TSTP Solution File: RNG004-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG004-2 : 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/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 : n029.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 10:54:41 EDT 2023

% Result   : Unsatisfiable 24.26s 11.84s
% Output   : CNFRefutation 24.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   81 (  32 unt;  10 typ;   0 def)
%            Number of atoms       :  145 (  28 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  150 (  76   ~;  74   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   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   :  174 (; 174   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > multiply > add > #nlpp > additive_inverse > d > c > b > additive_identity > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

tff(f_199,axiom,
    c != d,
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file(unknown,unknown) ).

tff(f_82,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file(unknown,unknown) ).

tff(f_45,axiom,
    ! [X] : sum(additive_identity,X,X),
    file(unknown,unknown) ).

tff(f_187,axiom,
    ! [X,Y,Z,W] :
      ( ~ sum(X,Y,Z)
      | ~ sum(X,W,Z)
      | ( Y = W ) ),
    file(unknown,unknown) ).

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

tff(f_196,axiom,
    product(a,b,c),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [X] : sum(X,additive_identity,X),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [V3,Z,V1,X,Y,V2,V4] :
      ( ~ product(X,Y,V1)
      | ~ product(X,Z,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(X,V3,V4)
      | sum(V1,V2,V4) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ! [X] : sum(X,additive_inverse(X),additive_identity),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(X,V,W)
      | sum(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_169,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | ( U = V ) ),
    file(unknown,unknown) ).

tff(f_197,axiom,
    product(additive_inverse(a),additive_inverse(b),d),
    file(unknown,unknown) ).

tff(f_146,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_195,axiom,
    ! [X,Y,Z,W] :
      ( ~ sum(X,Y,Z)
      | ~ sum(W,Y,Z)
      | ( X = W ) ),
    file(unknown,unknown) ).

tff(c_44,plain,
    d != c,
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_8,plain,
    ! [X_5,Y_6] : sum(X_5,Y_6,add(X_5,Y_6)),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_51,plain,
    ! [Y_88,X_89,Z_90] :
      ( sum(Y_88,X_89,Z_90)
      | ~ sum(X_89,Y_88,Z_90) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_62,plain,
    ! [Y_6,X_5] : sum(Y_6,X_5,add(X_5,Y_6)),
    inference(resolution,[status(thm)],[c_8,c_51]) ).

tff(c_2,plain,
    ! [X_1] : sum(additive_identity,X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_76,plain,
    ! [Y_93,W_94,X_95,Z_96] :
      ( ( Y_93 = W_94 )
      | ~ sum(X_95,W_94,Z_96)
      | ~ sum(X_95,Y_93,Z_96) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_95,plain,
    ! [Y_97,X_98] :
      ( ( Y_97 = X_98 )
      | ~ sum(additive_identity,Y_97,X_98) ),
    inference(resolution,[status(thm)],[c_2,c_76]) ).

tff(c_115,plain,
    ! [X_5] : ( add(X_5,additive_identity) = X_5 ),
    inference(resolution,[status(thm)],[c_62,c_95]) ).

tff(c_6,plain,
    ! [X_3,Y_4] : product(X_3,Y_4,multiply(X_3,Y_4)),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_40,plain,
    product(a,b,c),
    inference(cnfTransformation,[status(thm)],[f_196]) ).

tff(c_4,plain,
    ! [X_2] : sum(X_2,additive_identity,X_2),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_964,plain,
    ! [V2_195,V1_194,Y_192,Z_193,V4_191,X_196,V3_190] :
      ( sum(V1_194,V2_195,V4_191)
      | ~ product(X_196,V3_190,V4_191)
      | ~ sum(Y_192,Z_193,V3_190)
      | ~ product(X_196,Z_193,V2_195)
      | ~ product(X_196,Y_192,V1_194) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_14940,plain,
    ! [Y_513,Z_516,X_517,Y_518,V1_515,V2_514] :
      ( sum(V1_515,V2_514,multiply(X_517,Y_518))
      | ~ sum(Y_513,Z_516,Y_518)
      | ~ product(X_517,Z_516,V2_514)
      | ~ product(X_517,Y_513,V1_515) ),
    inference(resolution,[status(thm)],[c_6,c_964]) ).

tff(c_78030,plain,
    ! [V1_1104,V2_1105,X_1106,X_1107] :
      ( sum(V1_1104,V2_1105,multiply(X_1106,X_1107))
      | ~ product(X_1106,additive_identity,V2_1105)
      | ~ product(X_1106,X_1107,V1_1104) ),
    inference(resolution,[status(thm)],[c_4,c_14940]) ).

tff(c_94,plain,
    ! [Y_93,X_2] :
      ( ( additive_identity = Y_93 )
      | ~ sum(X_2,Y_93,X_2) ),
    inference(resolution,[status(thm)],[c_4,c_76]) ).

tff(c_78371,plain,
    ! [V2_1105,X_1106,X_1107] :
      ( ( additive_identity = V2_1105 )
      | ~ product(X_1106,additive_identity,V2_1105)
      | ~ product(X_1106,X_1107,multiply(X_1106,X_1107)) ),
    inference(resolution,[status(thm)],[c_78030,c_94]) ).

tff(c_78524,plain,
    ! [V2_1108,X_1109] :
      ( ( additive_identity = V2_1108 )
      | ~ product(X_1109,additive_identity,V2_1108) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_78371]) ).

tff(c_78559,plain,
    ! [X_3] : ( multiply(X_3,additive_identity) = additive_identity ),
    inference(resolution,[status(thm)],[c_6,c_78524]) ).

tff(c_10,plain,
    ! [X_7] : sum(additive_inverse(X_7),X_7,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_15046,plain,
    ! [V1_515,V2_514,X_517,X_7] :
      ( sum(V1_515,V2_514,multiply(X_517,additive_identity))
      | ~ product(X_517,X_7,V2_514)
      | ~ product(X_517,additive_inverse(X_7),V1_515) ),
    inference(resolution,[status(thm)],[c_10,c_14940]) ).

tff(c_98789,plain,
    ! [V1_1322,V2_1323,X_1324,X_1325] :
      ( sum(V1_1322,V2_1323,additive_identity)
      | ~ product(X_1324,X_1325,V2_1323)
      | ~ product(X_1324,additive_inverse(X_1325),V1_1322) ),
    inference(demodulation,[status(thm),theory(equality)],[c_78559,c_15046]) ).

tff(c_98865,plain,
    ! [V1_1326] :
      ( sum(V1_1326,c,additive_identity)
      | ~ product(a,additive_inverse(b),V1_1326) ),
    inference(resolution,[status(thm)],[c_40,c_98789]) ).

tff(c_98900,plain,
    sum(multiply(a,additive_inverse(b)),c,additive_identity),
    inference(resolution,[status(thm)],[c_6,c_98865]) ).

tff(c_12,plain,
    ! [X_8] : sum(X_8,additive_inverse(X_8),additive_identity),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_812,plain,
    ! [Z_168,U_170,Y_172,X_169,V_171,W_167] :
      ( sum(U_170,Z_168,W_167)
      | ~ sum(X_169,V_171,W_167)
      | ~ sum(Y_172,Z_168,V_171)
      | ~ sum(X_169,Y_172,U_170) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_1992,plain,
    ! [U_265,Z_266,X_267,Y_268] :
      ( sum(U_265,Z_266,X_267)
      | ~ sum(Y_268,Z_266,additive_identity)
      | ~ sum(X_267,Y_268,U_265) ),
    inference(resolution,[status(thm)],[c_4,c_812]) ).

tff(c_2058,plain,
    ! [U_271,X_272,X_273] :
      ( sum(U_271,additive_inverse(X_272),X_273)
      | ~ sum(X_273,X_272,U_271) ),
    inference(resolution,[status(thm)],[c_12,c_1992]) ).

tff(c_151,plain,
    ! [V_100,U_101,X_102,Y_103] :
      ( ( V_100 = U_101 )
      | ~ sum(X_102,Y_103,V_100)
      | ~ sum(X_102,Y_103,U_101) ),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_164,plain,
    ! [X_5,Y_6,U_101] :
      ( ( add(X_5,Y_6) = U_101 )
      | ~ sum(Y_6,X_5,U_101) ),
    inference(resolution,[status(thm)],[c_62,c_151]) ).

tff(c_2206,plain,
    ! [X_272,U_271,X_273] :
      ( ( add(additive_inverse(X_272),U_271) = X_273 )
      | ~ sum(X_273,X_272,U_271) ),
    inference(resolution,[status(thm)],[c_2058,c_164]) ).

tff(c_98916,plain,
    multiply(a,additive_inverse(b)) = add(additive_inverse(c),additive_identity),
    inference(resolution,[status(thm)],[c_98900,c_2206]) ).

tff(c_98989,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(demodulation,[status(thm),theory(equality)],[c_115,c_98916]) ).

tff(c_42,plain,
    product(additive_inverse(a),additive_inverse(b),d),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_1295,plain,
    ! [V4_226,V1_223,V3_224,Y_225,Z_222,X_227,V2_221] :
      ( sum(V1_223,V2_221,V4_226)
      | ~ product(V3_224,X_227,V4_226)
      | ~ sum(Y_225,Z_222,V3_224)
      | ~ product(Z_222,X_227,V2_221)
      | ~ product(Y_225,X_227,V1_223) ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_16048,plain,
    ! [Y_541,V2_538,X_540,Y_539,V1_537,Z_542] :
      ( sum(V1_537,V2_538,multiply(X_540,Y_541))
      | ~ sum(Y_539,Z_542,X_540)
      | ~ product(Z_542,Y_541,V2_538)
      | ~ product(Y_539,Y_541,V1_537) ),
    inference(resolution,[status(thm)],[c_6,c_1295]) ).

tff(c_76724,plain,
    ! [V1_1091,V2_1092,X_1093,Y_1094] :
      ( sum(V1_1091,V2_1092,multiply(X_1093,Y_1094))
      | ~ product(X_1093,Y_1094,V2_1092)
      | ~ product(additive_identity,Y_1094,V1_1091) ),
    inference(resolution,[status(thm)],[c_2,c_16048]) ).

tff(c_348,plain,
    ! [X_119,W_120,Y_121,Z_122] :
      ( ( X_119 = W_120 )
      | ~ sum(W_120,Y_121,Z_122)
      | ~ sum(X_119,Y_121,Z_122) ),
    inference(cnfTransformation,[status(thm)],[f_195]) ).

tff(c_365,plain,
    ! [X_119,X_1] :
      ( ( additive_identity = X_119 )
      | ~ sum(X_119,X_1,X_1) ),
    inference(resolution,[status(thm)],[c_2,c_348]) ).

tff(c_77051,plain,
    ! [V1_1091,X_1093,Y_1094] :
      ( ( additive_identity = V1_1091 )
      | ~ product(X_1093,Y_1094,multiply(X_1093,Y_1094))
      | ~ product(additive_identity,Y_1094,V1_1091) ),
    inference(resolution,[status(thm)],[c_76724,c_365]) ).

tff(c_77215,plain,
    ! [V1_1095,Y_1096] :
      ( ( additive_identity = V1_1095 )
      | ~ product(additive_identity,Y_1096,V1_1095) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_77051]) ).

tff(c_77291,plain,
    ! [Y_4] : ( multiply(additive_identity,Y_4) = additive_identity ),
    inference(resolution,[status(thm)],[c_6,c_77215]) ).

tff(c_16153,plain,
    ! [V1_537,V2_538,Y_541,X_8] :
      ( sum(V1_537,V2_538,multiply(additive_identity,Y_541))
      | ~ product(additive_inverse(X_8),Y_541,V2_538)
      | ~ product(X_8,Y_541,V1_537) ),
    inference(resolution,[status(thm)],[c_12,c_16048]) ).

tff(c_99139,plain,
    ! [V1_1327,V2_1328,X_1329,Y_1330] :
      ( sum(V1_1327,V2_1328,additive_identity)
      | ~ product(additive_inverse(X_1329),Y_1330,V2_1328)
      | ~ product(X_1329,Y_1330,V1_1327) ),
    inference(demodulation,[status(thm),theory(equality)],[c_77291,c_16153]) ).

tff(c_99289,plain,
    ! [V1_1332] :
      ( sum(V1_1332,d,additive_identity)
      | ~ product(a,additive_inverse(b),V1_1332) ),
    inference(resolution,[status(thm)],[c_42,c_99139]) ).

tff(c_99320,plain,
    sum(multiply(a,additive_inverse(b)),d,additive_identity),
    inference(resolution,[status(thm)],[c_6,c_99289]) ).

tff(c_99329,plain,
    sum(additive_inverse(c),d,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_98989,c_99320]) ).

tff(c_2227,plain,
    ! [U_274,X_275,X_276] :
      ( sum(U_274,X_275,X_276)
      | ~ sum(X_276,additive_inverse(X_275),U_274) ),
    inference(resolution,[status(thm)],[c_10,c_1992]) ).

tff(c_2469,plain,
    ! [X_281,X_282] : sum(add(X_281,additive_inverse(X_282)),X_282,X_281),
    inference(resolution,[status(thm)],[c_8,c_2227]) ).

tff(c_361,plain,
    ! [Y_6,X_119,X_5] :
      ( ( Y_6 = X_119 )
      | ~ sum(X_119,X_5,add(X_5,Y_6)) ),
    inference(resolution,[status(thm)],[c_62,c_348]) ).

tff(c_3908,plain,
    ! [X_307,Y_308] : ( add(add(X_307,Y_308),additive_inverse(X_307)) = Y_308 ),
    inference(resolution,[status(thm)],[c_2469,c_361]) ).

tff(c_89,plain,
    ! [Y_93,X_5,Y_6] :
      ( ( Y_93 = X_5 )
      | ~ sum(Y_6,Y_93,add(X_5,Y_6)) ),
    inference(resolution,[status(thm)],[c_62,c_76]) ).

tff(c_3969,plain,
    ! [X_307,Y_308,Y_93] :
      ( ( add(X_307,Y_308) = Y_93 )
      | ~ sum(additive_inverse(X_307),Y_93,Y_308) ),
    inference(superposition,[status(thm),theory(equality)],[c_3908,c_89]) ).

tff(c_99372,plain,
    add(c,additive_identity) = d,
    inference(resolution,[status(thm)],[c_99329,c_3969]) ).

tff(c_99464,plain,
    d = c,
    inference(demodulation,[status(thm),theory(equality)],[c_115,c_99372]) ).

tff(c_99466,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_44,c_99464]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 18:22:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 24.26/11.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.26/11.85  
% 24.26/11.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.26/11.89  
% 24.26/11.89  Inference rules
% 24.26/11.89  ----------------------
% 24.26/11.89  #Ref     : 0
% 24.26/11.89  #Sup     : 24611
% 24.26/11.89  #Fact    : 0
% 24.26/11.89  #Define  : 0
% 24.26/11.89  #Split   : 8
% 24.26/11.89  #Chain   : 0
% 24.26/11.89  #Close   : 0
% 24.26/11.89  
% 24.26/11.89  Ordering : KBO
% 24.26/11.89  
% 24.26/11.89  Simplification rules
% 24.26/11.89  ----------------------
% 24.26/11.89  #Subsume      : 6817
% 24.26/11.89  #Demod        : 11781
% 24.26/11.89  #Tautology    : 4293
% 24.26/11.89  #SimpNegUnit  : 12
% 24.26/11.89  #BackRed      : 12
% 24.26/11.89  
% 24.26/11.89  #Partial instantiations: 0
% 24.26/11.89  #Strategies tried      : 1
% 24.26/11.89  
% 24.26/11.89  Timing (in seconds)
% 24.26/11.89  ----------------------
% 24.81/11.89  Preprocessing        : 0.50
% 24.81/11.89  Parsing              : 0.26
% 24.81/11.89  CNF conversion       : 0.03
% 24.81/11.89  Main loop            : 10.32
% 24.81/11.89  Inferencing          : 1.54
% 24.81/11.89  Reduction            : 3.28
% 24.81/11.89  Demodulation         : 2.63
% 24.81/11.89  BG Simplification    : 0.13
% 24.81/11.89  Subsumption          : 4.55
% 24.81/11.89  Abstraction          : 0.17
% 24.81/11.89  MUC search           : 0.00
% 24.81/11.89  Cooper               : 0.00
% 24.81/11.89  Total                : 10.89
% 24.81/11.89  Index Insertion      : 0.00
% 24.81/11.89  Index Deletion       : 0.00
% 24.81/11.89  Index Matching       : 0.00
% 24.81/11.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------