TPTP Problem File: SWV249-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV249-2 : TPTP v9.0.0. Released v3.2.0.
% Domain : Software Verification (Security)
% Problem : Cryptographic protocol problem for messages
% Version : [Pau06] axioms : Reduced > Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names :
% Status : Unsatisfiable
% Rating : 0.23 v9.0.0, 0.25 v8.2.0, 0.33 v8.1.0, 0.44 v7.5.0, 0.30 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.43 v6.3.0, 0.17 v6.2.0, 0.00 v6.0.0, 0.44 v5.5.0, 0.75 v5.4.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.38 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.17 v3.4.0, 0.33 v3.3.0, 0.43 v3.2.0
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 28 ( 7 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 4 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments : The problems in the [Pau06] collection each have very many axioms,
% of which only a small selection are required for the refutation.
% The mission is to find those few axioms, after which a refutation
% can be quite easily found. This version has only the necessary
% axioms.
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ).
cnf(cls_Message_Oanalz__analz__Un_0,axiom,
c_Message_Oanalz(c_union(c_Message_Oanalz(V_G),V_H,tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)) ).
cnf(cls_Message_Oanalz__mono_0,axiom,
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) ).
cnf(cls_Message_Oanalz__synth__Un_0,axiom,
c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_Set_OUn__Diff__cancel2_0,axiom,
c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ).
cnf(cls_Set_OUn__Diff__cancel_0,axiom,
c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ).
cnf(cls_Set_OUn__insert__left_0,axiom,
c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ).
cnf(cls_Set_OUn__insert__right_0,axiom,
c_union(V_A,c_insert(V_a,V_B,T_a),T_a) = c_insert(V_a,c_union(V_A,V_B,T_a),T_a) ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_B,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_2,axiom,
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_Oinsert__subset_1,axiom,
( ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a))
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Oinsert__subset_2,axiom,
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(clsarity_set_2,axiom,
class_Orderings_Oorder(tc_set(T_1)) ).
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