TSTP Solution File: FLD043-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD043-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n019.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 10:37:35 EDT 2023

% Result   : Unsatisfiable 19.33s 8.53s
% Output   : CNFRefutation 19.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   60 (  19 unt;  12 typ;   0 def)
%            Number of atoms       :  103 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  114 (  59   ~;  55   |;   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  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   75 (;  75   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > b > additive_identity > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_253,axiom,
    ~ sum(additive_identity,b,additive_identity),
    file(unknown,unknown) ).

tff(f_249,axiom,
    defined(a),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ! [X] :
      ( sum(additive_inverse(X),X,additive_identity)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_250,axiom,
    defined(b),
    file(unknown,unknown) ).

tff(f_173,axiom,
    defined(multiplicative_identity),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [Y,X,Z] :
      ( sum(Y,X,Z)
      | ~ sum(X,Y,Z) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X] :
      ( product(multiplicative_identity,X,X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_251,axiom,
    product(additive_identity,a,b),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [A,Z,B,C,X,Y,D] :
      ( sum(C,D,B)
      | ~ sum(X,Y,A)
      | ~ product(A,Z,B)
      | ~ product(X,Z,C)
      | ~ product(Y,Z,D) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [W,U,Z,X,Y,V] :
      ( sum(X,V,W)
      | ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [W,U,Z,X,Y,V] :
      ( sum(U,Z,W)
      | ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(X,V,W) ),
    file(unknown,unknown) ).

tff(c_60,plain,
    ~ sum(additive_identity,b,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_54,plain,
    defined(a),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_8,plain,
    ! [X_14] :
      ( ~ defined(X_14)
      | sum(additive_inverse(X_14),X_14,additive_identity) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_56,plain,
    defined(b),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_34,plain,
    defined(multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_6,plain,
    ! [X_13] :
      ( ~ defined(X_13)
      | sum(additive_identity,X_13,X_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_81,plain,
    ! [X_84,Y_85,Z_86] :
      ( ~ sum(X_84,Y_85,Z_86)
      | sum(Y_85,X_84,Z_86) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_87,plain,
    ! [X_13] :
      ( sum(X_13,additive_identity,X_13)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_6,c_81]) ).

tff(c_16,plain,
    ! [X_30] :
      ( ~ defined(X_30)
      | product(multiplicative_identity,X_30,X_30) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_58,plain,
    product(additive_identity,a,b),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_763,plain,
    ! [X_178,Y_175,B_177,A_174,Z_176,D_180,C_179] :
      ( ~ product(Y_175,Z_176,D_180)
      | ~ product(X_178,Z_176,C_179)
      | ~ product(A_174,Z_176,B_177)
      | ~ sum(X_178,Y_175,A_174)
      | sum(C_179,D_180,B_177) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_23686,plain,
    ! [X_511,C_512,A_513,B_514] :
      ( ~ product(X_511,a,C_512)
      | ~ product(A_513,a,B_514)
      | ~ sum(X_511,additive_identity,A_513)
      | sum(C_512,b,B_514) ),
    inference(resolution,[status(thm)],[c_58,c_763]) ).

tff(c_23708,plain,
    ! [A_513,B_514] :
      ( ~ product(A_513,a,B_514)
      | ~ sum(multiplicative_identity,additive_identity,A_513)
      | sum(a,b,B_514)
      | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_16,c_23686]) ).

tff(c_40704,plain,
    ! [A_724,B_725] :
      ( ~ product(A_724,a,B_725)
      | ~ sum(multiplicative_identity,additive_identity,A_724)
      | sum(a,b,B_725) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_23708]) ).

tff(c_40771,plain,
    ( ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
    | sum(a,b,a)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_16,c_40704]) ).

tff(c_40814,plain,
    ( ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
    | sum(a,b,a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_40771]) ).

tff(c_40904,plain,
    ~ sum(multiplicative_identity,additive_identity,multiplicative_identity),
    inference(splitLeft,[status(thm)],[c_40814]) ).

tff(c_40910,plain,
    ~ defined(multiplicative_identity),
    inference(resolution,[status(thm)],[c_87,c_40904]) ).

tff(c_40915,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_40910]) ).

tff(c_40916,plain,
    sum(a,b,a),
    inference(splitRight,[status(thm)],[c_40814]) ).

tff(c_508,plain,
    ! [V_149,X_151,Y_148,W_152,U_150,Z_147] :
      ( ~ sum(U_150,Z_147,W_152)
      | ~ sum(Y_148,Z_147,V_149)
      | ~ sum(X_151,Y_148,U_150)
      | sum(X_151,V_149,W_152) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_532,plain,
    ! [Y_148,X_13,V_149,X_151] :
      ( ~ sum(Y_148,X_13,V_149)
      | ~ sum(X_151,Y_148,additive_identity)
      | sum(X_151,V_149,X_13)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_6,c_508]) ).

tff(c_40941,plain,
    ! [X_151] :
      ( ~ sum(X_151,a,additive_identity)
      | sum(X_151,a,b)
      | ~ defined(b) ),
    inference(resolution,[status(thm)],[c_40916,c_532]) ).

tff(c_41828,plain,
    ! [X_734] :
      ( ~ sum(X_734,a,additive_identity)
      | sum(X_734,a,b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_40941]) ).

tff(c_10,plain,
    ! [X_16,Y_15,Z_17] :
      ( ~ sum(X_16,Y_15,Z_17)
      | sum(Y_15,X_16,Z_17) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_42767,plain,
    ! [X_741] :
      ( sum(a,X_741,b)
      | ~ sum(X_741,a,additive_identity) ),
    inference(resolution,[status(thm)],[c_41828,c_10]) ).

tff(c_42779,plain,
    ( sum(a,additive_inverse(a),b)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_8,c_42767]) ).

tff(c_42785,plain,
    sum(a,additive_inverse(a),b),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_42779]) ).

tff(c_42846,plain,
    sum(additive_inverse(a),a,b),
    inference(resolution,[status(thm)],[c_42785,c_10]) ).

tff(c_687,plain,
    ! [Z_167,V_170,U_169,Y_172,W_168,X_171] :
      ( ~ sum(X_171,V_170,W_168)
      | ~ sum(Y_172,Z_167,V_170)
      | ~ sum(X_171,Y_172,U_169)
      | sum(U_169,Z_167,W_168) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_22866,plain,
    ! [Y_493,Z_494,X_495,U_496] :
      ( ~ sum(Y_493,Z_494,X_495)
      | ~ sum(additive_inverse(X_495),Y_493,U_496)
      | sum(U_496,Z_494,additive_identity)
      | ~ defined(X_495) ),
    inference(resolution,[status(thm)],[c_8,c_687]) ).

tff(c_22914,plain,
    ! [X_13,U_496] :
      ( ~ sum(additive_inverse(X_13),X_13,U_496)
      | sum(U_496,additive_identity,additive_identity)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_87,c_22866]) ).

tff(c_42852,plain,
    ( sum(b,additive_identity,additive_identity)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_42846,c_22914]) ).

tff(c_42891,plain,
    sum(b,additive_identity,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_42852]) ).

tff(c_42973,plain,
    sum(additive_identity,b,additive_identity),
    inference(resolution,[status(thm)],[c_42891,c_10]) ).

tff(c_43018,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_42973]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : FLD043-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n019.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 19:57:01 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 19.33/8.53  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.33/8.54  
% 19.33/8.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.33/8.57  
% 19.33/8.57  Inference rules
% 19.33/8.57  ----------------------
% 19.33/8.57  #Ref     : 0
% 19.33/8.57  #Sup     : 9703
% 19.33/8.57  #Fact    : 6
% 19.33/8.57  #Define  : 0
% 19.33/8.57  #Split   : 52
% 19.33/8.57  #Chain   : 0
% 19.33/8.57  #Close   : 0
% 19.33/8.57  
% 19.33/8.57  Ordering : KBO
% 19.33/8.57  
% 19.33/8.57  Simplification rules
% 19.33/8.57  ----------------------
% 19.33/8.57  #Subsume      : 679
% 19.33/8.57  #Demod        : 6720
% 19.33/8.57  #Tautology    : 1827
% 19.33/8.57  #SimpNegUnit  : 313
% 19.33/8.57  #BackRed      : 0
% 19.33/8.57  
% 19.33/8.57  #Partial instantiations: 0
% 19.33/8.57  #Strategies tried      : 1
% 19.33/8.57  
% 19.33/8.57  Timing (in seconds)
% 19.33/8.57  ----------------------
% 19.33/8.57  Preprocessing        : 0.51
% 19.33/8.57  Parsing              : 0.29
% 19.33/8.57  CNF conversion       : 0.03
% 19.33/8.57  Main loop            : 6.91
% 19.33/8.57  Inferencing          : 1.25
% 19.33/8.57  Reduction            : 2.59
% 19.33/8.57  Demodulation         : 2.03
% 19.33/8.57  BG Simplification    : 0.10
% 19.33/8.57  Subsumption          : 2.45
% 19.33/8.57  Abstraction          : 0.12
% 19.33/8.57  MUC search           : 0.00
% 19.33/8.57  Cooper               : 0.00
% 19.33/8.57  Total                : 7.47
% 19.33/8.57  Index Insertion      : 0.00
% 19.33/8.57  Index Deletion       : 0.00
% 19.33/8.57  Index Matching       : 0.00
% 19.33/8.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------