TSTP Solution File: KRS109+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KRS109+1 : 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 : n026.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 10:45:11 EDT 2023

% Result   : Unsatisfiable 3.78s 1.94s
% Output   : CNFRefutation 4.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   69 (   9 unt;  23 typ;   0 def)
%            Number of atoms       :   99 (   6 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   95 (  42   ~;  37   |;   5   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  22   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-1 aty)
%            Number of variables   :   55 (;  51   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ rs > rinvS > rinvF1 > rinvF > rf1 > rf > ra_Px1 > xsd_string > xsd_integer > cpxcomp > cp > cowlThing > cowlNothing > ca_Vx3 > ca_Ax2 > cUnsatisfiable > #nlpp > i2003_11_14_17_21_08508 > #skF_5 > #skF_2 > #skF_4 > #skF_1 > #skF_3 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(ca_Ax2,type,
    ca_Ax2: $i > $o ).

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

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

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

tff(i2003_11_14_17_21_08508,type,
    i2003_11_14_17_21_08508: $i ).

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

tff(ra_Px1,type,
    ra_Px1: ( $i * $i ) > $o ).

tff(ca_Vx3,type,
    ca_Vx3: $i > $o ).

tff(rf1,type,
    rf1: ( $i * $i ) > $o ).

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

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

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

tff(rinvF1,type,
    rinvF1: ( $i * $i ) > $o ).

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

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

tff(f_259,axiom,
    cUnsatisfiable(i2003_11_14_17_21_08508),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).

tff(f_187,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( cpxcomp(X)
        & ? [Y] :
            ( rf(X,Y)
            & ca_Ax2(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(f_240,axiom,
    ! [X,Y] :
      ( rinvF(X,Y)
    <=> rf(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

tff(f_213,axiom,
    ! [X] :
      ( ca_Ax2(X)
    <=> ( ! [Y] :
            ( rinvS(X,Y)
           => cp(Y) )
        & ! [Y] :
            ( rinvF(X,Y)
           => ca_Vx3(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

tff(f_221,axiom,
    ! [X] :
      ( ca_Vx3(X)
    <=> ? [Y] :
          ( rs(X,Y)
          & cp(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

tff(f_263,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rf(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).

tff(f_228,axiom,
    ! [X,Y,Z] :
      ( ( rf(X,Y)
        & rf(X,Z) )
     => ( Y = Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

tff(f_250,axiom,
    ! [X,Y] :
      ( rinvS(X,Y)
    <=> rs(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

tff(f_200,axiom,
    ! [X] :
      ( cpxcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

tff(f_194,axiom,
    ! [X] :
      ( cp(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

tff(c_108,plain,
    cUnsatisfiable(i2003_11_14_17_21_08508),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_58,plain,
    ! [X_63] :
      ( ca_Ax2('#skF_1'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_60,plain,
    ! [X_63] :
      ( rf(X_63,'#skF_1'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_96,plain,
    ! [X_92,Y_93] :
      ( rinvF(X_92,Y_93)
      | ~ rf(Y_93,X_92) ),
    inference(cnfTransformation,[status(thm)],[f_240]) ).

tff(c_220,plain,
    ! [Y_149,X_150] :
      ( ca_Vx3(Y_149)
      | ~ rinvF(X_150,Y_149)
      | ~ ca_Ax2(X_150) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_234,plain,
    ! [Y_153,X_154] :
      ( ca_Vx3(Y_153)
      | ~ ca_Ax2(X_154)
      | ~ rf(Y_153,X_154) ),
    inference(resolution,[status(thm)],[c_96,c_220]) ).

tff(c_255,plain,
    ! [X_160] :
      ( ca_Vx3(X_160)
      | ~ ca_Ax2('#skF_1'(X_160))
      | ~ cUnsatisfiable(X_160) ),
    inference(resolution,[status(thm)],[c_60,c_234]) ).

tff(c_259,plain,
    ! [X_63] :
      ( ca_Vx3(X_63)
      | ~ cUnsatisfiable(X_63) ),
    inference(resolution,[status(thm)],[c_58,c_255]) ).

tff(c_176,plain,
    ! [X_137] :
      ( rs(X_137,'#skF_6'(X_137))
      | ~ ca_Vx3(X_137) ),
    inference(cnfTransformation,[status(thm)],[f_221]) ).

tff(c_110,plain,
    ! [X_101,Y_102] :
      ( rf(X_101,Y_102)
      | ~ rs(X_101,Y_102) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_187,plain,
    ! [X_137] :
      ( rf(X_137,'#skF_6'(X_137))
      | ~ ca_Vx3(X_137) ),
    inference(resolution,[status(thm)],[c_176,c_110]) ).

tff(c_243,plain,
    ! [Z_155,Y_156,X_157] :
      ( ( Z_155 = Y_156 )
      | ~ rf(X_157,Z_155)
      | ~ rf(X_157,Y_156) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_300,plain,
    ! [Y_177,X_178] :
      ( ( Y_177 = '#skF_1'(X_178) )
      | ~ rf(X_178,Y_177)
      | ~ cUnsatisfiable(X_178) ),
    inference(resolution,[status(thm)],[c_60,c_243]) ).

tff(c_314,plain,
    ! [X_182] :
      ( ( '#skF_1'(X_182) = '#skF_6'(X_182) )
      | ~ cUnsatisfiable(X_182)
      | ~ ca_Vx3(X_182) ),
    inference(resolution,[status(thm)],[c_187,c_300]) ).

tff(c_328,plain,
    ! [X_184] :
      ( ( '#skF_1'(X_184) = '#skF_6'(X_184) )
      | ~ cUnsatisfiable(X_184) ),
    inference(resolution,[status(thm)],[c_259,c_314]) ).

tff(c_332,plain,
    '#skF_1'(i2003_11_14_17_21_08508) = '#skF_6'(i2003_11_14_17_21_08508),
    inference(resolution,[status(thm)],[c_108,c_328]) ).

tff(c_339,plain,
    ( ca_Ax2('#skF_6'(i2003_11_14_17_21_08508))
    | ~ cUnsatisfiable(i2003_11_14_17_21_08508) ),
    inference(superposition,[status(thm),theory(equality)],[c_332,c_58]) ).

tff(c_345,plain,
    ca_Ax2('#skF_6'(i2003_11_14_17_21_08508)),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_339]) ).

tff(c_336,plain,
    ( rf(i2003_11_14_17_21_08508,'#skF_6'(i2003_11_14_17_21_08508))
    | ~ cUnsatisfiable(i2003_11_14_17_21_08508) ),
    inference(superposition,[status(thm),theory(equality)],[c_332,c_60]) ).

tff(c_343,plain,
    rf(i2003_11_14_17_21_08508,'#skF_6'(i2003_11_14_17_21_08508)),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_336]) ).

tff(c_224,plain,
    ! [Y_93,X_92] :
      ( ca_Vx3(Y_93)
      | ~ ca_Ax2(X_92)
      | ~ rf(Y_93,X_92) ),
    inference(resolution,[status(thm)],[c_96,c_220]) ).

tff(c_361,plain,
    ( ca_Vx3(i2003_11_14_17_21_08508)
    | ~ ca_Ax2('#skF_6'(i2003_11_14_17_21_08508)) ),
    inference(resolution,[status(thm)],[c_343,c_224]) ).

tff(c_371,plain,
    ca_Vx3(i2003_11_14_17_21_08508),
    inference(demodulation,[status(thm),theory(equality)],[c_345,c_361]) ).

tff(c_104,plain,
    ! [X_96,Y_97] :
      ( rinvS(X_96,Y_97)
      | ~ rs(Y_97,X_96) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_207,plain,
    ! [X_148] :
      ( rinvS('#skF_6'(X_148),X_148)
      | ~ ca_Vx3(X_148) ),
    inference(resolution,[status(thm)],[c_176,c_104]) ).

tff(c_74,plain,
    ! [Y_80,X_75] :
      ( cp(Y_80)
      | ~ rinvS(X_75,Y_80)
      | ~ ca_Ax2(X_75) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_217,plain,
    ! [X_148] :
      ( cp(X_148)
      | ~ ca_Ax2('#skF_6'(X_148))
      | ~ ca_Vx3(X_148) ),
    inference(resolution,[status(thm)],[c_207,c_74]) ).

tff(c_350,plain,
    ( cp(i2003_11_14_17_21_08508)
    | ~ ca_Vx3(i2003_11_14_17_21_08508) ),
    inference(resolution,[status(thm)],[c_345,c_217]) ).

tff(c_393,plain,
    cp(i2003_11_14_17_21_08508),
    inference(demodulation,[status(thm),theory(equality)],[c_371,c_350]) ).

tff(c_62,plain,
    ! [X_63] :
      ( cpxcomp(X_63)
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_126,plain,
    ! [X_116] :
      ( ra_Px1(X_116,'#skF_3'(X_116))
      | ~ cpxcomp(X_116) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_64,plain,
    ! [X_67,Y_70] :
      ( ~ ra_Px1(X_67,Y_70)
      | ~ cp(X_67) ),
    inference(cnfTransformation,[status(thm)],[f_194]) ).

tff(c_135,plain,
    ! [X_117] :
      ( ~ cp(X_117)
      | ~ cpxcomp(X_117) ),
    inference(resolution,[status(thm)],[c_126,c_64]) ).

tff(c_139,plain,
    ! [X_63] :
      ( ~ cp(X_63)
      | ~ cUnsatisfiable(X_63) ),
    inference(resolution,[status(thm)],[c_62,c_135]) ).

tff(c_396,plain,
    ~ cUnsatisfiable(i2003_11_14_17_21_08508),
    inference(resolution,[status(thm)],[c_393,c_139]) ).

tff(c_400,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_396]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KRS109+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10  % 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
% 0.12/0.30  % Computer : n026.cluster.edu
% 0.12/0.30  % Model    : x86_64 x86_64
% 0.12/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30  % Memory   : 8042.1875MB
% 0.12/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30  % CPULimit : 300
% 0.12/0.30  % WCLimit  : 300
% 0.12/0.30  % DateTime : Thu Aug  3 20:24:17 EDT 2023
% 0.12/0.30  % CPUTime  : 
% 3.78/1.94  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.78/1.94  
% 3.78/1.94  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.05/1.97  
% 4.05/1.97  Inference rules
% 4.05/1.97  ----------------------
% 4.05/1.97  #Ref     : 0
% 4.05/1.97  #Sup     : 59
% 4.05/1.97  #Fact    : 0
% 4.05/1.97  #Define  : 0
% 4.05/1.97  #Split   : 0
% 4.05/1.97  #Chain   : 0
% 4.05/1.97  #Close   : 0
% 4.05/1.97  
% 4.05/1.97  Ordering : KBO
% 4.05/1.97  
% 4.05/1.97  Simplification rules
% 4.05/1.97  ----------------------
% 4.05/1.97  #Subsume      : 4
% 4.05/1.97  #Demod        : 9
% 4.05/1.97  #Tautology    : 42
% 4.05/1.97  #SimpNegUnit  : 0
% 4.05/1.97  #BackRed      : 0
% 4.05/1.97  
% 4.05/1.97  #Partial instantiations: 0
% 4.05/1.97  #Strategies tried      : 1
% 4.05/1.97  
% 4.05/1.97  Timing (in seconds)
% 4.05/1.97  ----------------------
% 4.05/1.98  Preprocessing        : 0.55
% 4.05/1.98  Parsing              : 0.29
% 4.05/1.98  CNF conversion       : 0.04
% 4.05/1.98  Main loop            : 0.33
% 4.05/1.98  Inferencing          : 0.14
% 4.05/1.98  Reduction            : 0.07
% 4.05/1.98  Demodulation         : 0.05
% 4.05/1.98  BG Simplification    : 0.03
% 4.05/1.98  Subsumption          : 0.06
% 4.05/1.98  Abstraction          : 0.01
% 4.05/1.98  MUC search           : 0.00
% 4.05/1.98  Cooper               : 0.00
% 4.05/1.98  Total                : 0.93
% 4.05/1.98  Index Insertion      : 0.00
% 4.05/1.98  Index Deletion       : 0.00
% 4.05/1.98  Index Matching       : 0.00
% 4.05/1.98  BG Taut test         : 0.00
%------------------------------------------------------------------------------