TSTP Solution File: SWV342-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV342-2 : 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 : n031.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 23:03:48 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV342-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n031.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Aug 29 10:15:11 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --no-flatten-goal
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(cls_Event_OSays__imp__analz__Spy__dest_0, axiom, ![V_A, V_B, V_X, V_evs]: (~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, axiom, ![V_c, V_evs2]: (~c_in(V_c, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs2)), tc_Message_Omsg) | c_in(V_c, c_Event_Oused(V_evs2), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Message_OMPair__analz_0, axiom, ![V_Y, V_H, V_X2]: (~c_in(c_Message_Omsg_OMPair(V_X2, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Message_OMPair__parts_0, axiom, ![V_H2, V_X2, V_Y2]: (~c_in(c_Message_Omsg_OMPair(V_X2, V_Y2), c_Message_Oparts(V_H2), tc_Message_Omsg) | c_in(V_Y2, c_Message_Oparts(V_H2), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Message_Oparts_OBody__dest_0, axiom, ![V_K, V_H2, V_X2]: (~c_in(c_Message_Omsg_OCrypt(V_K, V_X2), c_Message_Oparts(V_H2), tc_Message_Omsg) | c_in(V_X2, c_Message_Oparts(V_H2), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Message_Oparts_OInj_0, axiom, ![V_H2, V_X2]: (~c_in(V_X2, V_H2, tc_Message_Omsg) | c_in(V_X2, c_Message_Oparts(V_H2), tc_Message_Omsg))).
% 0.21/0.41 fof(cls_Message_Oparts__analz_0, axiom, ![V_H2]: c_Message_Oparts(c_Message_Oanalz(V_H2))=c_Message_Oparts(V_H2)).
% 0.21/0.41 fof(cls_conjecture_3, negated_conjecture, ~c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg)).
% 0.21/0.41 fof(cls_conjecture_9, 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_evs3, tc_Event_Oevent), tc_Event_Oevent)).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (cls_Message_Oparts__analz_0): c_Message_Oparts(c_Message_Oanalz(X)) = c_Message_Oparts(X).
% 0.21/0.41 Axiom 2 (cls_Message_Oparts_OInj_0): fresh(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 3 (cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0): fresh6(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 4 (cls_Event_OSays__imp__analz__Spy__dest_0): fresh5(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 5 (cls_Message_OMPair__analz_0): fresh4(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 6 (cls_Message_OMPair__parts_0): fresh3(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 7 (cls_Message_Oparts_OBody__dest_0): fresh2(X, X, Y, Z) = true.
% 0.21/0.41 Axiom 8 (cls_Message_Oparts_OInj_0): fresh(c_in(X, Y, tc_Message_Omsg), true, X, Y) = c_in(X, c_Message_Oparts(Y), tc_Message_Omsg).
% 0.21/0.41 Axiom 9 (cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0): fresh6(c_in(X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, Y)), tc_Message_Omsg), true, X, Y) = c_in(X, c_Event_Oused(Y), tc_Message_Omsg).
% 0.21/0.41 Axiom 10 (cls_Message_OMPair__analz_0): fresh4(c_in(c_Message_Omsg_OMPair(X, Y), c_Message_Oanalz(Z), tc_Message_Omsg), true, Y, Z) = c_in(Y, c_Message_Oanalz(Z), tc_Message_Omsg).
% 0.21/0.41 Axiom 11 (cls_Message_OMPair__parts_0): fresh3(c_in(c_Message_Omsg_OMPair(X, Y), c_Message_Oparts(Z), tc_Message_Omsg), true, Y, Z) = c_in(Y, c_Message_Oparts(Z), tc_Message_Omsg).
% 0.21/0.41 Axiom 12 (cls_Message_Oparts_OBody__dest_0): fresh2(c_in(c_Message_Omsg_OCrypt(X, Y), c_Message_Oparts(Z), tc_Message_Omsg), true, Y, Z) = c_in(Y, c_Message_Oparts(Z), tc_Message_Omsg).
% 0.21/0.41 Axiom 13 (cls_Event_OSays__imp__analz__Spy__dest_0): fresh5(c_in(c_Event_Oevent_OSays(X, Y, Z), c_List_Oset(W, tc_Event_Oevent), tc_Event_Oevent), true, Z, W) = c_in(Z, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, W)), tc_Message_Omsg).
% 0.21/0.41 Axiom 14 (cls_conjecture_9): 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_evs3, tc_Event_Oevent), tc_Event_Oevent) = true.
% 0.21/0.41
% 0.21/0.41 Goal 1 (cls_conjecture_3): c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg) = true.
% 0.21/0.41 Proof:
% 0.21/0.41 c_in(c_Message_Omsg_OKey(v_K), c_Event_Oused(v_evs3), tc_Message_Omsg)
% 0.21/0.41 = { by axiom 9 (cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) R->L }
% 0.21/0.41 fresh6(c_in(c_Message_Omsg_OKey(v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.41 = { by axiom 11 (cls_Message_OMPair__parts_0) R->L }
% 0.21/0.41 fresh6(fresh3(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.41 = { by axiom 12 (cls_Message_Oparts_OBody__dest_0) R->L }
% 0.21/0.41 fresh6(fresh3(fresh2(c_in(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_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 1 (cls_Message_Oparts__analz_0) R->L }
% 0.21/0.42 fresh6(fresh3(fresh2(c_in(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_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), tc_Message_Omsg), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 8 (cls_Message_Oparts_OInj_0) R->L }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 10 (cls_Message_OMPair__analz_0) R->L }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(fresh4(c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), tc_Message_Omsg), true, 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_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 13 (cls_Event_OSays__imp__analz__Spy__dest_0) R->L }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(fresh4(fresh5(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_evs3, tc_Event_Oevent), tc_Event_Oevent), true, 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)))), v_evs3), true, 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_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 14 (cls_conjecture_9) }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(fresh4(fresh5(true, true, 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)))), v_evs3), true, 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_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 4 (cls_Event_OSays__imp__analz__Spy__dest_0) }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(fresh4(true, true, 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_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 5 (cls_Message_OMPair__analz_0) }
% 0.21/0.42 fresh6(fresh3(fresh2(fresh(true, true, 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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3))), true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 2 (cls_Message_Oparts_OInj_0) }
% 0.21/0.42 fresh6(fresh3(fresh2(true, true, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 7 (cls_Message_Oparts_OBody__dest_0) }
% 0.21/0.42 fresh6(fresh3(true, true, c_Message_Omsg_OKey(v_K), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs3)), true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 6 (cls_Message_OMPair__parts_0) }
% 0.21/0.42 fresh6(true, true, c_Message_Omsg_OKey(v_K), v_evs3)
% 0.21/0.42 = { by axiom 3 (cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) }
% 0.21/0.42 true
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------