TSTP Solution File: FLD013-5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD013-5 : 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/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 : n014.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 10:37:28 EDT 2023

% Result   : Unsatisfiable 9.11s 3.13s
% Output   : CNFRefutation 9.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  102 (  40 unt;  16 typ;   0 def)
%            Number of atoms       :  173 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  181 (  94   ~;  87   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   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    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   97 (;  97   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > v > u > multiplicative_identity > d > c > 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(u,type,
    u: $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(v,type,
    v: $i ).

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

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

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

tff(f_204,axiom,
    ! [X,Y] :
      ( sum(additive_identity,X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(f_260,axiom,
    ~ sum(additive_identity,u,v),
    file(unknown,unknown) ).

tff(f_159,axiom,
    defined(additive_identity),
    file(unknown,unknown) ).

tff(f_222,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

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

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

tff(f_255,axiom,
    sum(additive_identity,a,b),
    file(unknown,unknown) ).

tff(f_233,axiom,
    ! [U,Z,X,Y,V] :
      ( less_or_equal(U,V)
      | ~ less_or_equal(X,Y)
      | ~ sum(X,Z,U)
      | ~ sum(Y,Z,V) ),
    file(unknown,unknown) ).

tff(f_251,axiom,
    defined(c),
    file(unknown,unknown) ).

tff(f_256,axiom,
    sum(additive_identity,c,d),
    file(unknown,unknown) ).

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

tff(f_257,axiom,
    sum(a,c,u),
    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(f_258,axiom,
    sum(d,b,v),
    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_250,axiom,
    defined(b),
    file(unknown,unknown) ).

tff(c_163,plain,
    ! [Y_100,X_101] :
      ( ~ less_or_equal(Y_100,X_101)
      | ~ less_or_equal(X_101,Y_100)
      | sum(additive_identity,X_101,Y_100) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_74,plain,
    ~ sum(additive_identity,u,v),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_174,plain,
    ( ~ less_or_equal(v,u)
    | ~ less_or_equal(u,v) ),
    inference(resolution,[status(thm)],[c_163,c_74]) ).

tff(c_178,plain,
    ~ less_or_equal(u,v),
    inference(splitLeft,[status(thm)],[c_174]) ).

tff(c_28,plain,
    defined(additive_identity),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_46,plain,
    ! [Y_65,X_64] :
      ( ~ defined(Y_65)
      | ~ defined(X_64)
      | less_or_equal(Y_65,X_64)
      | less_or_equal(X_64,Y_65) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_150,plain,
    ! [Y_65] :
      ( ~ defined(Y_65)
      | less_or_equal(Y_65,Y_65) ),
    inference(factorization,[status(thm),theory(equality)],[c_46]) ).

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

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

tff(c_66,plain,
    sum(additive_identity,a,b),
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_248,plain,
    ! [X_119,V_122,U_118,Y_121,Z_120] :
      ( ~ sum(Y_121,Z_120,V_122)
      | ~ sum(X_119,Z_120,U_118)
      | ~ less_or_equal(X_119,Y_121)
      | less_or_equal(U_118,V_122) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_857,plain,
    ! [X_173,U_174] :
      ( ~ sum(X_173,a,U_174)
      | ~ less_or_equal(X_173,additive_identity)
      | less_or_equal(U_174,b) ),
    inference(resolution,[status(thm)],[c_66,c_248]) ).

tff(c_880,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,b)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_6,c_857]) ).

tff(c_897,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_880]) ).

tff(c_1135,plain,
    ~ less_or_equal(additive_identity,additive_identity),
    inference(splitLeft,[status(thm)],[c_897]) ).

tff(c_1144,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_150,c_1135]) ).

tff(c_1154,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_1144]) ).

tff(c_1156,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(splitRight,[status(thm)],[c_897]) ).

tff(c_58,plain,
    defined(c),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_68,plain,
    sum(additive_identity,c,d),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_1169,plain,
    ! [X_178,U_179] :
      ( ~ sum(X_178,c,U_179)
      | ~ less_or_equal(X_178,additive_identity)
      | less_or_equal(U_179,d) ),
    inference(resolution,[status(thm)],[c_68,c_248]) ).

tff(c_1189,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(c,d)
    | ~ defined(c) ),
    inference(resolution,[status(thm)],[c_6,c_1169]) ).

tff(c_1209,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(c,d) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_1189]) ).

tff(c_1287,plain,
    less_or_equal(c,d),
    inference(demodulation,[status(thm),theory(equality)],[c_1156,c_1209]) ).

tff(c_88,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_104,plain,
    sum(a,additive_identity,b),
    inference(resolution,[status(thm)],[c_66,c_88]) ).

tff(c_70,plain,
    sum(a,c,u),
    inference(cnfTransformation,[status(thm)],[f_257]) ).

tff(c_479,plain,
    ! [V_141,X_142,U_140,W_139,Y_143,Z_138] :
      ( ~ sum(X_142,V_141,W_139)
      | ~ sum(Y_143,Z_138,V_141)
      | ~ sum(X_142,Y_143,U_140)
      | sum(U_140,Z_138,W_139) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_2746,plain,
    ! [Y_231,Z_232,U_233] :
      ( ~ sum(Y_231,Z_232,c)
      | ~ sum(a,Y_231,U_233)
      | sum(U_233,Z_232,u) ),
    inference(resolution,[status(thm)],[c_70,c_479]) ).

tff(c_2758,plain,
    ! [U_233] :
      ( ~ sum(a,additive_identity,U_233)
      | sum(U_233,c,u)
      | ~ defined(c) ),
    inference(resolution,[status(thm)],[c_6,c_2746]) ).

tff(c_2830,plain,
    ! [U_235] :
      ( ~ sum(a,additive_identity,U_235)
      | sum(U_235,c,u) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_2758]) ).

tff(c_2855,plain,
    sum(b,c,u),
    inference(resolution,[status(thm)],[c_104,c_2830]) ).

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_2885,plain,
    sum(c,b,u),
    inference(resolution,[status(thm)],[c_2855,c_10]) ).

tff(c_72,plain,
    sum(d,b,v),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_295,plain,
    ! [X_119,U_118] :
      ( ~ sum(X_119,b,U_118)
      | ~ less_or_equal(X_119,d)
      | less_or_equal(U_118,v) ),
    inference(resolution,[status(thm)],[c_72,c_248]) ).

tff(c_2890,plain,
    ( ~ less_or_equal(c,d)
    | less_or_equal(u,v) ),
    inference(resolution,[status(thm)],[c_2885,c_295]) ).

tff(c_2904,plain,
    less_or_equal(u,v),
    inference(demodulation,[status(thm),theory(equality)],[c_1287,c_2890]) ).

tff(c_2906,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_178,c_2904]) ).

tff(c_2907,plain,
    ~ less_or_equal(v,u),
    inference(splitRight,[status(thm)],[c_174]) ).

tff(c_3066,plain,
    ! [U_258,X_259,Y_261,Z_260,V_262] :
      ( ~ sum(Y_261,Z_260,V_262)
      | ~ sum(X_259,Z_260,U_258)
      | ~ less_or_equal(X_259,Y_261)
      | less_or_equal(U_258,V_262) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_3835,plain,
    ! [X_314,U_315] :
      ( ~ sum(X_314,a,U_315)
      | ~ less_or_equal(X_314,additive_identity)
      | less_or_equal(U_315,b) ),
    inference(resolution,[status(thm)],[c_66,c_3066]) ).

tff(c_3858,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,b)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_6,c_3835]) ).

tff(c_3875,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,b) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_3858]) ).

tff(c_4100,plain,
    ~ less_or_equal(additive_identity,additive_identity),
    inference(splitLeft,[status(thm)],[c_3875]) ).

tff(c_4109,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_150,c_4100]) ).

tff(c_4119,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_4109]) ).

tff(c_4121,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(splitRight,[status(thm)],[c_3875]) ).

tff(c_4469,plain,
    ! [X_329,X_330,U_331] :
      ( ~ sum(X_329,X_330,U_331)
      | ~ less_or_equal(X_329,additive_identity)
      | less_or_equal(U_331,X_330)
      | ~ defined(X_330) ),
    inference(resolution,[status(thm)],[c_6,c_3066]) ).

tff(c_4511,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(b,a)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_66,c_4469]) ).

tff(c_4551,plain,
    less_or_equal(b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_4121,c_4511]) ).

tff(c_42,plain,
    ! [Y_60,X_59] :
      ( ~ less_or_equal(Y_60,X_59)
      | ~ less_or_equal(X_59,Y_60)
      | sum(additive_identity,X_59,Y_60) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_3229,plain,
    ! [X_275,Y_272,W_276,U_274,Z_271,V_273] :
      ( ~ sum(U_274,Z_271,W_276)
      | ~ sum(Y_272,Z_271,V_273)
      | ~ sum(X_275,Y_272,U_274)
      | sum(X_275,V_273,W_276) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_7638,plain,
    ! [Y_405,X_406,V_407,X_408] :
      ( ~ sum(Y_405,X_406,V_407)
      | ~ sum(X_408,Y_405,additive_identity)
      | sum(X_408,V_407,X_406)
      | ~ defined(X_406) ),
    inference(resolution,[status(thm)],[c_6,c_3229]) ).

tff(c_7734,plain,
    ! [X_408] :
      ( ~ sum(X_408,additive_identity,additive_identity)
      | sum(X_408,d,c)
      | ~ defined(c) ),
    inference(resolution,[status(thm)],[c_68,c_7638]) ).

tff(c_7863,plain,
    ! [X_410] :
      ( ~ sum(X_410,additive_identity,additive_identity)
      | sum(X_410,d,c) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_7734]) ).

tff(c_7938,plain,
    ! [X_412] :
      ( sum(d,X_412,c)
      | ~ sum(X_412,additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[c_7863,c_10]) ).

tff(c_7944,plain,
    ( sum(d,additive_identity,c)
    | ~ less_or_equal(additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[c_42,c_7938]) ).

tff(c_7957,plain,
    sum(d,additive_identity,c),
    inference(demodulation,[status(thm),theory(equality)],[c_4121,c_7944]) ).

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

tff(c_3346,plain,
    ! [W_285,U_286,X_288,Z_284,V_287,Y_289] :
      ( ~ sum(X_288,V_287,W_285)
      | ~ sum(Y_289,Z_284,V_287)
      | ~ sum(X_288,Y_289,U_286)
      | sum(U_286,Z_284,W_285) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_5154,plain,
    ! [Y_344,Z_345,U_346] :
      ( ~ sum(Y_344,Z_345,b)
      | ~ sum(d,Y_344,U_346)
      | sum(U_346,Z_345,v) ),
    inference(resolution,[status(thm)],[c_72,c_3346]) ).

tff(c_5168,plain,
    ! [U_346] :
      ( ~ sum(d,additive_identity,U_346)
      | sum(U_346,b,v)
      | ~ defined(b) ),
    inference(resolution,[status(thm)],[c_6,c_5154]) ).

tff(c_5179,plain,
    ! [U_346] :
      ( ~ sum(d,additive_identity,U_346)
      | sum(U_346,b,v) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_5168]) ).

tff(c_8001,plain,
    sum(c,b,v),
    inference(resolution,[status(thm)],[c_7957,c_5179]) ).

tff(c_8106,plain,
    sum(b,c,v),
    inference(resolution,[status(thm)],[c_8001,c_10]) ).

tff(c_3111,plain,
    ! [X_259,U_258] :
      ( ~ sum(X_259,c,U_258)
      | ~ less_or_equal(X_259,a)
      | less_or_equal(U_258,u) ),
    inference(resolution,[status(thm)],[c_70,c_3066]) ).

tff(c_8197,plain,
    ( ~ less_or_equal(b,a)
    | less_or_equal(v,u) ),
    inference(resolution,[status(thm)],[c_8106,c_3111]) ).

tff(c_8224,plain,
    less_or_equal(v,u),
    inference(demodulation,[status(thm),theory(equality)],[c_4551,c_8197]) ).

tff(c_8226,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2907,c_8224]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD013-5 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % 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 : n014.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 19:52:33 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 9.11/3.13  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.11/3.14  
% 9.11/3.14  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.11/3.18  
% 9.11/3.18  Inference rules
% 9.11/3.18  ----------------------
% 9.11/3.18  #Ref     : 0
% 9.11/3.18  #Sup     : 1743
% 9.11/3.18  #Fact    : 10
% 9.11/3.18  #Define  : 0
% 9.11/3.18  #Split   : 43
% 9.11/3.18  #Chain   : 0
% 9.11/3.18  #Close   : 0
% 9.11/3.18  
% 9.11/3.18  Ordering : KBO
% 9.11/3.18  
% 9.11/3.18  Simplification rules
% 9.11/3.18  ----------------------
% 9.11/3.18  #Subsume      : 147
% 9.11/3.18  #Demod        : 1124
% 9.11/3.18  #Tautology    : 324
% 9.11/3.18  #SimpNegUnit  : 20
% 9.11/3.18  #BackRed      : 0
% 9.11/3.18  
% 9.11/3.18  #Partial instantiations: 0
% 9.11/3.18  #Strategies tried      : 1
% 9.11/3.18  
% 9.11/3.18  Timing (in seconds)
% 9.11/3.18  ----------------------
% 9.11/3.18  Preprocessing        : 0.51
% 9.11/3.18  Parsing              : 0.27
% 9.11/3.18  CNF conversion       : 0.03
% 9.11/3.18  Main loop            : 1.59
% 9.11/3.18  Inferencing          : 0.61
% 9.11/3.19  Reduction            : 0.48
% 9.11/3.19  Demodulation         : 0.34
% 9.11/3.19  BG Simplification    : 0.05
% 9.11/3.19  Subsumption          : 0.35
% 9.11/3.19  Abstraction          : 0.04
% 9.11/3.19  MUC search           : 0.00
% 9.11/3.19  Cooper               : 0.00
% 9.28/3.19  Total                : 2.17
% 9.28/3.19  Index Insertion      : 0.00
% 9.28/3.19  Index Deletion       : 0.00
% 9.28/3.19  Index Matching       : 0.00
% 9.28/3.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------