TSTP Solution File: SWV281-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV281-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 : 600s
% DateTime : Wed Jul 20 20:30:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of clauses : 64 ( 27 unt; 6 nHn; 36 RR)
% Number of literals : 113 ( 83 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 80 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
( V_U = V_V
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg) ) ).
cnf(cls_List_Olist_Odistinct__1_0,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ).
cnf(cls_Nat_Ole__add2_0,axiom,
c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat) ).
cnf(cls_Nat_Onat__add__right__cancel_0,axiom,
( c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat)
| V_m = V_n ) ).
cnf(cls_Nat_Oop_A_L_Oadd__0_0,axiom,
c_plus(c_0,V_y,tc_nat) = V_y ).
cnf(cls_Public_ONonce__supply__lemma_0,axiom,
( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat) ) ).
cnf(refute_0_0,plain,
( c_plus(c_0,X_9,tc_nat) != c_plus(X_11,X_9,tc_nat)
| c_0 = X_11 ),
inference(subst,[],[cls_Nat_Onat__add__right__cancel_0:[bind(V_k,$fot(X_9)),bind(V_m,$fot(c_0)),bind(V_n,$fot(X_11))]]) ).
cnf(refute_0_1,plain,
c_plus(c_0,X_9,tc_nat) = X_9,
inference(subst,[],[cls_Nat_Oop_A_L_Oadd__0_0:[bind(V_y,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( X_9 != c_plus(X_11,X_9,tc_nat)
| c_plus(c_0,X_9,tc_nat) != X_9
| c_plus(c_0,X_9,tc_nat) = c_plus(X_11,X_9,tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(c_0,X_9,tc_nat),X_9) ),[1],$fot(c_plus(X_11,X_9,tc_nat))]]) ).
cnf(refute_0_3,plain,
( X_9 != c_plus(X_11,X_9,tc_nat)
| c_plus(c_0,X_9,tc_nat) = c_plus(X_11,X_9,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_0,X_9,tc_nat),X_9) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( X_9 != c_plus(X_11,X_9,tc_nat)
| c_0 = X_11 ),
inference(resolve,[$cnf( $equal(c_plus(c_0,X_9,tc_nat),c_plus(X_11,X_9,tc_nat)) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( v_sko__urX(v_evs) != c_plus(X_11,v_sko__urX(v_evs),tc_nat)
| c_0 = X_11 ),
inference(subst,[],[refute_0_4:[bind(X_9,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_6,plain,
c_lessequals(v_sko__urX(v_evs_H),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add2_0:[bind(V_n,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_18),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs_H),X_18,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_18)),bind(V_evs,$fot(v_evs_H))]]) ).
cnf(refute_0_8,plain,
c_lessequals(X_2,c_plus(c_0,X_2,tc_nat),tc_nat),
inference(subst,[],[cls_Nat_Ole__add2_0:[bind(V_m,$fot(c_0)),bind(V_n,$fot(X_2))]]) ).
cnf(refute_0_9,plain,
c_plus(c_0,X_2,tc_nat) = X_2,
inference(subst,[],[cls_Nat_Oop_A_L_Oadd__0_0:[bind(V_y,$fot(X_2))]]) ).
cnf(refute_0_10,plain,
( c_plus(c_0,X_2,tc_nat) != X_2
| ~ c_lessequals(X_2,c_plus(c_0,X_2,tc_nat),tc_nat)
| c_lessequals(X_2,X_2,tc_nat) ),
introduced(tautology,[equality,[$cnf( c_lessequals(X_2,c_plus(c_0,X_2,tc_nat),tc_nat) ),[1],$fot(X_2)]]) ).
cnf(refute_0_11,plain,
( ~ c_lessequals(X_2,c_plus(c_0,X_2,tc_nat),tc_nat)
| c_lessequals(X_2,X_2,tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(c_0,X_2,tc_nat),X_2) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
c_lessequals(X_2,X_2,tc_nat),
inference(resolve,[$cnf( c_lessequals(X_2,c_plus(c_0,X_2,tc_nat),tc_nat) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(v_sko__urX(v_evs)))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(c_Message_Omsg_ONonce(X_14),c_Event_Oused(v_evs),tc_Message_Omsg)
| ~ c_lessequals(v_sko__urX(v_evs),X_14,tc_nat) ),
inference(subst,[],[cls_Public_ONonce__supply__lemma_0:[bind(V_U,$fot(X_14)),bind(V_evs,$fot(v_evs))]]) ).
cnf(refute_0_15,plain,
( X_14 = X_15
| c_in(c_Message_Omsg_ONonce(X_14),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X_15),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(X_14)),bind(V_V,$fot(X_15))]]) ).
cnf(refute_0_16,plain,
( ~ c_lessequals(v_sko__urX(v_evs),X_14,tc_nat)
| X_14 = X_15
| c_in(c_Message_Omsg_ONonce(X_15),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_14),c_Event_Oused(v_evs),tc_Message_Omsg) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat)
| v_sko__urX(v_evs) = X_17
| c_in(c_Message_Omsg_ONonce(X_17),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_16:[bind(X_14,$fot(v_sko__urX(v_evs))),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_18,plain,
( v_sko__urX(v_evs) = X_17
| c_in(c_Message_Omsg_ONonce(X_17),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( v_sko__urX(v_evs) = X_18
| c_in(c_Message_Omsg_ONonce(X_18),c_Event_Oused(v_evs_H),tc_Message_Omsg) ),
inference(subst,[],[refute_0_18:[bind(X_17,$fot(X_18))]]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),X_18,tc_nat)
| v_sko__urX(v_evs) = X_18 ),
inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(X_18),c_Event_Oused(v_evs_H),tc_Message_Omsg) )],[refute_0_19,refute_0_7]) ).
cnf(refute_0_21,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),tc_nat)
| v_sko__urX(v_evs) = c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) ),
inference(subst,[],[refute_0_20:[bind(X_18,$fot(c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)))]]) ).
cnf(refute_0_22,plain,
v_sko__urX(v_evs) = c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),tc_nat) )],[refute_0_6,refute_0_21]) ).
cnf(refute_0_23,plain,
c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_24,plain,
( ~ c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(subst,[],[refute_0_20:[bind(X_18,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_25,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs_H),
inference(resolve,[$cnf( c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( v_sko__urX(v_evs) != v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(v_sko__urX(v_evs_H)))]]) ).
cnf(refute_0_30,plain,
v_sko__urX(v_evs_H) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) = c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),
introduced(tautology,[refl,[$fot(c_plus(V_m,v_sko__urX(v_evs_H),tc_nat))]]) ).
cnf(refute_0_32,plain,
( c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) != c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) = c_plus(V_m,v_sko__urX(v_evs),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)) ),[1,1],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_33,plain,
( v_sko__urX(v_evs_H) != v_sko__urX(v_evs)
| c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) = c_plus(V_m,v_sko__urX(v_evs),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) = c_plus(V_m,v_sko__urX(v_evs),tc_nat),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( c_plus(V_m,v_sko__urX(v_evs_H),tc_nat) != c_plus(V_m,v_sko__urX(v_evs),tc_nat)
| v_sko__urX(v_evs) != c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs) = c_plus(V_m,v_sko__urX(v_evs),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(v_sko__urX(v_evs),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)) ),[1],$fot(c_plus(V_m,v_sko__urX(v_evs),tc_nat))]]) ).
cnf(refute_0_36,plain,
( v_sko__urX(v_evs) != c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)
| v_sko__urX(v_evs) = c_plus(V_m,v_sko__urX(v_evs),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(V_m,v_sko__urX(v_evs_H),tc_nat),c_plus(V_m,v_sko__urX(v_evs),tc_nat)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
v_sko__urX(v_evs) = c_plus(V_m,v_sko__urX(v_evs),tc_nat),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(V_m,v_sko__urX(v_evs_H),tc_nat)) )],[refute_0_22,refute_0_36]) ).
cnf(refute_0_38,plain,
v_sko__urX(v_evs) = c_plus(X_11,v_sko__urX(v_evs),tc_nat),
inference(subst,[],[refute_0_37:[bind(V_m,$fot(X_11))]]) ).
cnf(refute_0_39,plain,
( v_sko__urX(v_evs) != c_plus(X_11,v_sko__urX(v_evs),tc_nat)
| c_plus(X_11,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(v_sko__urX(v_evs))),bind(Y,$fot(c_plus(X_11,v_sko__urX(v_evs),tc_nat)))]]) ).
cnf(refute_0_40,plain,
c_plus(X_11,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(X_11,v_sko__urX(v_evs),tc_nat)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( c_plus(X_11,v_sko__urX(v_evs),tc_nat) != v_sko__urX(v_evs)
| v_sko__urX(v_evs) != v_sko__urX(v_evs)
| v_sko__urX(v_evs) = c_plus(X_11,v_sko__urX(v_evs),tc_nat) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_sko__urX(v_evs),c_plus(X_11,v_sko__urX(v_evs),tc_nat)) ),[1],$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_42,plain,
( v_sko__urX(v_evs) != v_sko__urX(v_evs)
| v_sko__urX(v_evs) = c_plus(X_11,v_sko__urX(v_evs),tc_nat) ),
inference(resolve,[$cnf( $equal(c_plus(X_11,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( v_sko__urX(v_evs) != v_sko__urX(v_evs)
| c_0 = X_11 ),
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),c_plus(X_11,v_sko__urX(v_evs),tc_nat)) )],[refute_0_42,refute_0_5]) ).
cnf(refute_0_44,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs),
introduced(tautology,[refl,[$fot(v_sko__urX(v_evs))]]) ).
cnf(refute_0_45,plain,
c_0 = X_11,
inference(resolve,[$cnf( $equal(v_sko__urX(v_evs),v_sko__urX(v_evs)) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,plain,
( c_0 != X_11
| X_11 = c_0 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(c_0)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_47,plain,
X_11 = c_0,
inference(resolve,[$cnf( $equal(c_0,X_11) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
c_List_Olist_ONil = c_0,
inference(subst,[],[refute_0_47:[bind(X_11,$fot(c_List_Olist_ONil))]]) ).
cnf(refute_0_49,plain,
( c_0 != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| c_List_Olist_ONil != c_0
| c_List_Olist_ONil = c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_List_Olist_ONil,c_0) ),[1],$fot(c_List_Olist_OCons(V_a_H,V_list_H,T_a))]]) ).
cnf(refute_0_50,plain,
( c_0 != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| c_List_Olist_ONil = c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(resolve,[$cnf( $equal(c_List_Olist_ONil,c_0) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) = c_0,
inference(subst,[],[refute_0_47:[bind(X_11,$fot(c_List_Olist_OCons(V_a_H,V_list_H,T_a)))]]) ).
cnf(refute_0_52,plain,
( c_0 != c_0
| c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_0
| c_0 = c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_0,c_List_Olist_OCons(V_a_H,V_list_H,T_a)) ),[1],$fot(c_0)]]) ).
cnf(refute_0_53,plain,
( c_0 != c_0
| c_0 = c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(resolve,[$cnf( $equal(c_List_Olist_OCons(V_a_H,V_list_H,T_a),c_0) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( c_0 != c_0
| c_List_Olist_ONil = c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(resolve,[$cnf( $equal(c_0,c_List_Olist_OCons(V_a_H,V_list_H,T_a)) )],[refute_0_53,refute_0_50]) ).
cnf(refute_0_55,plain,
c_0 != c_0,
inference(resolve,[$cnf( $equal(c_List_Olist_ONil,c_List_Olist_OCons(V_a_H,V_list_H,T_a)) )],[refute_0_54,cls_List_Olist_Odistinct__1_0]) ).
cnf(refute_0_56,plain,
c_0 = c_0,
introduced(tautology,[refl,[$fot(c_0)]]) ).
cnf(refute_0_57,plain,
$false,
inference(resolve,[$cnf( $equal(c_0,c_0) )],[refute_0_56,refute_0_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV281-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.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 : 600
% 0.13/0.34 % DateTime : Wed Jun 15 05:35:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.36
%------------------------------------------------------------------------------