TSTP Solution File: SWV756-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV756-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n005.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 23:06:09 EDT 2023
% Result : Unsatisfiable 130.67s 17.06s
% Output : Proof 130.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV756-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 08:07:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 130.67/17.06 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 130.67/17.06
% 130.67/17.06 % SZS status Unsatisfiable
% 130.67/17.06
% 130.67/17.06 % SZS output start Proof
% 130.67/17.06 Take the following subset of the input axioms:
% 130.67/17.06 fof(cls_Crypt__imp__keysFor_0, axiom, ![V_H, V_X, V_K]: (hBOOL(c_in(V_K, c_Message_OkeysFor(V_H), tc_nat)) | (~hBOOL(c_in(V_K, c_Message_OsymKeys, tc_nat)) | ~hBOOL(c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg))))).
% 130.67/17.06 fof(cls_conjecture_0, negated_conjecture, hBOOL(c_in(v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent)))).
% 130.67/17.06 fof(cls_conjecture_1, negated_conjecture, ~hBOOL(c_in(hAPP(c_Message_Omsg_OKey, v_KAB), c_Event_Oused(v_evs2), tc_Message_Omsg))).
% 130.67/17.06 fof(cls_conjecture_10, negated_conjecture, hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg))).
% 130.67/17.06 fof(cls_conjecture_2, negated_conjecture, hBOOL(c_in(v_KAB, c_Message_OsymKeys, tc_nat))).
% 130.67/17.06 fof(cls_mem__def_0, axiom, ![V_x, T_a, V_S]: (hBOOL(hAPP(V_S, V_x)) | ~hBOOL(c_in(V_x, V_S, T_a)))).
% 130.67/17.06 fof(cls_mem__def_1, axiom, ![V_x2, T_a2, V_S2]: (hBOOL(c_in(V_x2, V_S2, T_a2)) | ~hBOOL(hAPP(V_S2, V_x2)))).
% 130.67/17.06 fof(cls_new__keys__not__used_0, axiom, ![V_evs, V_K2]: (~hBOOL(c_in(V_K2, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs))), tc_nat)) | (~hBOOL(c_in(V_evs, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent))) | (~hBOOL(c_in(V_K2, c_Message_OsymKeys, tc_nat)) | hBOOL(c_in(hAPP(c_Message_Omsg_OKey, V_K2), c_Event_Oused(V_evs), tc_Message_Omsg)))))).
% 130.67/17.06 fof(cls_parts__analz_0, axiom, ![V_H2]: c_Message_Oparts(c_Message_Oanalz(V_H2))=c_Message_Oparts(V_H2)).
% 130.67/17.06
% 130.67/17.06 Now clausify the problem and encode Horn clauses using encoding 3 of
% 130.67/17.06 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 130.67/17.06 We repeatedly replace C & s=t => u=v by the two clauses:
% 130.67/17.06 fresh(y, y, x1...xn) = u
% 130.67/17.06 C => fresh(s, t, x1...xn) = v
% 130.67/17.06 where fresh is a fresh function symbol and x1..xn are the free
% 130.67/17.06 variables of u and v.
% 130.67/17.06 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 130.67/17.06 input problem has no model of domain size 1).
% 130.67/17.06
% 130.67/17.06 The encoding turns the above axioms into the following unit equations and goals:
% 130.67/17.06
% 130.67/17.06 Axiom 1 (cls_parts__analz_0): c_Message_Oparts(c_Message_Oanalz(X)) = c_Message_Oparts(X).
% 130.67/17.07 Axiom 2 (cls_conjecture_2): hBOOL(c_in(v_KAB, c_Message_OsymKeys, tc_nat)) = true2.
% 130.67/17.07 Axiom 3 (cls_Crypt__imp__keysFor_0): fresh340(X, X, Y, Z) = true2.
% 130.67/17.07 Axiom 4 (cls_mem__def_0): fresh187(X, X, Y, Z) = true2.
% 130.67/17.07 Axiom 5 (cls_new__keys__not__used_0): fresh179(X, X, Y, Z) = true2.
% 130.67/17.07 Axiom 6 (cls_Crypt__imp__keysFor_0): fresh341(X, X, Y, Z) = hBOOL(c_in(Y, c_Message_OkeysFor(Z), tc_nat)).
% 130.67/17.07 Axiom 7 (cls_conjecture_0): hBOOL(c_in(v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent))) = true2.
% 130.67/17.07 Axiom 8 (cls_mem__def_1): fresh186(X, X, Y, Z, W) = true2.
% 130.67/17.07 Axiom 9 (cls_new__keys__not__used_0): fresh362(X, X, Y, Z) = hBOOL(c_in(hAPP(c_Message_Omsg_OKey, Y), c_Event_Oused(Z), tc_Message_Omsg)).
% 130.67/17.07 Axiom 10 (cls_new__keys__not__used_0): fresh361(X, X, Y, Z) = fresh362(hBOOL(c_in(Y, c_Message_OsymKeys, tc_nat)), true2, Y, Z).
% 130.67/17.07 Axiom 11 (cls_mem__def_0): fresh187(hBOOL(c_in(X, Y, Z)), true2, Y, X) = hBOOL(hAPP(Y, X)).
% 130.67/17.07 Axiom 12 (cls_mem__def_1): fresh186(hBOOL(hAPP(X, Y)), true2, Y, X, Z) = hBOOL(c_in(Y, X, Z)).
% 130.67/17.07 Axiom 13 (cls_conjecture_10): hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg)) = true2.
% 130.67/17.07 Axiom 14 (cls_Crypt__imp__keysFor_0): fresh341(hBOOL(c_in(c_Message_Omsg_OCrypt(X, Y), Z, tc_Message_Omsg)), true2, X, Z) = fresh340(hBOOL(c_in(X, c_Message_OsymKeys, tc_nat)), true2, X, Z).
% 130.67/17.07 Axiom 15 (cls_new__keys__not__used_0): fresh361(hBOOL(c_in(X, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent))), true2, Y, X) = fresh179(hBOOL(c_in(Y, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, X))), tc_nat)), true2, Y, X).
% 130.67/17.07
% 130.67/17.07 Lemma 16: hBOOL(c_in(v_KAB, c_Message_OsymKeys, X)) = true2.
% 130.67/17.07 Proof:
% 130.67/17.07 hBOOL(c_in(v_KAB, c_Message_OsymKeys, X))
% 130.67/17.07 = { by axiom 12 (cls_mem__def_1) R->L }
% 130.67/17.07 fresh186(hBOOL(hAPP(c_Message_OsymKeys, v_KAB)), true2, v_KAB, c_Message_OsymKeys, X)
% 130.67/17.07 = { by axiom 11 (cls_mem__def_0) R->L }
% 130.67/17.07 fresh186(fresh187(hBOOL(c_in(v_KAB, c_Message_OsymKeys, tc_nat)), true2, c_Message_OsymKeys, v_KAB), true2, v_KAB, c_Message_OsymKeys, X)
% 130.67/17.07 = { by axiom 2 (cls_conjecture_2) }
% 130.67/17.07 fresh186(fresh187(true2, true2, c_Message_OsymKeys, v_KAB), true2, v_KAB, c_Message_OsymKeys, X)
% 130.67/17.07 = { by axiom 4 (cls_mem__def_0) }
% 130.67/17.07 fresh186(true2, true2, v_KAB, c_Message_OsymKeys, X)
% 130.67/17.07 = { by axiom 8 (cls_mem__def_1) }
% 130.67/17.07 true2
% 130.67/17.07
% 130.67/17.07 Goal 1 (cls_conjecture_1): hBOOL(c_in(hAPP(c_Message_Omsg_OKey, v_KAB), c_Event_Oused(v_evs2), tc_Message_Omsg)) = true2.
% 130.67/17.07 Proof:
% 130.67/17.07 hBOOL(c_in(hAPP(c_Message_Omsg_OKey, v_KAB), c_Event_Oused(v_evs2), tc_Message_Omsg))
% 130.67/17.07 = { by axiom 9 (cls_new__keys__not__used_0) R->L }
% 130.67/17.07 fresh362(true2, true2, v_KAB, v_evs2)
% 130.67/17.07 = { by lemma 16 R->L }
% 130.67/17.07 fresh362(hBOOL(c_in(v_KAB, c_Message_OsymKeys, tc_nat)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 10 (cls_new__keys__not__used_0) R->L }
% 130.67/17.07 fresh361(true2, true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 8 (cls_mem__def_1) R->L }
% 130.67/17.07 fresh361(fresh186(true2, true2, v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 4 (cls_mem__def_0) R->L }
% 130.67/17.07 fresh361(fresh186(fresh187(true2, true2, c_NS__Shared__Mirabelle_Ons__shared, v_evs2), true2, v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 7 (cls_conjecture_0) R->L }
% 130.67/17.07 fresh361(fresh186(fresh187(hBOOL(c_in(v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent))), true2, c_NS__Shared__Mirabelle_Ons__shared, v_evs2), true2, v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 11 (cls_mem__def_0) }
% 130.67/17.07 fresh361(fresh186(hBOOL(hAPP(c_NS__Shared__Mirabelle_Ons__shared, v_evs2)), true2, v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 12 (cls_mem__def_1) }
% 130.67/17.07 fresh361(hBOOL(c_in(v_evs2, c_NS__Shared__Mirabelle_Ons__shared, tc_List_Olist(tc_Event_Oevent))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 15 (cls_new__keys__not__used_0) }
% 130.67/17.07 fresh179(hBOOL(c_in(v_KAB, c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2))), tc_nat)), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 6 (cls_Crypt__imp__keysFor_0) R->L }
% 130.67/17.07 fresh179(fresh341(true2, true2, v_KAB, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 1 (cls_parts__analz_0) R->L }
% 130.67/17.07 fresh179(fresh341(true2, true2, v_KAB, c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 13 (cls_conjecture_10) R->L }
% 130.67/17.07 fresh179(fresh341(hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)), tc_Message_Omsg)), true2, v_KAB, c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 1 (cls_parts__analz_0) R->L }
% 130.67/17.07 fresh179(fresh341(hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB, c_Message_Omsg_ONonce(v_NB)), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2))), tc_Message_Omsg)), true2, v_KAB, c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 14 (cls_Crypt__imp__keysFor_0) }
% 130.67/17.07 fresh179(fresh340(hBOOL(c_in(v_KAB, c_Message_OsymKeys, tc_nat)), true2, v_KAB, c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by lemma 16 }
% 130.67/17.07 fresh179(fresh340(true2, true2, v_KAB, c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs2)))), true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 3 (cls_Crypt__imp__keysFor_0) }
% 130.67/17.07 fresh179(true2, true2, v_KAB, v_evs2)
% 130.67/17.07 = { by axiom 5 (cls_new__keys__not__used_0) }
% 130.67/17.07 true2
% 130.67/17.07 % SZS output end Proof
% 130.67/17.07
% 130.67/17.07 RESULT: Unsatisfiable (the axioms are contradictory).
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