TSTP Solution File: ALG210+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% 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 : n002.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 10:32:21 EDT 2023

% Result   : Theorem 4.91s 2.35s
% Output   : CNFRefutation 4.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   51 (  33 unt;   6 typ;   0 def)
%            Number of atoms       :   60 (  42 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   28 (  13   ~;  10   |;   3   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (;  37   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ element > times > #nlpp > #skF_1 > #skF_2 > #skF_3 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(f_43,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( element(A)
          & element(B)
          & ( C = times(A,B) ) )
       => element(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).

tff(f_34,axiom,
    ! [B] :
      ( element(B)
    <=> ? [C] :
          ( ( times(B,C) = B )
          & ( times(B,B) = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(f_27,axiom,
    ! [A,B,C] : ( times(times(A,B),C) = times(B,times(C,A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

tff(c_10,plain,
    ~ element('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_14,plain,
    element('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_30,plain,
    ! [B_9] :
      ( ( times(B_9,B_9) = '#skF_1'(B_9) )
      | ~ element(B_9) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_35,plain,
    times('#skF_3','#skF_3') = '#skF_1'('#skF_3'),
    inference(resolution,[status(thm)],[c_14,c_30]) ).

tff(c_54,plain,
    ! [A_11,B_12,C_13] : ( times(times(A_11,B_12),C_13) = times(B_12,times(C_13,A_11)) ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_84,plain,
    ! [C_13] : ( times('#skF_1'('#skF_3'),C_13) = times('#skF_3',times(C_13,'#skF_3')) ),
    inference(superposition,[status(thm),theory(equality)],[c_35,c_54]) ).

tff(c_12,plain,
    times('#skF_2','#skF_3') = '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_8,plain,
    ! [B_4] :
      ( ( times(B_4,'#skF_1'(B_4)) = B_4 )
      | ~ element(B_4) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_205,plain,
    ! [B_17,C_18] :
      ( ( times('#skF_1'(B_17),times(C_18,B_17)) = times(B_17,C_18) )
      | ~ element(B_17) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_54]) ).

tff(c_266,plain,
    ( ( times('#skF_1'('#skF_3'),'#skF_4') = times('#skF_3','#skF_2') )
    | ~ element('#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_205]) ).

tff(c_288,plain,
    times('#skF_3',times('#skF_4','#skF_3')) = times('#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_84,c_266]) ).

tff(c_94,plain,
    ! [C_13] : ( times('#skF_3',times(C_13,'#skF_2')) = times('#skF_4',C_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_54]) ).

tff(c_16,plain,
    element('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_36,plain,
    times('#skF_2','#skF_2') = '#skF_1'('#skF_2'),
    inference(resolution,[status(thm)],[c_16,c_30]) ).

tff(c_127,plain,
    ! [C_15] : ( times('#skF_1'('#skF_2'),C_15) = times('#skF_2',times(C_15,'#skF_2')) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_54]) ).

tff(c_134,plain,
    times('#skF_3',times('#skF_2',times('#skF_2','#skF_2'))) = times('#skF_4','#skF_1'('#skF_2')),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_94]) ).

tff(c_158,plain,
    times('#skF_3',times('#skF_2','#skF_1'('#skF_2'))) = times('#skF_4','#skF_1'('#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_134]) ).

tff(c_442,plain,
    ( ( times('#skF_4','#skF_1'('#skF_2')) = times('#skF_3','#skF_2') )
    | ~ element('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_158]) ).

tff(c_449,plain,
    times('#skF_4','#skF_1'('#skF_2')) = times('#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_442]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( times(times(A_1,B_2),C_3) = times(B_2,times(C_3,A_1)) ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_99,plain,
    ! [C_14] : ( times('#skF_3',times(C_14,'#skF_2')) = times('#skF_4',C_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_54]) ).

tff(c_335,plain,
    ! [B_19,A_20] : ( times('#skF_3',times(B_19,times('#skF_2',A_20))) = times('#skF_4',times(A_20,B_19)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_99]) ).

tff(c_1080,plain,
    ! [B_29] : ( times('#skF_3',times(B_29,'#skF_1'('#skF_2'))) = times('#skF_4',times('#skF_2',B_29)) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_335]) ).

tff(c_1122,plain,
    times('#skF_3',times('#skF_3','#skF_2')) = times('#skF_4',times('#skF_2','#skF_4')),
    inference(superposition,[status(thm),theory(equality)],[c_449,c_1080]) ).

tff(c_1154,plain,
    times('#skF_4',times('#skF_2','#skF_4')) = times('#skF_4','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_1122]) ).

tff(c_112,plain,
    ! [B_2,A_1] : ( times('#skF_3',times(B_2,times('#skF_2',A_1))) = times('#skF_4',times(A_1,B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_99]) ).

tff(c_1170,plain,
    times('#skF_3',times('#skF_4','#skF_3')) = times('#skF_4',times('#skF_4','#skF_4')),
    inference(superposition,[status(thm),theory(equality)],[c_1154,c_112]) ).

tff(c_1181,plain,
    times('#skF_4',times('#skF_4','#skF_4')) = times('#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_288,c_1170]) ).

tff(c_4,plain,
    ! [B_4] :
      ( element(B_4)
      | ( times(B_4,times(B_4,B_4)) != B_4 ) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_1200,plain,
    ( element('#skF_4')
    | ( times('#skF_3','#skF_2') != '#skF_4' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1181,c_4]) ).

tff(c_1207,plain,
    times('#skF_3','#skF_2') != '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_10,c_1200]) ).

tff(c_81,plain,
    ! [C_13] : ( times('#skF_1'('#skF_2'),C_13) = times('#skF_2',times(C_13,'#skF_2')) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_54]) ).

tff(c_245,plain,
    ! [C_18] :
      ( ( times('#skF_2',times(times(C_18,'#skF_2'),'#skF_2')) = times('#skF_2',C_18) )
      | ~ element('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_205]) ).

tff(c_485,plain,
    ! [C_21] : ( times('#skF_2',times('#skF_2',times('#skF_2',C_21))) = times('#skF_2',C_21) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_2,c_245]) ).

tff(c_531,plain,
    times('#skF_2',times('#skF_2','#skF_4')) = times('#skF_2','#skF_3'),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_485]) ).

tff(c_547,plain,
    times('#skF_2',times('#skF_2','#skF_4')) = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_531]) ).

tff(c_87,plain,
    ! [B_4,C_13] :
      ( ( times('#skF_1'(B_4),times(C_13,B_4)) = times(B_4,C_13) )
      | ~ element(B_4) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_54]) ).

tff(c_75,plain,
    ! [B_2,C_3,A_1,C_13] : ( times(times(B_2,times(C_3,A_1)),C_13) = times(C_3,times(C_13,times(A_1,B_2))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_54]) ).

tff(c_1865,plain,
    ! [C_34] : ( times('#skF_2',times(C_34,times('#skF_4','#skF_2'))) = times('#skF_4',C_34) ),
    inference(superposition,[status(thm),theory(equality)],[c_547,c_75]) ).

tff(c_1923,plain,
    ( ( times('#skF_2',times('#skF_2','#skF_4')) = times('#skF_4','#skF_1'('#skF_2')) )
    | ~ element('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_87,c_1865]) ).

tff(c_1956,plain,
    times('#skF_3','#skF_2') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_547,c_449,c_1923]) ).

tff(c_1958,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1207,c_1956]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 20:40:16 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 4.91/2.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/2.36  
% 4.91/2.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.39  
% 4.91/2.39  Inference rules
% 4.91/2.39  ----------------------
% 4.91/2.39  #Ref     : 0
% 4.91/2.39  #Sup     : 487
% 4.91/2.39  #Fact    : 0
% 4.91/2.39  #Define  : 0
% 4.91/2.39  #Split   : 0
% 4.91/2.39  #Chain   : 0
% 4.91/2.39  #Close   : 0
% 4.91/2.39  
% 4.91/2.39  Ordering : KBO
% 4.91/2.39  
% 4.91/2.39  Simplification rules
% 4.91/2.39  ----------------------
% 4.91/2.39  #Subsume      : 12
% 4.91/2.39  #Demod        : 1316
% 4.91/2.39  #Tautology    : 169
% 4.91/2.39  #SimpNegUnit  : 2
% 4.91/2.39  #BackRed      : 5
% 4.91/2.39  
% 4.91/2.39  #Partial instantiations: 0
% 4.91/2.39  #Strategies tried      : 1
% 4.91/2.39  
% 4.91/2.39  Timing (in seconds)
% 4.91/2.39  ----------------------
% 4.91/2.39  Preprocessing        : 0.49
% 4.91/2.39  Parsing              : 0.25
% 4.91/2.39  CNF conversion       : 0.03
% 4.91/2.39  Main loop            : 0.82
% 4.91/2.39  Inferencing          : 0.25
% 4.91/2.39  Reduction            : 0.37
% 4.91/2.39  Demodulation         : 0.31
% 4.91/2.39  BG Simplification    : 0.03
% 4.91/2.39  Subsumption          : 0.12
% 4.91/2.39  Abstraction          : 0.04
% 4.91/2.39  MUC search           : 0.00
% 4.91/2.39  Cooper               : 0.00
% 4.91/2.39  Total                : 1.36
% 4.91/2.39  Index Insertion      : 0.00
% 4.91/2.39  Index Deletion       : 0.00
% 4.91/2.39  Index Matching       : 0.00
% 4.91/2.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------