TSTP Solution File: SWV802-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV802-1 : 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 : n016.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 23:06:20 EDT 2023
% Result : Unsatisfiable 32.90s 4.56s
% Output : Proof 33.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV802-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % 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 : n016.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 08:35:30 EDT 2023
% 0.12/0.34 % CPUTime :
% 32.90/4.56 Command-line arguments: --no-flatten-goal
% 32.90/4.56
% 32.90/4.56 % SZS status Unsatisfiable
% 32.90/4.56
% 32.90/4.57 % SZS output start Proof
% 32.90/4.57 Take the following subset of the input axioms:
% 33.21/4.57 fof(cls_NS3__msg__in__parts__spies_0, axiom, ![V_evs, V_A, V_X, V_B, V_K, V_N, V_S, V_KA]: (c_in(V_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | ~c_in(c_Event_Oevent_OSays(V_S, V_A, c_Message_Omsg_OCrypt(V_KA, c_Message_Omsg_OMPair(V_N, c_Message_Omsg_OMPair(V_B, c_Message_Omsg_OMPair(V_K, V_X))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))).
% 33.21/4.57 fof(cls_conjecture_10, negated_conjecture, c_in(c_Event_Oevent_OSays(v_A, v_B, c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB)))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg) | ~c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg))).
% 33.21/4.57 fof(cls_conjecture_4, negated_conjecture, c_in(c_Event_Oevent_OSays(v_S, v_Aa, c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_Ka), v_Xa))))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent)).
% 33.21/4.57 fof(cls_conjecture_7, negated_conjecture, c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg)).
% 33.21/4.57 fof(cls_conjecture_8, negated_conjecture, c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg)).
% 33.21/4.57 fof(cls_conjecture_9, negated_conjecture, ~c_in(c_Event_Oevent_OSays(v_A, v_B, c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB)))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent)).
% 33.21/4.57 fof(cls_parts__cut__eq_0, axiom, ![V_H, V_X2]: (c_Message_Oparts(c_Set_Oinsert(V_X2, V_H, tc_Message_Omsg))=c_Message_Oparts(V_H) | ~c_in(V_X2, c_Message_Oparts(V_H), tc_Message_Omsg))).
% 33.21/4.57
% 33.21/4.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.21/4.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.21/4.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.21/4.57 fresh(y, y, x1...xn) = u
% 33.21/4.57 C => fresh(s, t, x1...xn) = v
% 33.21/4.57 where fresh is a fresh function symbol and x1..xn are the free
% 33.21/4.57 variables of u and v.
% 33.21/4.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.21/4.57 input problem has no model of domain size 1).
% 33.21/4.57
% 33.21/4.57 The encoding turns the above axioms into the following unit equations and goals:
% 33.21/4.57
% 33.21/4.57 Axiom 1 (cls_conjecture_10): fresh222(X, X) = true2.
% 33.21/4.57 Axiom 2 (cls_NS3__msg__in__parts__spies_0): fresh295(X, X, Y, Z) = true2.
% 33.21/4.57 Axiom 3 (cls_parts__cut__eq_0): fresh153(X, X, Y, Z) = c_Message_Oparts(Z).
% 33.21/4.57 Axiom 4 (cls_knows__Spy__Notes_0): fresh195(X, X, Y, Z, W) = c_Set_Oinsert(Z, c_Event_Oknows(c_Message_Oagent_OSpy, W), tc_Message_Omsg).
% 33.21/4.57 Axiom 5 (cls_parts__cut__eq_0): fresh153(c_in(X, c_Message_Oparts(Y), tc_Message_Omsg), true2, X, Y) = c_Message_Oparts(c_Set_Oinsert(X, Y, tc_Message_Omsg)).
% 33.21/4.57 Axiom 6 (cls_conjecture_10): fresh223(X, X) = c_in(c_Event_Oevent_OSays(v_A, v_B, c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB)))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent).
% 33.21/4.57 Axiom 7 (cls_conjecture_8): c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg) = true2.
% 33.21/4.57 Axiom 8 (cls_NS3__msg__in__parts__spies_0): fresh295(c_in(c_Event_Oevent_OSays(X, Y, c_Message_Omsg_OCrypt(Z, c_Message_Omsg_OMPair(W, c_Message_Omsg_OMPair(V, c_Message_Omsg_OMPair(U, T))))), c_List_Oset(S, tc_Event_Oevent), tc_Event_Oevent), true2, T, S) = c_in(T, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, S)), tc_Message_Omsg).
% 33.21/4.57 Axiom 9 (cls_conjecture_10): fresh223(c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true2) = fresh222(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true2).
% 33.21/4.57 Axiom 10 (cls_conjecture_4): c_in(c_Event_Oevent_OSays(v_S, v_Aa, c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_Ka), v_Xa))))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent) = true2.
% 33.21/4.57 Axiom 11 (cls_conjecture_7): c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg) = true2.
% 33.21/4.57
% 33.21/4.57 Lemma 12: c_Message_Oparts(fresh195(X, X, Y, v_Xa, v_evs3)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)).
% 33.21/4.57 Proof:
% 33.21/4.57 c_Message_Oparts(fresh195(X, X, Y, v_Xa, v_evs3))
% 33.21/4.57 = { by axiom 4 (cls_knows__Spy__Notes_0) }
% 33.21/4.57 c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg))
% 33.21/4.57 = { by axiom 5 (cls_parts__cut__eq_0) R->L }
% 33.21/4.57 fresh153(c_in(v_Xa, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true2, v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))
% 33.21/4.57 = { by axiom 8 (cls_NS3__msg__in__parts__spies_0) R->L }
% 33.21/4.57 fresh153(fresh295(c_in(c_Event_Oevent_OSays(v_S, v_Aa, c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_Ka), v_Xa))))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent), true2, v_Xa, v_evs3), true2, v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))
% 33.21/4.57 = { by axiom 10 (cls_conjecture_4) }
% 33.21/4.57 fresh153(fresh295(true2, true2, v_Xa, v_evs3), true2, v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))
% 33.21/4.57 = { by axiom 2 (cls_NS3__msg__in__parts__spies_0) }
% 33.21/4.57 fresh153(true2, true2, v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))
% 33.21/4.57 = { by axiom 3 (cls_parts__cut__eq_0) }
% 33.21/4.57 c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))
% 33.21/4.57
% 33.21/4.57 Goal 1 (cls_conjecture_9): c_in(c_Event_Oevent_OSays(v_A, v_B, c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB)))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent) = true2.
% 33.21/4.57 Proof:
% 33.21/4.57 c_in(c_Event_Oevent_OSays(v_A, v_B, c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB)))), c_List_Oset(v_evs3, tc_Event_Oevent), tc_Event_Oevent)
% 33.21/4.57 = { by axiom 6 (cls_conjecture_10) R->L }
% 33.21/4.57 fresh223(true2, true2)
% 33.21/4.57 = { by axiom 7 (cls_conjecture_8) R->L }
% 33.21/4.57 fresh223(c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by axiom 4 (cls_knows__Spy__Notes_0) R->L }
% 33.21/4.57 fresh223(c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(fresh195(X, X, Y, v_Xa, v_evs3)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by lemma 12 }
% 33.21/4.57 fresh223(c_in(c_Message_Omsg_OCrypt(v_K, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_ONonce(v_NB))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by axiom 9 (cls_conjecture_10) }
% 33.21/4.57 fresh222(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by lemma 12 R->L }
% 33.21/4.57 fresh222(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(fresh195(Z, Z, W, v_Xa, v_evs3)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by axiom 4 (cls_knows__Spy__Notes_0) }
% 33.21/4.57 fresh222(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK, v_A), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey, v_K), v_X)))), c_Message_Oparts(c_Set_Oinsert(v_Xa, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3), tc_Message_Omsg)), tc_Message_Omsg), true2)
% 33.21/4.57 = { by axiom 11 (cls_conjecture_7) }
% 33.21/4.57 fresh222(true2, true2)
% 33.21/4.57 = { by axiom 1 (cls_conjecture_10) }
% 33.21/4.57 true2
% 33.21/4.57 % SZS output end Proof
% 33.21/4.57
% 33.21/4.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------