TSTP Solution File: SWV346-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV346-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.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 23:03:50 EDT 2023
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV346-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 04:44:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.39 Command-line arguments: --no-flatten-goal
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 Take the following subset of the input axioms:
% 0.14/0.40 fof(cls_Yahalom_Ounique__session__keys__dest_2, axiom, ![V_evs, V_A_H, V_B_H, V_K, V_na_H, V_nb_H, V_X_H, V_A, V_B, V_na, V_nb, V_X]: (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | V_na=V_na_H)))).
% 0.14/0.40 fof(cls_conjecture_2, negated_conjecture, c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))).
% 0.14/0.40 fof(cls_conjecture_3, negated_conjecture, c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)).
% 0.14/0.40 fof(cls_conjecture_4, negated_conjecture, c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent)).
% 0.14/0.40 fof(cls_conjecture_7, negated_conjecture, v_na!=c_Message_Omsg_ONonce(v_NA)).
% 0.14/0.40
% 0.14/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.40 fresh(y, y, x1...xn) = u
% 0.14/0.40 C => fresh(s, t, x1...xn) = v
% 0.14/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.40 variables of u and v.
% 0.14/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.40 input problem has no model of domain size 1).
% 0.14/0.40
% 0.14/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.40
% 0.14/0.40 Axiom 1 (cls_Yahalom_Ounique__session__keys__dest_2): fresh3(X, X, Y, Z) = Y.
% 0.14/0.40 Axiom 2 (cls_conjecture_2): c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) = true.
% 0.14/0.40 Axiom 3 (cls_Yahalom_Ounique__session__keys__dest_2): fresh(X, X, Y, Z, W) = W.
% 0.14/0.40 Axiom 4 (cls_Yahalom_Ounique__session__keys__dest_2): fresh2(X, X, Y, Z, W, V, U, T, S, X2) = fresh3(c_in(Y, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), true, V, U).
% 0.14/0.40 Axiom 5 (cls_conjecture_3): c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) = true.
% 0.14/0.40 Axiom 6 (cls_conjecture_4): c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent) = true.
% 0.14/0.40 Axiom 7 (cls_Yahalom_Ounique__session__keys__dest_2): fresh2(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, X, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(Y), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(Z), c_Message_Omsg_OMPair(W, V)))), U)), c_List_Oset(T, tc_Event_Oevent), tc_Event_Oevent), true, T, S, Z, X2, W, Y2, Z2, W2) = fresh(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, S, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(S), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(Y2), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(Z), c_Message_Omsg_OMPair(X2, Z2)))), W2)), c_List_Oset(T, tc_Event_Oevent), tc_Event_Oevent), true, T, X2, W).
% 0.14/0.40
% 0.14/0.40 Goal 1 (cls_conjecture_7): v_na = c_Message_Omsg_ONonce(v_NA).
% 0.14/0.40 Proof:
% 0.14/0.40 v_na
% 0.14/0.40 = { by axiom 3 (cls_Yahalom_Ounique__session__keys__dest_2) R->L }
% 0.14/0.40 fresh(true, true, v_evso, c_Message_Omsg_ONonce(v_NA), v_na)
% 0.14/0.40 = { by axiom 5 (cls_conjecture_3) R->L }
% 0.14/0.40 fresh(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent), true, v_evso, c_Message_Omsg_ONonce(v_NA), v_na)
% 0.14/0.40 = { by axiom 7 (cls_Yahalom_Ounique__session__keys__dest_2) R->L }
% 0.14/0.40 fresh2(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(v_na, v_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evso, tc_Event_Oevent), tc_Event_Oevent), true, v_evso, v_Aa, v_K, c_Message_Omsg_ONonce(v_NA), v_na, v_Ba, c_Message_Omsg_ONonce(v_NB), v_X)
% 0.14/0.40 = { by axiom 6 (cls_conjecture_4) }
% 0.14/0.40 fresh2(true, true, v_evso, v_Aa, v_K, c_Message_Omsg_ONonce(v_NA), v_na, v_Ba, c_Message_Omsg_ONonce(v_NB), v_X)
% 0.14/0.40 = { by axiom 4 (cls_Yahalom_Ounique__session__keys__dest_2) }
% 0.14/0.40 fresh3(c_in(v_evso, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)), true, c_Message_Omsg_ONonce(v_NA), v_na)
% 0.14/0.40 = { by axiom 2 (cls_conjecture_2) }
% 0.14/0.40 fresh3(true, true, c_Message_Omsg_ONonce(v_NA), v_na)
% 0.14/0.40 = { by axiom 1 (cls_Yahalom_Ounique__session__keys__dest_2) }
% 0.14/0.40 c_Message_Omsg_ONonce(v_NA)
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40
% 0.14/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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