57 | (1) ? [v0: $i] : ? [v1: $i] : (generate_key(an_a_nonce) = v0 &
% 6.53/1.57 | b_holds(v1) = 0 & key(v0, a) = v1 & $i(v1) & $i(v0))
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (ax2) implies:
% 6.53/1.57 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 6.53/1.57 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 6.53/1.57 | (generate_expiration_time(an_a_nonce) = v1 & triple(a, v0, v1) = v2 &
% 6.53/1.57 | generate_b_nonce(an_a_nonce) = v4 & encrypt(v4, v0) = v5 &
% 6.53/1.57 | encrypt(v2, bt) = v3 & generate_key(an_a_nonce) = v0 & pair(v3, v5) =
% 6.53/1.57 | v6 & sent(a, b, v6) = v7 & message(v7) = 0 & $i(v7) & $i(v6) & $i(v5)
% 6.53/1.57 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (ax3) implies:
% 6.53/1.57 | (3) ? [v0: $i] : ? [v1: $i] : (generate_key(an_a_nonce) = v0 & key(v0, b)
% 6.53/1.57 | = v1 & a_holds(v1) = 0 & $i(v1) & $i(v0))
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (ax4) implies:
% 6.53/1.57 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 6.53/1.57 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (quadruple(b,
% 6.53/1.57 | an_a_nonce, v0, v1) = v2 & generate_expiration_time(an_a_nonce) =
% 6.53/1.57 | v1 & triple(v3, v5, v6) = v7 & triple(a, v0, v1) = v4 &
% 6.53/1.57 | generate_b_nonce(an_a_nonce) = v6 & encrypt(v4, bt) = v5 &
% 6.53/1.57 | encrypt(v2, at) = v3 & generate_key(an_a_nonce) = v0 & sent(t, a, v7)
% 6.53/1.57 | = v8 & message(v8) = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 6.53/1.57 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (co1) implies:
% 6.53/1.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (key(v0, b) = v1) | ~ $i(v0) | ? [v2:
% 6.53/1.57 | any] : ? [v3: $i] : ? [v4: any] : (b_holds(v3) = v4 & key(v0, a)
% 6.53/1.57 | = v3 & a_holds(v1) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 6.53/1.57 |
% 6.53/1.57 | ALPHA: (function-axioms) implies:
% 6.53/1.58 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.53/1.58 | (v1 = v0 | ~ (a_holds(v2) = v1) | ~ (a_holds(v2) = v0))
% 6.53/1.58 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.53/1.58 | (v1 = v0 | ~ (b_holds(v2) = v1) | ~ (b_holds(v2) = v0))
% 6.53/1.58 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 6.53/1.58 | (generate_key(v2) = v1) | ~ (generate_key(v2) = v0))
% 6.53/1.58 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.53/1.58 | (key(v3, v2) = v1) | ~ (key(v3, v2) = v0))
% 6.53/1.58 |
% 6.53/1.58 | DELTA: instantiating (1) with fresh symbols all_17_0, all_17_1 gives:
% 6.53/1.58 | (10) generate_key(an_a_nonce) = all_17_1 & b_holds(all_17_0) = 0 &
% 6.53/1.58 | key(all_17_1, a) = all_17_0 & $i(all_17_0) & $i(all_17_1)
% 6.53/1.58 |
% 6.53/1.58 | ALPHA: (10) implies:
% 6.53/1.58 | (11) key(all_17_1, a) = all_17_0
% 6.53/1.58 | (12) b_holds(all_17_0) = 0
% 6.53/1.58 | (13) generate_key(an_a_nonce) = all_17_1
% 6.53/1.58 |
% 6.53/1.58 | DELTA: instantiating (3) with fresh symbols all_21_0, all_21_1 gives:
% 6.53/1.58 | (14) generate_key(an_a_nonce) = all_21_1 & key(all_21_1, b) = all_21_0 &
% 6.53/1.58 | a_holds(all_21_0) = 0 & $i(all_21_0) & $i(all_21_1)
% 6.53/1.58 |
% 6.53/1.58 | ALPHA: (14) implies:
% 6.53/1.58 | (15) $i(all_21_1)
% 6.53/1.58 | (16) a_holds(all_21_0) = 0
% 6.53/1.58 | (17) key(all_21_1, b) = all_21_0
% 6.53/1.58 | (18) generate_key(an_a_nonce) = all_21_1
% 6.53/1.58 |
% 6.53/1.58 | DELTA: instantiating (2) with fresh symbols all_25_0, all_25_1, all_25_2,
% 6.53/1.58 | all_25_3, all_25_4, all_25_5, all_25_6, all_25_7 gives:
% 6.53/1.58 | (19) generate_expiration_time(an_a_nonce) = all_25_6 & triple(a, all_25_7,
% 6.53/1.58 | all_25_6) = all_25_5 & generate_b_nonce(an_a_nonce) = all_25_3 &
% 6.53/1.58 | encrypt(all_25_3, all_25_7) = all_25_2 & encrypt(all_25_5, bt) =
% 6.53/1.58 | all_25_4 & generate_key(an_a_nonce) = all_25_7 & pair(all_25_4,
% 6.53/1.58 | all_25_2) = all_25_1 & sent(a, b, all_25_1) = all_25_0 &
% 6.53/1.58 | message(all_25_0) = 0 & $i(all_25_0) & $i(all_25_1) & $i(all_25_2) &
% 6.53/1.58 | $i(all_25_3) & $i(all_25_4) & $i(all_25_5) & $i(all_25_6) &
% 6.53/1.58 | $i(all_25_7)
% 6.53/1.58 |
% 6.53/1.58 | ALPHA: (19) implies:
% 6.53/1.58 | (20) generate_key(an_a_nonce) = all_25_7
% 6.53/1.58 |
% 6.53/1.58 | DELTA: instantiating (4) with fresh symbols all_27_0, all_27_1, all_27_2,
% 6.53/1.58 | all_27_3, all_27_4, all_27_5, all_27_6, all_27_7, all_27_8 gives:
% 6.53/1.58 | (21) quadruple(b, an_a_nonce, all_27_8, all_27_7) = all_27_6 &
% 6.53/1.58 | generate_expiration_time(an_a_nonce) = all_27_7 & triple(all_27_5,
% 6.53/1.58 | all_27_3, all_27_2) = all_27_1 & triple(a, all_27_8, all_27_7) =
% 6.53/1.58 | all_27_4 & generate_b_nonce(an_a_nonce) = all_27_2 & encrypt(all_27_4,
% 6.53/1.58 | bt) = all_27_3 & encrypt(all_27_6, at) = all_27_5 &
% 6.53/1.58 | generate_key(an_a_nonce) = all_27_8 & sent(t, a, all_27_1) = all_27_0
% 6.53/1.58 | & message(all_27_0) = 0 & $i(all_27_0) & $i(all_27_1) & $i(all_27_2) &
% 6.53/1.58 | $i(all_27_3) & $i(all_27_4) & $i(all_27_5) & $i(all_27_6) &
% 6.53/1.58 | $i(all_27_7) & $i(all_27_8)
% 6.53/1.58 |
% 6.53/1.58 | ALPHA: (21) implies:
% 6.53/1.59 | (22) generate_key(an_a_nonce) = all_27_8
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (8) with all_17_1, all_25_7, an_a_nonce,
% 6.53/1.59 | simplifying with (13), (20) gives:
% 6.53/1.59 | (23) all_25_7 = all_17_1
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (8) with all_25_7, all_27_8, an_a_nonce,
% 6.53/1.59 | simplifying with (20), (22) gives:
% 6.53/1.59 | (24) all_27_8 = all_25_7
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (8) with all_21_1, all_27_8, an_a_nonce,
% 6.53/1.59 | simplifying with (18), (22) gives:
% 6.53/1.59 | (25) all_27_8 = all_21_1
% 6.53/1.59 |
% 6.53/1.59 | COMBINE_EQS: (24), (25) imply:
% 6.53/1.59 | (26) all_25_7 = all_21_1
% 6.53/1.59 |
% 6.53/1.59 | SIMP: (26) implies:
% 6.53/1.59 | (27) all_25_7 = all_21_1
% 6.53/1.59 |
% 6.53/1.59 | COMBINE_EQS: (23), (27) imply:
% 6.53/1.59 | (28) all_21_1 = all_17_1
% 6.53/1.59 |
% 6.53/1.59 | REDUCE: (17), (28) imply:
% 6.53/1.59 | (29) key(all_17_1, b) = all_21_0
% 6.53/1.59 |
% 6.53/1.59 | REDUCE: (15), (28) imply:
% 6.53/1.59 | (30) $i(all_17_1)
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (5) with all_17_1, all_21_0, simplifying with (29),
% 6.53/1.59 | (30) gives:
% 6.53/1.59 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (b_holds(v1) = v2 &
% 6.53/1.59 | key(all_17_1, a) = v1 & a_holds(all_21_0) = v0 & $i(v1) & ( ~ (v2 =
% 6.53/1.59 | 0) | ~ (v0 = 0)))
% 6.53/1.59 |
% 6.53/1.59 | DELTA: instantiating (31) with fresh symbols all_46_0, all_46_1, all_46_2
% 6.53/1.59 | gives:
% 6.53/1.59 | (32) b_holds(all_46_1) = all_46_0 & key(all_17_1, a) = all_46_1 &
% 6.53/1.59 | a_holds(all_21_0) = all_46_2 & $i(all_46_1) & ( ~ (all_46_0 = 0) | ~
% 6.53/1.59 | (all_46_2 = 0))
% 6.53/1.59 |
% 6.53/1.59 | ALPHA: (32) implies:
% 6.53/1.59 | (33) a_holds(all_21_0) = all_46_2
% 6.53/1.59 | (34) key(all_17_1, a) = all_46_1
% 6.53/1.59 | (35) b_holds(all_46_1) = all_46_0
% 6.53/1.59 | (36) ~ (all_46_0 = 0) | ~ (all_46_2 = 0)
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (6) with 0, all_46_2, all_21_0, simplifying with
% 6.53/1.59 | (16), (33) gives:
% 6.53/1.59 | (37) all_46_2 = 0
% 6.53/1.59 |
% 6.53/1.59 | GROUND_INST: instantiating (9) with all_17_0, all_46_1, a, all_17_1,
% 6.53/1.59 | simplifying with (11), (34) gives:
% 6.53/1.59 | (38) all_46_1 = all_17_0
% 6.53/1.59 |
% 6.53/1.59 | REDUCE: (35), (38) imply:
% 6.53/1.59 | (39) b_holds(all_17_0) = all_46_0
% 6.53/1.59 |
% 6.53/1.59 | BETA: splitting (36) gives:
% 6.53/1.59 |
% 6.53/1.59 | Case 1:
% 6.53/1.59 | |
% 6.53/1.59 | | (40) ~ (all_46_0 = 0)
% 6.53/1.59 | |
% 6.53/1.59 | | GROUND_INST: instantiating (7) with 0, all_46_0, all_17_0, simplifying with
% 6.53/1.59 | | (12), (39) gives:
% 6.53/1.59 | | (41) all_46_0 = 0
% 6.53/1.59 | |
% 6.53/1.59 | | REDUCE: (40), (41) imply:
% 6.53/1.59 | | (42) $false
% 6.53/1.59 | |
% 6.53/1.59 | | CLOSE: (42) is inconsistent.
% 6.53/1.59 | |
% 6.53/1.59 | Case 2:
% 6.53/1.59 | |
% 6.53/1.59 | | (43) ~ (all_46_2 = 0)
% 6.53/1.59 | |
% 6.53/1.60 | | REDUCE: (37), (43) imply:
% 6.53/1.60 | | (44) $false
% 6.53/1.60 | |
% 6.53/1.60 | | CLOSE: (44) is inconsistent.
% 6.53/1.60 | |
% 6.53/1.60 | End of split
% 6.53/1.60 |
% 6.53/1.60 End of proof
% 6.53/1.60 % SZS output end Proof for theBenchmark
% 6.53/1.60
% 6.53/1.60 1068ms
%------------------------------------------------------------------------------