TSTP Solution File: KRS112+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KRS112+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 : n020.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 10:45:12 EDT 2023

% Result   : Unsatisfiable 4.15s 1.98s
% Output   : CNFRefutation 4.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   70 (   7 unt;  23 typ;   0 def)
%            Number of atoms       :  104 (  12 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  103 (  46   ~;  39   |;   7   &)
%                                         (   6 <=>;   5  =>;   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   :   63 (;  58   !;   5   ?;   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_19256 > #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(i2003_11_14_17_21_19256,type,
    i2003_11_14_17_21_19256: $i ).

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(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_19256),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).

tff(f_190,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rf1(X,Y)
            & ca_Ax2(Y) )
        & ? [Y] :
            ( rf(X,Y)
            & cp(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(f_245,axiom,
    ! [X,Y] :
      ( rinvF1(X,Y)
    <=> rf1(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

tff(f_213,axiom,
    ! [X] :
      ( ca_Ax2(X)
    <=> ( cpxcomp(X)
        & ! [Y] :
            ( rinvF1(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)
          & cowlThing(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_203,axiom,
    ! [X] :
      ( cpxcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

tff(f_197,axiom,
    ! [X] :
      ( cp(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

tff(f_267,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rf1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).

tff(f_235,axiom,
    ! [X,Y,Z] :
      ( ( rf1(X,Y)
        & rf1(X,Z) )
     => ( Y = Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

tff(c_106,plain,
    cUnsatisfiable(i2003_11_14_17_21_19256),
    inference(cnfTransformation,[status(thm)],[f_259]) ).

tff(c_62,plain,
    ! [X_63] :
      ( ca_Ax2('#skF_1'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_64,plain,
    ! [X_63] :
      ( rf1(X_63,'#skF_1'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_98,plain,
    ! [X_94,Y_95] :
      ( rinvF1(X_94,Y_95)
      | ~ rf1(Y_95,X_94) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_232,plain,
    ! [Y_153,X_154] :
      ( ca_Vx3(Y_153)
      | ~ rinvF1(X_154,Y_153)
      | ~ ca_Ax2(X_154) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_237,plain,
    ! [Y_155,X_156] :
      ( ca_Vx3(Y_155)
      | ~ ca_Ax2(X_156)
      | ~ rf1(Y_155,X_156) ),
    inference(resolution,[status(thm)],[c_98,c_232]) ).

tff(c_246,plain,
    ! [X_157] :
      ( ca_Vx3(X_157)
      | ~ ca_Ax2('#skF_1'(X_157))
      | ~ cUnsatisfiable(X_157) ),
    inference(resolution,[status(thm)],[c_64,c_237]) ).

tff(c_250,plain,
    ! [X_63] :
      ( ca_Vx3(X_63)
      | ~ cUnsatisfiable(X_63) ),
    inference(resolution,[status(thm)],[c_62,c_246]) ).

tff(c_86,plain,
    ! [X_82] :
      ( rs(X_82,'#skF_6'(X_82))
      | ~ ca_Vx3(X_82) ),
    inference(cnfTransformation,[status(thm)],[f_221]) ).

tff(c_135,plain,
    ! [X_122,Y_123] :
      ( rf(X_122,Y_123)
      | ~ rs(X_122,Y_123) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_139,plain,
    ! [X_82] :
      ( rf(X_82,'#skF_6'(X_82))
      | ~ ca_Vx3(X_82) ),
    inference(resolution,[status(thm)],[c_86,c_135]) ).

tff(c_60,plain,
    ! [X_63] :
      ( rf(X_63,'#skF_2'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_256,plain,
    ! [Z_159,Y_160,X_161] :
      ( ( Z_159 = Y_160 )
      | ~ rf(X_161,Z_159)
      | ~ rf(X_161,Y_160) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_302,plain,
    ! [Y_174,X_175] :
      ( ( Y_174 = '#skF_2'(X_175) )
      | ~ rf(X_175,Y_174)
      | ~ cUnsatisfiable(X_175) ),
    inference(resolution,[status(thm)],[c_60,c_256]) ).

tff(c_343,plain,
    ! [X_183] :
      ( ( '#skF_2'(X_183) = '#skF_6'(X_183) )
      | ~ cUnsatisfiable(X_183)
      | ~ ca_Vx3(X_183) ),
    inference(resolution,[status(thm)],[c_139,c_302]) ).

tff(c_348,plain,
    ! [X_184] :
      ( ( '#skF_2'(X_184) = '#skF_6'(X_184) )
      | ~ cUnsatisfiable(X_184) ),
    inference(resolution,[status(thm)],[c_250,c_343]) ).

tff(c_352,plain,
    '#skF_2'(i2003_11_14_17_21_19256) = '#skF_6'(i2003_11_14_17_21_19256),
    inference(resolution,[status(thm)],[c_106,c_348]) ).

tff(c_58,plain,
    ! [X_63] :
      ( cp('#skF_2'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_76,plain,
    ! [X_78] :
      ( cpxcomp(X_78)
      | ~ ca_Ax2(X_78) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_151,plain,
    ! [X_130] :
      ( ra_Px1(X_130,'#skF_4'(X_130))
      | ~ cpxcomp(X_130) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_66,plain,
    ! [X_70,Y_73] :
      ( ~ ra_Px1(X_70,Y_73)
      | ~ cp(X_70) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_161,plain,
    ! [X_132] :
      ( ~ cp(X_132)
      | ~ cpxcomp(X_132) ),
    inference(resolution,[status(thm)],[c_151,c_66]) ).

tff(c_166,plain,
    ! [X_133] :
      ( ~ cp(X_133)
      | ~ ca_Ax2(X_133) ),
    inference(resolution,[status(thm)],[c_76,c_161]) ).

tff(c_170,plain,
    ! [X_63] :
      ( ~ ca_Ax2('#skF_2'(X_63))
      | ~ cUnsatisfiable(X_63) ),
    inference(resolution,[status(thm)],[c_58,c_166]) ).

tff(c_356,plain,
    ( ~ ca_Ax2('#skF_6'(i2003_11_14_17_21_19256))
    | ~ cUnsatisfiable(i2003_11_14_17_21_19256) ),
    inference(superposition,[status(thm),theory(equality)],[c_352,c_170]) ).

tff(c_366,plain,
    ~ ca_Ax2('#skF_6'(i2003_11_14_17_21_19256)),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_356]) ).

tff(c_140,plain,
    ! [X_124,Y_125] :
      ( rf1(X_124,Y_125)
      | ~ rs(X_124,Y_125) ),
    inference(cnfTransformation,[status(thm)],[f_267]) ).

tff(c_144,plain,
    ! [X_82] :
      ( rf1(X_82,'#skF_6'(X_82))
      | ~ ca_Vx3(X_82) ),
    inference(resolution,[status(thm)],[c_86,c_140]) ).

tff(c_264,plain,
    ! [Z_163,Y_164,X_165] :
      ( ( Z_163 = Y_164 )
      | ~ rf1(X_165,Z_163)
      | ~ rf1(X_165,Y_164) ),
    inference(cnfTransformation,[status(thm)],[f_235]) ).

tff(c_312,plain,
    ! [Y_176,X_177] :
      ( ( Y_176 = '#skF_1'(X_177) )
      | ~ rf1(X_177,Y_176)
      | ~ cUnsatisfiable(X_177) ),
    inference(resolution,[status(thm)],[c_64,c_264]) ).

tff(c_444,plain,
    ! [X_192] :
      ( ( '#skF_1'(X_192) = '#skF_6'(X_192) )
      | ~ cUnsatisfiable(X_192)
      | ~ ca_Vx3(X_192) ),
    inference(resolution,[status(thm)],[c_144,c_312]) ).

tff(c_449,plain,
    ! [X_193] :
      ( ( '#skF_1'(X_193) = '#skF_6'(X_193) )
      | ~ cUnsatisfiable(X_193) ),
    inference(resolution,[status(thm)],[c_250,c_444]) ).

tff(c_453,plain,
    '#skF_1'(i2003_11_14_17_21_19256) = '#skF_6'(i2003_11_14_17_21_19256),
    inference(resolution,[status(thm)],[c_106,c_449]) ).

tff(c_460,plain,
    ( ca_Ax2('#skF_6'(i2003_11_14_17_21_19256))
    | ~ cUnsatisfiable(i2003_11_14_17_21_19256) ),
    inference(superposition,[status(thm),theory(equality)],[c_453,c_62]) ).

tff(c_466,plain,
    ca_Ax2('#skF_6'(i2003_11_14_17_21_19256)),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_460]) ).

tff(c_468,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_366,c_466]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% 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
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 20:04:07 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 4.15/1.98  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.15/1.99  
% 4.15/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.36/2.02  
% 4.36/2.02  Inference rules
% 4.36/2.02  ----------------------
% 4.36/2.02  #Ref     : 0
% 4.36/2.02  #Sup     : 74
% 4.36/2.02  #Fact    : 0
% 4.36/2.02  #Define  : 0
% 4.36/2.02  #Split   : 0
% 4.36/2.02  #Chain   : 0
% 4.36/2.02  #Close   : 0
% 4.36/2.02  
% 4.36/2.02  Ordering : KBO
% 4.36/2.02  
% 4.36/2.02  Simplification rules
% 4.36/2.02  ----------------------
% 4.36/2.02  #Subsume      : 9
% 4.36/2.02  #Demod        : 13
% 4.36/2.02  #Tautology    : 52
% 4.36/2.02  #SimpNegUnit  : 1
% 4.36/2.02  #BackRed      : 0
% 4.36/2.02  
% 4.36/2.02  #Partial instantiations: 0
% 4.36/2.02  #Strategies tried      : 1
% 4.36/2.02  
% 4.36/2.02  Timing (in seconds)
% 4.36/2.02  ----------------------
% 4.36/2.02  Preprocessing        : 0.58
% 4.36/2.02  Parsing              : 0.31
% 4.36/2.02  CNF conversion       : 0.05
% 4.36/2.02  Main loop            : 0.35
% 4.36/2.02  Inferencing          : 0.15
% 4.36/2.02  Reduction            : 0.08
% 4.36/2.02  Demodulation         : 0.05
% 4.36/2.03  BG Simplification    : 0.03
% 4.36/2.03  Subsumption          : 0.07
% 4.36/2.03  Abstraction          : 0.02
% 4.36/2.03  MUC search           : 0.00
% 4.36/2.03  Cooper               : 0.00
% 4.36/2.03  Total                : 0.98
% 4.36/2.03  Index Insertion      : 0.00
% 4.36/2.03  Index Deletion       : 0.00
% 4.36/2.03  Index Matching       : 0.00
% 4.36/2.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------