TSTP Solution File: NUN085+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 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 : n010.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 10:53:25 EDT 2023

% Result   : Theorem 4.36s 2.14s
% Output   : CNFRefutation 4.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   92 (  49 unt;  29 typ;   0 def)
%            Number of atoms       :   92 (  40 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   55 (  26   ~;  17   |;  12   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  23   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;   6 con; 0-2 aty)
%            Number of variables   :   76 (;  67   !;   9   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > r1 > #nlpp > #skF_11 > #skF_16 > #skF_6 > #skF_2 > #skF_18 > #skF_19 > #skF_25 > #skF_3 > #skF_15 > #skF_12 > #skF_10 > #skF_1 > #skF_8 > #skF_21 > #skF_13 > #skF_17 > #skF_22 > #skF_14 > #skF_24 > #skF_23 > #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_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_25',type,
    '#skF_25': $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('#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_22',type,
    '#skF_22': $i ).

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

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $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_205,negated_conjecture,
    ~ ! [Y1] :
        ( ! [Y2] :
            ( ! [Y3] :
                ( ~ r1(Y3)
                | ~ r3(Y3,Y2,Y1) )
            | ! [Y4] :
                ( ~ r1(Y4)
                | ~ r2(Y4,Y2) ) )
        | ! [Y5] :
            ( ( Y1 != Y5 )
            | ~ r1(Y5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplusoneidzero) ).

tff(f_114,axiom,
    ! [X1,X8] :
    ? [Y4] :
      ( ? [Y5] :
          ( ? [Y15] :
              ( r2(X8,Y15)
              & r3(X1,Y15,Y5) )
          & ( Y5 = Y4 ) )
      & ? [Y7] :
          ( r2(Y7,Y4)
          & r3(X1,X8,Y7) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).

tff(f_87,axiom,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( ( ~ r3(X13,X14,X15)
        & ( X15 != Y22 ) )
      | ( r3(X13,X14,X15)
        & ( X15 = Y22 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).

tff(f_63,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( ~ r1(X19)
        & ( X19 != Y24 ) )
      | ( r1(X19)
        & ( X19 = Y24 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).

tff(f_149,axiom,
    ! [X4] :
    ? [Y9] :
      ( ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) )
      & ( Y9 = X4 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).

tff(f_75,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & ( X12 != Y21 ) )
      | ( r2(X11,X12)
        & ( X12 = Y21 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).

tff(f_180,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ r1(Y20)
          | ( Y20 != Y10 ) )
      | ~ r2(X7,Y10) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).

tff(c_94,plain,
    r1('#skF_23'),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_38,plain,
    ! [X1_23,X8_24] : r3(X1_23,X8_24,'#skF_8'(X1_23,X8_24)),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_501,plain,
    ! [X13_144,X14_145,X15_146] :
      ( ~ r3(X13_144,X14_145,X15_146)
      | ( X15_146 = '#skF_3'(X13_144,X14_145) ) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_553,plain,
    ! [X1_151,X8_152] : ( '#skF_3'(X1_151,X8_152) = '#skF_8'(X1_151,X8_152) ),
    inference(resolution,[status(thm)],[c_38,c_501]) ).

tff(c_117,plain,
    ! [X19_97] :
      ( ~ r1(X19_97)
      | ( X19_97 = '#skF_1' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_146,plain,
    '#skF_1' = '#skF_23',
    inference(resolution,[status(thm)],[c_94,c_117]) ).

tff(c_90,plain,
    r1('#skF_24'),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_143,plain,
    '#skF_1' = '#skF_24',
    inference(resolution,[status(thm)],[c_90,c_117]) ).

tff(c_168,plain,
    '#skF_24' = '#skF_23',
    inference(demodulation,[status(thm),theory(equality)],[c_146,c_143]) ).

tff(c_86,plain,
    '#skF_25' = '#skF_21',
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_84,plain,
    r1('#skF_25'),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_95,plain,
    r1('#skF_21'),
    inference(demodulation,[status(thm),theory(equality)],[c_86,c_84]) ).

tff(c_142,plain,
    '#skF_1' = '#skF_21',
    inference(resolution,[status(thm)],[c_95,c_117]) ).

tff(c_154,plain,
    '#skF_21' = '#skF_24',
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_142]) ).

tff(c_92,plain,
    r3('#skF_23','#skF_22','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_173,plain,
    r3('#skF_23','#skF_22','#skF_24'),
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_92]) ).

tff(c_244,plain,
    r3('#skF_23','#skF_22','#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_173]) ).

tff(c_518,plain,
    '#skF_3'('#skF_23','#skF_22') = '#skF_23',
    inference(resolution,[status(thm)],[c_244,c_501]) ).

tff(c_559,plain,
    '#skF_8'('#skF_23','#skF_22') = '#skF_23',
    inference(superposition,[status(thm),theory(equality)],[c_553,c_518]) ).

tff(c_64,plain,
    ! [X4_63] : r1('#skF_14'(X4_63)),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_139,plain,
    ! [X4_63] : ( '#skF_14'(X4_63) = '#skF_1' ),
    inference(resolution,[status(thm)],[c_64,c_117]) ).

tff(c_198,plain,
    ! [X4_63] : ( '#skF_14'(X4_63) = '#skF_23' ),
    inference(demodulation,[status(thm),theory(equality)],[c_146,c_139]) ).

tff(c_60,plain,
    ! [X4_63] : ( '#skF_13'(X4_63) = X4_63 ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_62,plain,
    ! [X4_63] : r3(X4_63,'#skF_14'(X4_63),'#skF_13'(X4_63)),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_97,plain,
    ! [X4_63] : r3(X4_63,'#skF_14'(X4_63),X4_63),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_62]) ).

tff(c_260,plain,
    ! [X4_63] : r3(X4_63,'#skF_23',X4_63),
    inference(demodulation,[status(thm),theory(equality)],[c_198,c_97]) ).

tff(c_517,plain,
    ! [X4_63] : ( '#skF_3'(X4_63,'#skF_23') = X4_63 ),
    inference(resolution,[status(thm)],[c_260,c_501]) ).

tff(c_587,plain,
    ! [X4_153] : ( '#skF_8'(X4_153,'#skF_23') = X4_153 ),
    inference(superposition,[status(thm),theory(equality)],[c_517,c_553]) ).

tff(c_40,plain,
    ! [X1_23,X8_24] : r2('#skF_8'(X1_23,X8_24),'#skF_5'(X1_23,X8_24)),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_626,plain,
    ! [X4_156] : r2(X4_156,'#skF_5'(X4_156,'#skF_23')),
    inference(superposition,[status(thm),theory(equality)],[c_587,c_40]) ).

tff(c_14,plain,
    ! [X11_3,X12_8] :
      ( ~ r2(X11_3,X12_8)
      | ( X12_8 = '#skF_2'(X11_3) ) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_666,plain,
    ! [X4_161] : ( '#skF_2'(X4_161) = '#skF_5'(X4_161,'#skF_23') ),
    inference(resolution,[status(thm)],[c_626,c_14]) ).

tff(c_88,plain,
    r2('#skF_24','#skF_22'),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_182,plain,
    r2('#skF_23','#skF_22'),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_88]) ).

tff(c_308,plain,
    ! [X11_129,X12_130] :
      ( ~ r2(X11_129,X12_130)
      | ( X12_130 = '#skF_2'(X11_129) ) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_323,plain,
    '#skF_2'('#skF_23') = '#skF_22',
    inference(resolution,[status(thm)],[c_182,c_308]) ).

tff(c_672,plain,
    '#skF_5'('#skF_23','#skF_23') = '#skF_22',
    inference(superposition,[status(thm),theory(equality)],[c_666,c_323]) ).

tff(c_633,plain,
    ! [X4_156] : ( '#skF_2'(X4_156) = '#skF_5'(X4_156,'#skF_23') ),
    inference(resolution,[status(thm)],[c_626,c_14]) ).

tff(c_46,plain,
    ! [X8_24,X1_23] : r2(X8_24,'#skF_7'(X1_23,X8_24)),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_321,plain,
    ! [X1_23,X8_24] : ( '#skF_7'(X1_23,X8_24) = '#skF_2'(X8_24) ),
    inference(resolution,[status(thm)],[c_46,c_308]) ).

tff(c_661,plain,
    ! [X1_23,X8_24] : ( '#skF_7'(X1_23,X8_24) = '#skF_5'(X8_24,'#skF_23') ),
    inference(demodulation,[status(thm),theory(equality)],[c_633,c_321]) ).

tff(c_42,plain,
    ! [X1_23,X8_24] : ( '#skF_6'(X1_23,X8_24) = '#skF_5'(X1_23,X8_24) ),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_44,plain,
    ! [X1_23,X8_24] : r3(X1_23,'#skF_7'(X1_23,X8_24),'#skF_6'(X1_23,X8_24)),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_99,plain,
    ! [X1_23,X8_24] : r3(X1_23,'#skF_7'(X1_23,X8_24),'#skF_5'(X1_23,X8_24)),
    inference(demodulation,[status(thm),theory(equality)],[c_42,c_44]) ).

tff(c_879,plain,
    ! [X1_186,X8_187] : r3(X1_186,'#skF_5'(X8_187,'#skF_23'),'#skF_5'(X1_186,X8_187)),
    inference(demodulation,[status(thm),theory(equality)],[c_661,c_99]) ).

tff(c_885,plain,
    r3('#skF_23','#skF_5'('#skF_23','#skF_23'),'#skF_22'),
    inference(superposition,[status(thm),theory(equality)],[c_672,c_879]) ).

tff(c_889,plain,
    r3('#skF_23','#skF_22','#skF_22'),
    inference(demodulation,[status(thm),theory(equality)],[c_672,c_885]) ).

tff(c_514,plain,
    ! [X1_23,X8_24] : ( '#skF_3'(X1_23,X8_24) = '#skF_8'(X1_23,X8_24) ),
    inference(resolution,[status(thm)],[c_38,c_501]) ).

tff(c_23,plain,
    ! [X13_9,X14_10,X15_15] :
      ( ~ r3(X13_9,X14_10,X15_15)
      | ( X15_15 = '#skF_3'(X13_9,X14_10) ) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1059,plain,
    ! [X13_198,X14_199,X15_200] :
      ( ~ r3(X13_198,X14_199,X15_200)
      | ( X15_200 = '#skF_8'(X13_198,X14_199) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_514,c_23]) ).

tff(c_1077,plain,
    '#skF_8'('#skF_23','#skF_22') = '#skF_22',
    inference(resolution,[status(thm)],[c_889,c_1059]) ).

tff(c_1096,plain,
    '#skF_22' = '#skF_23',
    inference(demodulation,[status(thm),theory(equality)],[c_559,c_1077]) ).

tff(c_245,plain,
    ! [X7_106,Y20_107] :
      ( ~ r2(X7_106,Y20_107)
      | ~ r1(Y20_107) ),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

tff(c_256,plain,
    ~ r1('#skF_22'),
    inference(resolution,[status(thm)],[c_182,c_245]) ).

tff(c_1118,plain,
    ~ r1('#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_1096,c_256]) ).

tff(c_1128,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_1118]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN085+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 18:28:13 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 4.36/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/2.14  
% 4.36/2.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.51/2.18  
% 4.51/2.18  Inference rules
% 4.51/2.18  ----------------------
% 4.51/2.18  #Ref     : 0
% 4.51/2.18  #Sup     : 249
% 4.51/2.18  #Fact    : 0
% 4.51/2.18  #Define  : 0
% 4.51/2.18  #Split   : 1
% 4.51/2.18  #Chain   : 0
% 4.51/2.18  #Close   : 0
% 4.51/2.18  
% 4.51/2.18  Ordering : KBO
% 4.51/2.18  
% 4.51/2.18  Simplification rules
% 4.51/2.18  ----------------------
% 4.51/2.18  #Subsume      : 38
% 4.51/2.18  #Demod        : 142
% 4.51/2.18  #Tautology    : 157
% 4.51/2.18  #SimpNegUnit  : 0
% 4.51/2.18  #BackRed      : 46
% 4.51/2.18  
% 4.51/2.18  #Partial instantiations: 0
% 4.51/2.18  #Strategies tried      : 1
% 4.51/2.18  
% 4.51/2.18  Timing (in seconds)
% 4.51/2.18  ----------------------
% 4.51/2.18  Preprocessing        : 0.55
% 4.51/2.18  Parsing              : 0.27
% 4.51/2.18  CNF conversion       : 0.05
% 4.51/2.18  Main loop            : 0.51
% 4.51/2.18  Inferencing          : 0.18
% 4.51/2.18  Reduction            : 0.16
% 4.51/2.18  Demodulation         : 0.12
% 4.51/2.18  BG Simplification    : 0.03
% 4.51/2.18  Subsumption          : 0.09
% 4.51/2.18  Abstraction          : 0.02
% 4.51/2.18  MUC search           : 0.00
% 4.51/2.18  Cooper               : 0.00
% 4.51/2.18  Total                : 1.13
% 4.51/2.18  Index Insertion      : 0.00
% 4.51/2.18  Index Deletion       : 0.00
% 4.51/2.18  Index Matching       : 0.00
% 4.51/2.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------