TSTP Solution File: NUN062+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n005.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 10:53:20 EDT 2023

% Result   : Theorem 4.42s 2.21s
% Output   : CNFRefutation 4.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   57 (  10 unt;  27 typ;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   71 (  34   ~;  25   |;  12   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  25   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (;  50   !;   9   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > id > r1 > #nlpp > #skF_11 > #skF_22 > #skF_16 > #skF_6 > #skF_2 > #skF_18 > #skF_19 > #skF_3 > #skF_15 > #skF_12 > #skF_10 > #skF_1 > #skF_8 > #skF_21 > #skF_13 > #skF_17 > #skF_14 > #skF_7 > #skF_9 > #skF_5 > #skF_4 > #skF_20

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff('#skF_22',type,
    '#skF_22': ( $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': $i > $i ).

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_19',type,
    '#skF_19': $i > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff(r2,type,
    r2: ( $i * $i ) > $o ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff(r3,type,
    r3: ( $i * $i * $i ) > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

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

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': $i ).

tff(r4,type,
    r4: ( $i * $i * $i ) > $o ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff('#skF_14',type,
    '#skF_14': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff(r1,type,
    r1: $i > $o ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

tff(f_102,axiom,
    ! [X20] : id(X20,X20),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).

tff(f_197,axiom,
    ! [X1,X8] :
    ? [Y4] :
      ( ? [Y5] :
          ( id(Y5,Y4)
          & ? [Y15] :
              ( r2(X8,Y15)
              & r3(X1,Y15,Y5) ) )
      & ? [Y7] :
          ( r2(Y7,Y4)
          & r3(X1,X8,Y7) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).

tff(f_279,negated_conjecture,
    ~ ! [X1] :
      ? [Y2,Y1] :
        ( ! [Y4] :
            ( ~ id(Y1,Y4)
            | ~ r1(Y4) )
        & ? [Y3] :
            ( id(Y3,Y2)
            & r3(X1,Y1,Y3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).

tff(f_128,axiom,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ( ~ r1(X26)
        & ~ r1(X27) )
      | ( r1(X26)
        & r1(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).

tff(f_64,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( id(X19,Y24)
        & r1(X19) )
      | ( ~ r1(X19)
        & ~ id(X19,Y24) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).

tff(f_107,axiom,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).

tff(f_76,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( id(X12,Y21)
        & r2(X11,X12) )
      | ( ~ r2(X11,X12)
        & ~ id(X12,Y21) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).

tff(f_263,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ id(Y20,Y10)
          | ~ r1(Y20) )
      | ~ r2(X7,Y10) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).

tff(c_34,plain,
    ! [X20_23] : id(X20_23,X20_23),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_192,plain,
    ! [X1_144,X8_145] : r3(X1_144,X8_145,'#skF_8'(X1_144,X8_145)),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_118,plain,
    ! [Y2_114,Y1_115,Y3_118] :
      ( r1('#skF_22'(Y2_114,Y1_115))
      | ~ r3('#skF_21',Y1_115,Y3_118)
      | ~ id(Y3_118,Y2_114) ),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_393,plain,
    ! [Y2_173,X8_174] :
      ( r1('#skF_22'(Y2_173,X8_174))
      | ~ id('#skF_8'('#skF_21',X8_174),Y2_173) ),
    inference(resolution,[status(thm)],[c_192,c_118]) ).

tff(c_418,plain,
    ! [X8_174] : r1('#skF_22'('#skF_8'('#skF_21',X8_174),X8_174)),
    inference(resolution,[status(thm)],[c_34,c_393]) ).

tff(c_120,plain,
    ! [Y1_115,Y2_114,Y3_118] :
      ( id(Y1_115,'#skF_22'(Y2_114,Y1_115))
      | ~ r3('#skF_21',Y1_115,Y3_118)
      | ~ id(Y3_118,Y2_114) ),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_464,plain,
    ! [X8_185,Y2_186] :
      ( id(X8_185,'#skF_22'(Y2_186,X8_185))
      | ~ id('#skF_8'('#skF_21',X8_185),Y2_186) ),
    inference(resolution,[status(thm)],[c_192,c_120]) ).

tff(c_485,plain,
    ! [X8_187] : id(X8_187,'#skF_22'('#skF_8'('#skF_21',X8_187),X8_187)),
    inference(resolution,[status(thm)],[c_34,c_464]) ).

tff(c_44,plain,
    ! [X27_30,X26_29] :
      ( ~ r1(X27_30)
      | r1(X26_29)
      | ~ id(X26_29,X27_30) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_495,plain,
    ! [X8_187] :
      ( ~ r1('#skF_22'('#skF_8'('#skF_21',X8_187),X8_187))
      | r1(X8_187) ),
    inference(resolution,[status(thm)],[c_485,c_44]) ).

tff(c_505,plain,
    ! [X8_187] : r1(X8_187),
    inference(demodulation,[status(thm),theory(equality)],[c_418,c_495]) ).

tff(c_8,plain,
    ! [X19_2] :
      ( id(X19_2,'#skF_1')
      | ~ r1(X19_2) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_532,plain,
    ! [X19_2] : id(X19_2,'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_8]) ).

tff(c_146,plain,
    ! [X22_134,X21_135] :
      ( id(X22_134,X21_135)
      | ~ id(X21_135,X22_134) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_155,plain,
    ! [X19_2] :
      ( id('#skF_1',X19_2)
      | ~ r1(X19_2) ),
    inference(resolution,[status(thm)],[c_8,c_146]) ).

tff(c_257,plain,
    ! [X11_155,X12_156] :
      ( r2(X11_155,X12_156)
      | ~ id(X12_156,'#skF_2'(X11_155)) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_274,plain,
    ! [X11_155] :
      ( r2(X11_155,'#skF_1')
      | ~ r1('#skF_2'(X11_155)) ),
    inference(resolution,[status(thm)],[c_155,c_257]) ).

tff(c_520,plain,
    ! [X11_155] : r2(X11_155,'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_274]) ).

tff(c_116,plain,
    ! [X7_104,Y10_105,Y20_107] :
      ( ~ r2(X7_104,Y10_105)
      | ~ r1(Y20_107)
      | ~ id(Y20_107,Y10_105) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_611,plain,
    ! [X7_202,Y10_203,Y20_204] :
      ( ~ r2(X7_202,Y10_203)
      | ~ id(Y20_204,Y10_203) ),
    inference(demodulation,[status(thm),theory(equality)],[c_505,c_116]) ).

tff(c_615,plain,
    ! [Y20_204] : ~ id(Y20_204,'#skF_1'),
    inference(resolution,[status(thm)],[c_520,c_611]) ).

tff(c_630,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_532,c_615]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.37  % Computer : n005.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 18:35:57 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 4.42/2.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/2.21  
% 4.42/2.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.70/2.24  
% 4.70/2.24  Inference rules
% 4.70/2.24  ----------------------
% 4.70/2.24  #Ref     : 0
% 4.70/2.24  #Sup     : 100
% 4.70/2.24  #Fact    : 0
% 4.70/2.24  #Define  : 0
% 4.70/2.24  #Split   : 1
% 4.70/2.24  #Chain   : 0
% 4.70/2.24  #Close   : 0
% 4.70/2.24  
% 4.70/2.24  Ordering : KBO
% 4.70/2.24  
% 4.70/2.24  Simplification rules
% 4.70/2.24  ----------------------
% 4.70/2.24  #Subsume      : 5
% 4.70/2.24  #Demod        : 55
% 4.70/2.24  #Tautology    : 63
% 4.70/2.24  #SimpNegUnit  : 0
% 4.70/2.24  #BackRed      : 3
% 4.70/2.24  
% 4.70/2.24  #Partial instantiations: 0
% 4.70/2.24  #Strategies tried      : 1
% 4.70/2.24  
% 4.70/2.24  Timing (in seconds)
% 4.70/2.24  ----------------------
% 4.70/2.25  Preprocessing        : 0.59
% 4.70/2.25  Parsing              : 0.30
% 4.70/2.25  CNF conversion       : 0.06
% 4.70/2.25  Main loop            : 0.43
% 4.70/2.25  Inferencing          : 0.17
% 4.70/2.25  Reduction            : 0.12
% 4.70/2.25  Demodulation         : 0.09
% 4.70/2.25  BG Simplification    : 0.04
% 4.70/2.25  Subsumption          : 0.10
% 4.70/2.25  Abstraction          : 0.01
% 4.70/2.25  MUC search           : 0.00
% 4.70/2.25  Cooper               : 0.00
% 4.70/2.25  Total                : 1.08
% 4.70/2.25  Index Insertion      : 0.00
% 4.70/2.25  Index Deletion       : 0.00
% 4.70/2.25  Index Matching       : 0.00
% 4.70/2.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------