TSTP Solution File: SWV312-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV312-1 : 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 : n006.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 23:03:36 EDT 2023
% Result : Unsatisfiable 48.59s 6.51s
% Output : Proof 48.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV312-1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 10:51:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 48.59/6.51 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 48.59/6.51
% 48.59/6.51 % SZS status Unsatisfiable
% 48.59/6.51
% 48.59/6.51 % SZS output start Proof
% 48.59/6.51 Take the following subset of the input axioms:
% 48.69/6.52 fof(cls_Datatype_Ooption_Odistinct__1__iff1_0, axiom, ![T_a, V_a_H]: c_Datatype_Ooption_ONone!=c_Datatype_Ooption_OSome(V_a_H, T_a)).
% 48.69/6.52 fof(cls_Datatype_Ooption_Odistinct__2__iff1_0, axiom, ![T_a2, V_a_H2]: c_Datatype_Ooption_OSome(V_a_H2, T_a2)!=c_Datatype_Ooption_ONone).
% 48.69/6.52 fof(cls_Datatype__Universe_OAtom__not__Scons__iff1_0, axiom, ![T_b, V_N, V_M, V_a, T_a2]: c_Datatype__Universe_OAtom(V_a, T_a2, T_b)!=c_Datatype__Universe_OScons(V_M, V_N, T_a2, T_b)).
% 48.69/6.52 fof(cls_Datatype__Universe_OIn0__not__In1__iff1_0, axiom, ![T_a2, T_b2, V_N2, V_M2]: c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)!=c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OIn1__not__In0__iff1_0, axiom, ![T_a2, T_b2, V_N2, V_M2]: c_Datatype__Universe_OIn1(V_N2, T_a2, T_b2)!=c_Datatype__Universe_OIn0(V_M2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OLeaf__not__Numb__iff1_0, axiom, ![V_k, T_a2, T_b2, V_a2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OLeaf__not__Scons__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_N2, V_M2]: c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_ONumb__not__Leaf__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_k2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_ONumb__not__Scons__iff1_0, axiom, ![T_a2, T_b2, V_N2, V_M2, V_k2]: c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)!=c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OScons__not__Atom__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_N2, V_M2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OAtom(V_a2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OScons__not__Leaf__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_N2, V_M2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_OLeaf(V_a2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Datatype__Universe_OScons__not__Numb__iff1_0, axiom, ![T_a2, T_b2, V_N2, V_M2, V_k2]: c_Datatype__Universe_OScons(V_M2, V_N2, T_a2, T_b2)!=c_Datatype__Universe_ONumb(V_k2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__1__iff1_0, axiom, ![V_agent1, V_agent2, V_msg, V_agent_H, V_msg_H]: c_Event_Oevent_OSays(V_agent1, V_agent2, V_msg)!=c_Event_Oevent_OGets(V_agent_H, V_msg_H)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__2__iff1_0, axiom, ![V_msg2, V_agent_H2, V_msg_H2, V_agent1_2, V_agent2_2]: c_Event_Oevent_OGets(V_agent_H2, V_msg_H2)!=c_Event_Oevent_OSays(V_agent1_2, V_agent2_2, V_msg2)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__3__iff1_0, axiom, ![V_msg2, V_agent_H2, V_msg_H2, V_agent1_2, V_agent2_2]: c_Event_Oevent_OSays(V_agent1_2, V_agent2_2, V_msg2)!=c_Event_Oevent_ONotes(V_agent_H2, V_msg_H2)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__4__iff1_0, axiom, ![V_msg2, V_agent_H2, V_msg_H2, V_agent1_2, V_agent2_2]: c_Event_Oevent_ONotes(V_agent_H2, V_msg_H2)!=c_Event_Oevent_OSays(V_agent1_2, V_agent2_2, V_msg2)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__5__iff1_0, axiom, ![V_agent, V_msg2, V_agent_H2, V_msg_H2]: c_Event_Oevent_OGets(V_agent, V_msg2)!=c_Event_Oevent_ONotes(V_agent_H2, V_msg_H2)).
% 48.69/6.52 fof(cls_Event_Oevent_Odistinct__6__iff1_0, axiom, ![V_msg2, V_agent_H2, V_msg_H2, V_agent3]: c_Event_Oevent_ONotes(V_agent_H2, V_msg_H2)!=c_Event_Oevent_OGets(V_agent3, V_msg2)).
% 48.69/6.52 fof(cls_List_ONil2__notin__lex__iff1_0, axiom, ![V_r, V_xs, T_a2]: ~c_in(c_Pair(V_xs, c_List_Olist_ONil, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 48.69/6.52 fof(cls_List_ONil__notin__lex__iff1_0, axiom, ![V_ys, T_a2, V_r2]: ~c_in(c_Pair(c_List_Olist_ONil, V_ys, tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olex(V_r2, T_a2), tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2)))).
% 48.69/6.52 fof(cls_List_Olength__greater__0__conv__iff1_0, axiom, ![T_a2]: ~c_less(c_0, c_Nat_Osize(c_List_Olist_ONil, tc_List_Olist(T_a2)), tc_nat)).
% 48.69/6.52 fof(cls_List_Olist_Odistinct__1__iff1_0, axiom, ![V_list_H, T_a2, V_a_H2]: c_List_Olist_ONil!=c_List_Olist_OCons(V_a_H2, V_list_H, T_a2)).
% 48.69/6.52 fof(cls_List_Olist_Odistinct__2__iff1_0, axiom, ![T_a2, V_a_H2, V_list_H2]: c_List_Olist_OCons(V_a_H2, V_list_H2, T_a2)!=c_List_Olist_ONil).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__1__iff1_0, axiom, ![V_A, V_X, V_Y]: c_Message_Omsg_OAgent(V_A)!=c_Message_OHPair(V_X, V_Y)).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__2__iff1_0, axiom, ![V_N2, V_X2, V_Y2]: c_Message_Omsg_ONonce(V_N2)!=c_Message_OHPair(V_X2, V_Y2)).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__3__iff1_0, axiom, ![V_N2, V_X2, V_Y2]: c_Message_Omsg_ONumber(V_N2)!=c_Message_OHPair(V_X2, V_Y2)).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__4__iff1_0, axiom, ![V_K, V_X2, V_Y2]: c_Message_Omsg_OKey(V_K)!=c_Message_OHPair(V_X2, V_Y2)).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__5__iff1_0, axiom, ![V_Z, V_X2, V_Y2]: c_Message_Omsg_OHash(V_Z)!=c_Message_OHPair(V_X2, V_Y2)).
% 48.69/6.52 fof(cls_Message_OHPair__neqs__6__iff1_0, axiom, ![V_X_H, V_X2, V_Y2, V_K2]: c_Message_Omsg_OCrypt(V_K2, V_X_H)!=c_Message_OHPair(V_X2, V_Y2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, axiom, ![V_A2, V_X2, V_Y2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_OAgent(V_A2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0, axiom, ![V_X2, V_Y2, V_K2, V_X_H2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_OCrypt(V_K2, V_X_H2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0, axiom, ![V_X2, V_Y2, V_Z2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_OHash(V_Z2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0, axiom, ![V_X2, V_Y2, V_K2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_OKey(V_K2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, axiom, ![V_N2, V_X2, V_Y2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_ONonce(V_N2)).
% 48.69/6.52 fof(cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, axiom, ![V_N2, V_X2, V_Y2]: c_Message_OHPair(V_X2, V_Y2)!=c_Message_Omsg_ONumber(V_N2)).
% 48.69/6.52 fof(cls_Message_Oagent_Odistinct__1__iff1_0, axiom, ![V_nat_H]: c_Message_Oagent_OServer!=c_Message_Oagent_OFriend(V_nat_H)).
% 48.69/6.52 fof(cls_Message_Oagent_Odistinct__2__iff1_0, axiom, ![V_nat_H2]: c_Message_Oagent_OFriend(V_nat_H2)!=c_Message_Oagent_OServer).
% 48.69/6.52 fof(cls_Message_Oagent_Odistinct__5__iff1_0, axiom, ![V_nat]: c_Message_Oagent_OFriend(V_nat)!=c_Message_Oagent_OSpy).
% 48.69/6.52 fof(cls_Message_Oagent_Odistinct__6__iff1_0, axiom, ![V_nat2]: c_Message_Oagent_OSpy!=c_Message_Oagent_OFriend(V_nat2)).
% 48.69/6.52 fof(cls_Message_Oparts__emptyE_0, axiom, ![V_X2]: ~c_in(V_X2, c_Message_Oparts(c_emptyset), tc_Message_Omsg)).
% 48.69/6.52 fof(cls_Nat_OSuc__not__Zero__iff1_0, axiom, ![V_m]: c_Suc(V_m)!=c_0).
% 48.69/6.52 fof(cls_Nat_OZero__not__Suc__iff1_0, axiom, ![V_m2]: c_0!=c_Suc(V_m2)).
% 48.69/6.52 fof(cls_Nat_Oless__irrefl_0, axiom, ![V_n]: ~c_less(V_n, V_n, tc_nat)).
% 48.69/6.52 fof(cls_Nat_Onot__add__less1__iff1_0, axiom, ![V_i, V_j]: ~c_less(c_plus(V_i, V_j, tc_nat), V_i, tc_nat)).
% 48.69/6.52 fof(cls_Nat_Onot__add__less2__iff1_0, axiom, ![V_i2, V_j2]: ~c_less(c_plus(V_j2, V_i2, tc_nat), V_i2, tc_nat)).
% 48.69/6.52 fof(cls_Nat_Onot__less0__iff1_0, axiom, ![V_n2]: ~c_less(V_n2, c_0, tc_nat)).
% 48.69/6.52 fof(cls_Orderings_Oorder__less__irrefl__iff1_0, axiom, ![V_x, T_a2]: (~class_Orderings_Oorder(T_a2) | ~c_less(V_x, V_x, T_a2))).
% 48.69/6.52 fof(cls_Public_ONonce__notin__initState__iff1_0, axiom, ![V_B, V_N2]: ~c_in(c_Message_Omsg_ONonce(V_N2), c_Message_Oparts(c_Event_OinitState(V_B)), tc_Message_Omsg)).
% 48.69/6.52 fof(cls_Public_Onot__symKeys__priK__iff1_0, axiom, ![V_b, V_A2]: ~c_in(c_Message_OinvKey(c_Public_OpublicKey(V_b, V_A2)), c_Message_OsymKeys, tc_nat)).
% 48.69/6.52 fof(cls_Public_Onot__symKeys__pubK__iff1_0, axiom, ![V_b2, V_A2]: ~c_in(c_Public_OpublicKey(V_b2, V_A2), c_Message_OsymKeys, tc_nat)).
% 48.69/6.52 fof(cls_Public_OpriK__neq__shrK__iff1_0, axiom, ![V_C, V_b2, V_A2]: c_Public_OshrK(V_A2)!=c_Message_OinvKey(c_Public_OpublicKey(V_b2, V_C))).
% 48.69/6.52 fof(cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0, axiom, ![V_c, V_A_H, V_b2, V_A2]: c_Message_OinvKey(c_Public_OpublicKey(V_b2, V_A2))!=c_Public_OpublicKey(V_c, V_A_H)).
% 48.69/6.52 fof(cls_Public_OpubK__neq__shrK__iff1_0, axiom, ![V_b2, V_A2, V_C2]: c_Public_OshrK(V_A2)!=c_Public_OpublicKey(V_b2, V_C2)).
% 48.69/6.52 fof(cls_Public_OpublicKey__neq__privateKey__iff1_0, axiom, ![V_b2, V_A2, V_c2, V_A_H2]: c_Public_OpublicKey(V_c2, V_A_H2)!=c_Message_OinvKey(c_Public_OpublicKey(V_b2, V_A2))).
% 48.69/6.52 fof(cls_Set_OComplD__dest_0, axiom, ![T_a2, V_A2, V_c2]: (~c_in(V_c2, V_A2, T_a2) | ~c_in(V_c2, c_uminus(V_A2, tc_set(T_a2)), T_a2))).
% 48.69/6.52 fof(cls_Set_ODiffE_0, axiom, ![T_a2, V_A2, V_B2, V_c2]: (~c_in(V_c2, V_B2, T_a2) | ~c_in(V_c2, c_minus(V_A2, V_B2, tc_set(T_a2)), T_a2))).
% 48.69/6.52 fof(cls_Set_OemptyE_0, axiom, ![T_a2, V_a2]: ~c_in(V_a2, c_emptyset, T_a2)).
% 48.69/6.52 fof(cls_Set_Onot__psubset__empty__iff1_0, axiom, ![T_a2, V_A2]: ~c_less(V_A2, c_emptyset, tc_set(T_a2))).
% 48.69/6.52 fof(cls_Set_OpsubsetE_0, axiom, ![T_a2, V_A2, V_B2]: (~c_less(V_A2, V_B2, tc_set(T_a2)) | ~c_lessequals(V_B2, V_A2, tc_set(T_a2)))).
% 48.69/6.52 fof(cls_Sum__Type_OInl__not__Inr__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_b2]: c_Sum__Type_OInl(V_a2, T_a2, T_b2)!=c_Sum__Type_OInr(V_b2, T_b2, T_a2)).
% 48.69/6.52 fof(cls_Sum__Type_OInr__not__Inl__iff1_0, axiom, ![T_a2, T_b2, V_a2, V_b2]: c_Sum__Type_OInr(V_b2, T_b2, T_a2)!=c_Sum__Type_OInl(V_a2, T_a2, T_b2)).
% 48.69/6.52 fof(cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, axiom, ![V_y, V_x2, T_a2, V_r2]: (~c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(V_y, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~c_in(c_Pair(V_x2, V_y, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)))).
% 48.69/6.52 fof(cls_Wellfounded__Recursion_Owf__insert__iff1_1, axiom, ![V_x2, T_a2, V_y2, V_r2]: (~c_Wellfounded__Recursion_Owf(c_insert(c_Pair(V_y2, V_x2, T_a2, T_a2), V_r2, tc_prod(T_a2, T_a2)), T_a2) | ~c_in(c_Pair(V_x2, V_y2, T_a2, T_a2), c_Transitive__Closure_Ortrancl(V_r2, T_a2), tc_prod(T_a2, T_a2)))).
% 48.69/6.52 fof(cls_conjecture_5, negated_conjecture, c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)).
% 48.69/6.52 fof(cls_conjecture_6, negated_conjecture, ![V_U]: ~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(V_U, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)).
% 48.69/6.52 fof(cls_conjecture_7, negated_conjecture, c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_x, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | ~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)).
% 48.69/6.53 fof(cls_conjecture_8, negated_conjecture, ![V_U2]: (c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(V_U2, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B))))))))!=v_X | (v_NA!=c_Message_Omsg_ONonce(v_NAa) | (c_Message_Oagent_OServer!=v_Aa | v_B!=v_Ba)))).
% 48.69/6.53
% 48.69/6.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 48.69/6.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 48.69/6.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 48.69/6.53 fresh(y, y, x1...xn) = u
% 48.69/6.53 C => fresh(s, t, x1...xn) = v
% 48.69/6.53 where fresh is a fresh function symbol and x1..xn are the free
% 48.69/6.53 variables of u and v.
% 48.69/6.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 48.69/6.53 input problem has no model of domain size 1).
% 48.69/6.53
% 48.69/6.53 The encoding turns the above axioms into the following unit equations and goals:
% 48.69/6.53
% 48.69/6.53 Axiom 1 (cls_conjecture_7): fresh995(X, X) = true2.
% 48.69/6.53 Axiom 2 (cls_conjecture_5): c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) = true2.
% 48.69/6.53 Axiom 3 (cls_conjecture_7): fresh995(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent), true2) = c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_x, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent).
% 48.69/6.53
% 48.69/6.53 Goal 1 (cls_conjecture_6): c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) = true2.
% 48.69/6.53 The goal is true when:
% 48.69/6.53 X = v_x
% 48.69/6.53
% 48.69/6.53 Proof:
% 48.69/6.53 c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_x, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)
% 48.69/6.53 = { by axiom 3 (cls_conjecture_7) R->L }
% 48.69/6.53 fresh995(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent), true2)
% 48.69/6.53 = { by axiom 2 (cls_conjecture_5) }
% 48.69/6.53 fresh995(true2, true2)
% 48.69/6.53 = { by axiom 1 (cls_conjecture_7) }
% 48.69/6.53 true2
% 48.69/6.53 % SZS output end Proof
% 48.69/6.53
% 48.69/6.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------