TSTP Solution File: ANA021-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ANA021-2 : 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 : n021.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 10:32:49 EDT 2023

% Result   : Unsatisfiable 2.74s 1.62s
% Output   : CNFRefutation 2.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   29 (   9 unt;  14 typ;   0 def)
%            Number of atoms       :   22 (   7 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   17 (  10   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :    8 (;   8   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > c_times > c_minus > c_HOL_Oabs > #nlpp > v_h > v_f > c_Suc > v_x > v_c > tc_nat > t_a > c_1 > c_0

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(c_0,type,
    c_0: $i ).

tff(c_1,type,
    c_1: $i ).

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

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

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

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

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

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

tff(f_38,axiom,
    v_x != c_0,
    file(unknown,unknown) ).

tff(f_34,axiom,
    ! [V_n] :
      ( c_less(c_0,V_n,tc_nat)
      | ( V_n = c_0 ) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [V_x] :
      ( ~ c_less(c_0,V_x,tc_nat)
      | ( V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    file(unknown,unknown) ).

tff(c_8,plain,
    v_x != c_0,
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_4,plain,
    ! [V_n_2] :
      ( ( c_0 = V_n_2 )
      | c_less(c_0,V_n_2,tc_nat) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_2,plain,
    ! [V_x_1] :
      ( ( c_Suc(c_minus(V_x_1,c_1,tc_nat)) = V_x_1 )
      | ~ c_less(c_0,V_x_1,tc_nat) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_21,plain,
    ! [V_U_6] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U_6)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U_6)),t_a),t_a),t_a),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_28,plain,
    ! [V_x_7] :
      ( c_lessequals(c_HOL_Oabs(v_f(V_x_7),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(V_x_7,c_1,tc_nat))),t_a),t_a),t_a)
      | ~ c_less(c_0,V_x_7,tc_nat) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_21]) ).

tff(c_36,plain,
    ! [V_x_9] :
      ( c_lessequals(c_HOL_Oabs(v_f(V_x_9),t_a),c_times(v_c,c_HOL_Oabs(v_h(V_x_9),t_a),t_a),t_a)
      | ~ c_less(c_0,V_x_9,tc_nat)
      | ~ c_less(c_0,V_x_9,tc_nat) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).

tff(c_10,plain,
    ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_40,plain,
    ~ c_less(c_0,v_x,tc_nat),
    inference(resolution,[status(thm)],[c_36,c_10]) ).

tff(c_43,plain,
    v_x = c_0,
    inference(resolution,[status(thm)],[c_4,c_40]) ).

tff(c_47,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ANA021-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % 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
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 15:27:21 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 2.74/1.62  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.74/1.63  
% 2.74/1.63  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.83/1.65  
% 2.83/1.65  Inference rules
% 2.83/1.65  ----------------------
% 2.83/1.65  #Ref     : 0
% 2.83/1.65  #Sup     : 8
% 2.83/1.65  #Fact    : 0
% 2.83/1.65  #Define  : 0
% 2.83/1.65  #Split   : 0
% 2.83/1.65  #Chain   : 0
% 2.83/1.65  #Close   : 0
% 2.83/1.65  
% 2.83/1.65  Ordering : KBO
% 2.83/1.65  
% 2.83/1.65  Simplification rules
% 2.83/1.65  ----------------------
% 2.83/1.65  #Subsume      : 0
% 2.83/1.65  #Demod        : 0
% 2.83/1.65  #Tautology    : 2
% 2.83/1.65  #SimpNegUnit  : 1
% 2.83/1.65  #BackRed      : 0
% 2.83/1.65  
% 2.83/1.65  #Partial instantiations: 0
% 2.83/1.65  #Strategies tried      : 1
% 2.83/1.65  
% 2.83/1.65  Timing (in seconds)
% 2.83/1.65  ----------------------
% 2.83/1.65  Preprocessing        : 0.43
% 2.83/1.65  Parsing              : 0.23
% 2.83/1.65  CNF conversion       : 0.02
% 2.83/1.66  Main loop            : 0.17
% 2.83/1.66  Inferencing          : 0.08
% 2.83/1.66  Reduction            : 0.04
% 2.83/1.66  Demodulation         : 0.03
% 2.83/1.66  BG Simplification    : 0.01
% 2.83/1.66  Subsumption          : 0.03
% 2.83/1.66  Abstraction          : 0.01
% 2.83/1.66  MUC search           : 0.00
% 2.83/1.66  Cooper               : 0.00
% 2.83/1.66  Total                : 0.65
% 2.83/1.66  Index Insertion      : 0.00
% 2.83/1.66  Index Deletion       : 0.00
% 2.83/1.66  Index Matching       : 0.00
% 2.83/1.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------