TSTP Solution File: BOO013-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : BOO013-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : n028.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 10:34:25 EDT 2023

% Result   : Unsatisfiable 7.31s 2.81s
% Output   : CNFRefutation 7.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   56 (  25 unt;  10 typ;   0 def)
%            Number of atoms       :   90 (  12 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   90 (  46   ~;  44   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   90 (;  90   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > inverse > z > y > x > multiplicative_identity > additive_identity

%Foreground sorts:

%Background operators:

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

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

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

tff(inverse,type,
    inverse: $i > $i ).

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

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

tff(multiply,type,
    multiply: ( $i * $i ) > $i ).

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

tff(add,type,
    add: ( $i * $i ) > $i ).

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

tff(f_214,axiom,
    y != z,
    file(unknown,unknown) ).

tff(f_212,axiom,
    product(x,z,additive_identity),
    file(unknown,unknown) ).

tff(f_211,axiom,
    product(x,y,additive_identity),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | product(Y,X,Z) ),
    file(unknown,unknown) ).

tff(f_210,axiom,
    sum(x,z,multiplicative_identity),
    file(unknown,unknown) ).

tff(f_65,axiom,
    ! [X] : product(multiplicative_identity,X,X),
    file(unknown,unknown) ).

tff(f_109,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] :
      ( ~ product(Y,X,V1)
      | ~ product(Z,X,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(V3,X,V4)
      | sum(V1,V2,V4) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X] : sum(additive_identity,X,X),
    file(unknown,unknown) ).

tff(f_196,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | ( U = V ) ),
    file(unknown,unknown) ).

tff(f_209,axiom,
    sum(x,y,multiplicative_identity),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file(unknown,unknown) ).

tff(f_63,axiom,
    ! [X] : sum(X,additive_identity,X),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] :
      ( ~ product(Y,X,V1)
      | ~ product(Z,X,V2)
      | ~ sum(Y,Z,V3)
      | ~ sum(V1,V2,V4)
      | product(V3,X,V4) ),
    file(unknown,unknown) ).

tff(f_204,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | ( U = V ) ),
    file(unknown,unknown) ).

tff(c_56,plain,
    z != y,
    inference(cnfTransformation,[status(thm)],[f_214]) ).

tff(c_54,plain,
    product(x,z,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_52,plain,
    product(x,y,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_4,plain,
    ! [X_3,Y_4] : product(X_3,Y_4,multiply(X_3,Y_4)),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_126,plain,
    ! [Y_100,X_101,Z_102] :
      ( product(Y_100,X_101,Z_102)
      | ~ product(X_101,Y_100,Z_102) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_141,plain,
    ! [Y_4,X_3] : product(Y_4,X_3,multiply(X_3,Y_4)),
    inference(resolution,[status(thm)],[c_4,c_126]) ).

tff(c_50,plain,
    sum(x,z,multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_14,plain,
    ! [X_13] : product(multiplicative_identity,X_13,X_13),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_1046,plain,
    ! [V3_188,Z_189,X_185,Y_183,V4_184,V2_187,V1_186] :
      ( sum(V1_186,V2_187,V4_184)
      | ~ product(V3_188,X_185,V4_184)
      | ~ sum(Y_183,Z_189,V3_188)
      | ~ product(Z_189,X_185,V2_187)
      | ~ product(Y_183,X_185,V1_186) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_1993,plain,
    ! [Z_262,Y_263,X_261,V1_260,V2_264] :
      ( sum(V1_260,V2_264,X_261)
      | ~ sum(Y_263,Z_262,multiplicative_identity)
      | ~ product(Z_262,X_261,V2_264)
      | ~ product(Y_263,X_261,V1_260) ),
    inference(resolution,[status(thm)],[c_14,c_1046]) ).

tff(c_2128,plain,
    ! [V1_270,V2_271,X_272] :
      ( sum(V1_270,V2_271,X_272)
      | ~ product(z,X_272,V2_271)
      | ~ product(x,X_272,V1_270) ),
    inference(resolution,[status(thm)],[c_50,c_1993]) ).

tff(c_10,plain,
    ! [X_11] : sum(additive_identity,X_11,X_11),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_173,plain,
    ! [V_105,U_106,X_107,Y_108] :
      ( ( V_105 = U_106 )
      | ~ sum(X_107,Y_108,V_105)
      | ~ sum(X_107,Y_108,U_106) ),
    inference(cnfTransformation,[status(thm)],[f_196]) ).

tff(c_201,plain,
    ! [X_11,U_106] :
      ( ( X_11 = U_106 )
      | ~ sum(additive_identity,X_11,U_106) ),
    inference(resolution,[status(thm)],[c_10,c_173]) ).

tff(c_2716,plain,
    ! [X_304,V2_305] :
      ( ( X_304 = V2_305 )
      | ~ product(z,X_304,V2_305)
      | ~ product(x,X_304,additive_identity) ),
    inference(resolution,[status(thm)],[c_2128,c_201]) ).

tff(c_2742,plain,
    ! [X_306] :
      ( ( multiply(X_306,z) = X_306 )
      | ~ product(x,X_306,additive_identity) ),
    inference(resolution,[status(thm)],[c_141,c_2716]) ).

tff(c_2754,plain,
    multiply(y,z) = y,
    inference(resolution,[status(thm)],[c_52,c_2742]) ).

tff(c_2802,plain,
    product(y,z,y),
    inference(superposition,[status(thm),theory(equality)],[c_2754,c_4]) ).

tff(c_48,plain,
    sum(x,y,multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_100,plain,
    ! [Y_97,X_98,Z_99] :
      ( sum(Y_97,X_98,Z_99)
      | ~ sum(X_98,Y_97,Z_99) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_124,plain,
    sum(y,x,multiplicative_identity),
    inference(resolution,[status(thm)],[c_48,c_100]) ).

tff(c_12,plain,
    ! [X_12] : sum(X_12,additive_identity,X_12),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_792,plain,
    ! [Z_163,V2_165,X_166,V1_164,Y_162,V4_161,V3_160] :
      ( product(V3_160,X_166,V4_161)
      | ~ sum(V1_164,V2_165,V4_161)
      | ~ sum(Y_162,Z_163,V3_160)
      | ~ product(Z_163,X_166,V2_165)
      | ~ product(Y_162,X_166,V1_164) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_4265,plain,
    ! [Z_395,X_394,X_392,V3_391,Y_393] :
      ( product(V3_391,X_392,X_394)
      | ~ sum(Y_393,Z_395,V3_391)
      | ~ product(Z_395,X_392,additive_identity)
      | ~ product(Y_393,X_392,X_394) ),
    inference(resolution,[status(thm)],[c_12,c_792]) ).

tff(c_4359,plain,
    ! [X_402,X_403] :
      ( product(multiplicative_identity,X_402,X_403)
      | ~ product(x,X_402,additive_identity)
      | ~ product(y,X_402,X_403) ),
    inference(resolution,[status(thm)],[c_124,c_4265]) ).

tff(c_4362,plain,
    ( product(multiplicative_identity,z,y)
    | ~ product(x,z,additive_identity) ),
    inference(resolution,[status(thm)],[c_2802,c_4359]) ).

tff(c_4387,plain,
    product(multiplicative_identity,z,y),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_4362]) ).

tff(c_259,plain,
    ! [V_113,U_114,X_115,Y_116] :
      ( ( V_113 = U_114 )
      | ~ product(X_115,Y_116,V_113)
      | ~ product(X_115,Y_116,U_114) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_287,plain,
    ! [X_13,U_114] :
      ( ( X_13 = U_114 )
      | ~ product(multiplicative_identity,X_13,U_114) ),
    inference(resolution,[status(thm)],[c_14,c_259]) ).

tff(c_4428,plain,
    z = y,
    inference(resolution,[status(thm)],[c_4387,c_287]) ).

tff(c_4454,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_56,c_4428]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : BOO013-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % 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
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 18:51:24 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 7.31/2.81  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.31/2.82  
% 7.31/2.82  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.31/2.85  
% 7.31/2.85  Inference rules
% 7.31/2.85  ----------------------
% 7.31/2.85  #Ref     : 0
% 7.31/2.85  #Sup     : 1111
% 7.31/2.85  #Fact    : 0
% 7.31/2.85  #Define  : 0
% 7.31/2.85  #Split   : 22
% 7.31/2.85  #Chain   : 0
% 7.31/2.85  #Close   : 0
% 7.31/2.85  
% 7.31/2.85  Ordering : KBO
% 7.31/2.85  
% 7.31/2.85  Simplification rules
% 7.31/2.85  ----------------------
% 7.31/2.85  #Subsume      : 73
% 7.31/2.85  #Demod        : 329
% 7.31/2.85  #Tautology    : 434
% 7.31/2.85  #SimpNegUnit  : 2
% 7.31/2.85  #BackRed      : 1
% 7.31/2.85  
% 7.31/2.85  #Partial instantiations: 0
% 7.31/2.85  #Strategies tried      : 1
% 7.31/2.85  
% 7.31/2.85  Timing (in seconds)
% 7.31/2.85  ----------------------
% 7.31/2.86  Preprocessing        : 0.51
% 7.31/2.86  Parsing              : 0.27
% 7.31/2.86  CNF conversion       : 0.03
% 7.31/2.86  Main loop            : 1.27
% 7.31/2.86  Inferencing          : 0.42
% 7.31/2.86  Reduction            : 0.40
% 7.31/2.86  Demodulation         : 0.28
% 7.31/2.86  BG Simplification    : 0.04
% 7.31/2.86  Subsumption          : 0.32
% 7.31/2.86  Abstraction          : 0.04
% 7.31/2.86  MUC search           : 0.00
% 7.31/2.86  Cooper               : 0.00
% 7.31/2.86  Total                : 1.82
% 7.31/2.86  Index Insertion      : 0.00
% 7.31/2.86  Index Deletion       : 0.00
% 7.31/2.86  Index Matching       : 0.00
% 7.31/2.86  BG Taut test         : 0.00
%------------------------------------------------------------------------------