TSTP Solution File: SWV284-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV284-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% 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 : Tue Aug 22 11:03:31 EDT 2023

% Result   : Unsatisfiable 2.95s 1.77s
% Output   : CNFRefutation 2.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   35 (   7 unt;  15 typ;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   30 (  17   ~;  13   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   9   >;   8   *;   0   +;   0  <<)
%            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   :   35 (;  35   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_plus > c_insert > #nlpp > v_x > v_sko__upX > c_Message_Oparts > c_Message_Omsg_ONonce > c_Event_Oused > v_msg > v_list > v_N > tc_nat > tc_Message_Omsg > c_emptyset

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(v_sko__upX,type,
    v_sko__upX: $i > $i ).

tff(c_emptyset,type,
    c_emptyset: $i ).

tff(c_lessequals,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(c_in,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(tc_nat,type,
    tc_nat: $i ).

tff(v_msg,type,
    v_msg: $i ).

tff(c_Event_Oused,type,
    c_Event_Oused: $i > $i ).

tff(tc_Message_Omsg,type,
    tc_Message_Omsg: $i ).

tff(c_Message_Oparts,type,
    c_Message_Oparts: $i > $i ).

tff(c_plus,type,
    c_plus: ( $i * $i * $i ) > $i ).

tff(c_Message_Omsg_ONonce,type,
    c_Message_Omsg_ONonce: $i > $i ).

tff(v_x,type,
    v_x: $i > $i ).

tff(v_N,type,
    v_N: $i ).

tff(c_insert,type,
    c_insert: ( $i * $i * $i ) > $i ).

tff(v_list,type,
    v_list: $i ).

tff(f_27,axiom,
    ! [V_U] : c_lessequals(V_U,v_x(V_U),tc_nat),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [V_m,V_k,V_n] :
      ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
      | c_lessequals(V_k,V_n,tc_nat) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [V_m,V_k,V_n] :
      ( ~ c_lessequals(c_plus(V_m,V_k,tc_nat),V_n,tc_nat)
      | c_lessequals(V_m,V_n,tc_nat) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ! [V_U] :
      ( 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) ),
    file(unknown,unknown) ).

tff(f_43,axiom,
    ! [V_U,V_msg] :
      ( ~ 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) ),
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [V_U] :
      ( ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_list),tc_Message_Omsg)
      | ~ c_lessequals(v_N,V_U,tc_nat) ),
    file(unknown,unknown) ).

tff(c_2,plain,
    ! [V_U_1] : c_lessequals(V_U_1,v_x(V_U_1),tc_nat),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_15,plain,
    ! [V_k_14,V_n_15,V_m_16] :
      ( c_lessequals(V_k_14,V_n_15,tc_nat)
      | ~ c_lessequals(c_plus(V_m_16,V_k_14,tc_nat),V_n_15,tc_nat) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_21,plain,
    ! [V_k_17,V_m_18] : c_lessequals(V_k_17,v_x(c_plus(V_m_18,V_k_17,tc_nat)),tc_nat),
    inference(resolution,[status(thm)],[c_2,c_15]) ).

tff(c_10,plain,
    ! [V_k_7,V_n_8,V_m_6] :
      ( c_lessequals(V_k_7,V_n_8,tc_nat)
      | ~ c_lessequals(c_plus(V_m_6,V_k_7,tc_nat),V_n_8,tc_nat) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_26,plain,
    ! [V_k_7,V_m_18,V_m_6] : c_lessequals(V_k_7,v_x(c_plus(V_m_18,c_plus(V_m_6,V_k_7,tc_nat),tc_nat)),tc_nat),
    inference(resolution,[status(thm)],[c_21,c_10]) ).

tff(c_27,plain,
    ! [V_m_19,V_n_20,V_k_21] :
      ( c_lessequals(V_m_19,V_n_20,tc_nat)
      | ~ c_lessequals(c_plus(V_m_19,V_k_21,tc_nat),V_n_20,tc_nat) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_37,plain,
    ! [V_m_19,V_k_21] : c_lessequals(V_m_19,v_x(c_plus(V_m_19,V_k_21,tc_nat)),tc_nat),
    inference(resolution,[status(thm)],[c_2,c_27]) ).

tff(c_72,plain,
    ! [V_U_32] :
      ( c_in(c_Message_Omsg_ONonce(v_x(V_U_32)),c_Message_Oparts(c_insert(v_msg,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(v_x(V_U_32)),c_Event_Oused(v_list),tc_Message_Omsg) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_8,plain,
    ! [V_msg_5,V_U_4] :
      ( ~ c_lessequals(v_sko__upX(V_msg_5),V_U_4,tc_nat)
      | ~ c_in(c_Message_Omsg_ONonce(V_U_4),c_Message_Oparts(c_insert(V_msg_5,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_99,plain,
    ! [V_U_39] :
      ( ~ c_lessequals(v_sko__upX(v_msg),v_x(V_U_39),tc_nat)
      | c_in(c_Message_Omsg_ONonce(v_x(V_U_39)),c_Event_Oused(v_list),tc_Message_Omsg) ),
    inference(resolution,[status(thm)],[c_72,c_8]) ).

tff(c_4,plain,
    ! [V_U_2] :
      ( ~ c_lessequals(v_N,V_U_2,tc_nat)
      | ~ c_in(c_Message_Omsg_ONonce(V_U_2),c_Event_Oused(v_list),tc_Message_Omsg) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_104,plain,
    ! [V_U_40] :
      ( ~ c_lessequals(v_N,v_x(V_U_40),tc_nat)
      | ~ c_lessequals(v_sko__upX(v_msg),v_x(V_U_40),tc_nat) ),
    inference(resolution,[status(thm)],[c_99,c_4]) ).

tff(c_140,plain,
    ! [V_k_41] : ~ c_lessequals(v_N,v_x(c_plus(v_sko__upX(v_msg),V_k_41,tc_nat)),tc_nat),
    inference(resolution,[status(thm)],[c_37,c_104]) ).

tff(c_151,plain,
    $false,
    inference(resolution,[status(thm)],[c_26,c_140]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SWV284-2 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 23:16:45 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 2.95/1.77  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.95/1.78  
% 2.95/1.78  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.95/1.81  
% 2.95/1.81  Inference rules
% 2.95/1.81  ----------------------
% 2.95/1.81  #Ref     : 0
% 2.95/1.81  #Sup     : 26
% 2.95/1.81  #Fact    : 0
% 2.95/1.81  #Define  : 0
% 2.95/1.81  #Split   : 0
% 2.95/1.81  #Chain   : 0
% 2.95/1.81  #Close   : 0
% 2.95/1.81  
% 2.95/1.81  Ordering : KBO
% 2.95/1.81  
% 2.95/1.81  Simplification rules
% 2.95/1.81  ----------------------
% 2.95/1.81  #Subsume      : 0
% 2.95/1.81  #Demod        : 0
% 2.95/1.81  #Tautology    : 0
% 2.95/1.81  #SimpNegUnit  : 0
% 2.95/1.81  #BackRed      : 0
% 2.95/1.81  
% 2.95/1.81  #Partial instantiations: 0
% 2.95/1.81  #Strategies tried      : 1
% 2.95/1.81  
% 2.95/1.81  Timing (in seconds)
% 2.95/1.81  ----------------------
% 2.95/1.82  Preprocessing        : 0.41
% 2.95/1.82  Parsing              : 0.23
% 2.95/1.82  CNF conversion       : 0.02
% 2.95/1.82  Main loop            : 0.25
% 2.95/1.82  Inferencing          : 0.11
% 2.95/1.82  Reduction            : 0.06
% 2.95/1.82  Demodulation         : 0.04
% 2.95/1.82  BG Simplification    : 0.01
% 2.95/1.82  Subsumption          : 0.06
% 2.95/1.82  Abstraction          : 0.01
% 2.95/1.82  MUC search           : 0.00
% 2.95/1.82  Cooper               : 0.00
% 2.95/1.82  Total                : 0.71
% 2.95/1.82  Index Insertion      : 0.00
% 2.95/1.82  Index Deletion       : 0.00
% 2.95/1.82  Index Matching       : 0.00
% 2.95/1.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------