TSTP Solution File: SWV284-2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV284-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 20:30:52 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   26 (  14 unt;   1 nHn;  14 RR)
%            Number of literals    :   38 (   0 equ;  17 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :   48 (  17 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(V_U,v_x(V_U),tc_nat) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg)
    | ~ c_lessequals(v_N,V_U,tc_nat) ) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( c_in(c_Message_Omsg_ONonce(v_x(V_U)),c_Event_Oused(v_list),tc_Message_Omsg)
    | c_in(c_Message_Omsg_ONonce(v_x(V_U)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ) ).

cnf(cls_Message_Omsg__Nonce__supply_0,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(V_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
    | ~ c_lessequals(v_sko__upX(V_msg),V_U,tc_nat) ) ).

cnf(cls_Nat_Oadd__leE_0,axiom,
    ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
    | c_lessequals(V_k,V_n,tc_nat) ) ).

cnf(cls_Nat_Oadd__leE_1,axiom,
    ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
    | c_lessequals(V_m,V_n,tc_nat) ) ).

cnf(refute_0_0,plain,
    ( ~ c_in(c_Message_Omsg_ONonce(v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg)
    | ~ c_lessequals(v_N,v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat)),tc_nat) ),
    inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat))))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat)),tc_nat)
    | c_lessequals(V_m,v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat)),tc_nat) ),
    inference(subst,[],[cls_Nat_Oadd__leE_1:[bind(V_n,$fot(v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat))))]]) ).

cnf(refute_0_2,plain,
    c_lessequals(c_plus(X_4,X_3,tc_nat),v_x(c_plus(X_4,X_3,tc_nat)),tc_nat),
    inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(c_plus(X_4,X_3,tc_nat)))]]) ).

cnf(refute_0_3,plain,
    ( ~ c_lessequals(c_plus(X_4,X_3,tc_nat),v_x(c_plus(X_4,X_3,tc_nat)),tc_nat)
    | c_lessequals(X_4,v_x(c_plus(X_4,X_3,tc_nat)),tc_nat) ),
    inference(subst,[],[cls_Nat_Oadd__leE_1:[bind(V_k,$fot(X_3)),bind(V_m,$fot(X_4)),bind(V_n,$fot(v_x(c_plus(X_4,X_3,tc_nat))))]]) ).

cnf(refute_0_4,plain,
    c_lessequals(X_4,v_x(c_plus(X_4,X_3,tc_nat)),tc_nat),
    inference(resolve,[$cnf( c_lessequals(c_plus(X_4,X_3,tc_nat),v_x(c_plus(X_4,X_3,tc_nat)),tc_nat) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    c_lessequals(c_plus(V_m,V_k,tc_nat),v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat)),tc_nat),
    inference(subst,[],[refute_0_4:[bind(X_3,$fot(X_6)),bind(X_4,$fot(c_plus(V_m,V_k,tc_nat)))]]) ).

cnf(refute_0_6,plain,
    c_lessequals(V_m,v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat)),tc_nat),
    inference(resolve,[$cnf( c_lessequals(c_plus(V_m,V_k,tc_nat),v_x(c_plus(c_plus(V_m,V_k,tc_nat),X_6,tc_nat)),tc_nat) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    c_lessequals(v_sko__upX(v_msg),v_x(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat)),tc_nat),
    inference(subst,[],[refute_0_6:[bind(V_m,$fot(v_sko__upX(v_msg)))]]) ).

cnf(refute_0_8,plain,
    ( ~ c_in(c_Message_Omsg_ONonce(v_x(V_U)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
    | ~ c_lessequals(v_sko__upX(v_msg),v_x(V_U),tc_nat) ),
    inference(subst,[],[cls_Message_Omsg__Nonce__supply_0:[bind(V_U,$fot(v_x(V_U))),bind(V_msg,$fot(v_msg))]]) ).

cnf(refute_0_9,plain,
    ( ~ c_lessequals(v_sko__upX(v_msg),v_x(V_U),tc_nat)
    | c_in(c_Message_Omsg_ONonce(v_x(V_U)),c_Event_Oused(v_list),tc_Message_Omsg) ),
    inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(v_x(V_U)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) )],[cls_conjecture_2,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ c_lessequals(v_sko__upX(v_msg),v_x(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat)),tc_nat)
    | c_in(c_Message_Omsg_ONonce(v_x(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) ),
    inference(subst,[],[refute_0_9:[bind(V_U,$fot(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat)))]]) ).

cnf(refute_0_11,plain,
    c_in(c_Message_Omsg_ONonce(v_x(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
    inference(resolve,[$cnf( c_lessequals(v_sko__upX(v_msg),v_x(c_plus(c_plus(v_sko__upX(v_msg),V_k,tc_nat),X_6,tc_nat)),tc_nat) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    c_in(c_Message_Omsg_ONonce(v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg),
    inference(subst,[],[refute_0_11:[bind(V_k,$fot(X_20)),bind(X_6,$fot(X_21))]]) ).

cnf(refute_0_13,plain,
    ~ c_lessequals(v_N,v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat)),tc_nat),
    inference(resolve,[$cnf( c_in(c_Message_Omsg_ONonce(v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),X_21,tc_nat))),c_Event_Oused(v_list),tc_Message_Omsg) )],[refute_0_12,refute_0_0]) ).

cnf(refute_0_14,plain,
    ~ c_lessequals(v_N,v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),v_N,tc_nat)),tc_nat),
    inference(subst,[],[refute_0_13:[bind(X_21,$fot(v_N))]]) ).

cnf(refute_0_15,plain,
    c_lessequals(c_plus(X_30,X_29,tc_nat),v_x(c_plus(X_30,X_29,tc_nat)),tc_nat),
    inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(c_plus(X_30,X_29,tc_nat)))]]) ).

cnf(refute_0_16,plain,
    ( ~ c_lessequals(c_plus(X_30,X_29,tc_nat),v_x(c_plus(X_30,X_29,tc_nat)),tc_nat)
    | c_lessequals(X_29,v_x(c_plus(X_30,X_29,tc_nat)),tc_nat) ),
    inference(subst,[],[cls_Nat_Oadd__leE_0:[bind(V_k,$fot(X_29)),bind(V_m,$fot(X_30)),bind(V_n,$fot(v_x(c_plus(X_30,X_29,tc_nat))))]]) ).

cnf(refute_0_17,plain,
    c_lessequals(X_29,v_x(c_plus(X_30,X_29,tc_nat)),tc_nat),
    inference(resolve,[$cnf( c_lessequals(c_plus(X_30,X_29,tc_nat),v_x(c_plus(X_30,X_29,tc_nat)),tc_nat) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    c_lessequals(v_N,v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),v_N,tc_nat)),tc_nat),
    inference(subst,[],[refute_0_17:[bind(X_29,$fot(v_N)),bind(X_30,$fot(c_plus(v_sko__upX(v_msg),X_20,tc_nat)))]]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(v_N,v_x(c_plus(c_plus(v_sko__upX(v_msg),X_20,tc_nat),v_N,tc_nat)),tc_nat) )],[refute_0_18,refute_0_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV284-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 15 10:20:06 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------