TSTP Solution File: FLD016-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD016-3 : 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/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 : n022.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 69.96s 56.98s
% Output   : CNFRefutation 69.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   90 (  28 unt;  14 typ;   0 def)
%            Number of atoms       :  158 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  166 (  84   ~;  82   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   96 (;  96   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > v > u > 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(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(f_256,axiom,
    ~ sum(additive_identity,u,v),
    file(unknown,unknown) ).

tff(f_252,axiom,
    defined(v),
    file(unknown,unknown) ).

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

tff(f_249,axiom,
    defined(a),
    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_254,axiom,
    sum(a,v,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_204,axiom,
    ! [X,Y] :
      ( sum(additive_identity,X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    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_83,axiom,
    ! [Y,X,Z] :
      ( sum(Y,X,Z)
      | ~ sum(X,Y,Z) ),
    file(unknown,unknown) ).

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

tff(f_253,axiom,
    sum(a,u,b),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    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_66,plain,
    ~ sum(additive_identity,u,v),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_60,plain,
    defined(v),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

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

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

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_39377,plain,
    ! [Y_65] :
      ( ~ defined(Y_65)
      | less_or_equal(Y_65,Y_65) ),
    inference(factorization,[status(thm),theory(equality)],[c_46]) ).

tff(c_64,plain,
    sum(a,v,b),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_39512,plain,
    ! [V_687,X_684,Y_686,Z_685,U_683] :
      ( ~ sum(Y_686,Z_685,V_687)
      | ~ sum(X_684,Z_685,U_683)
      | ~ less_or_equal(X_684,Y_686)
      | less_or_equal(U_683,V_687) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_39549,plain,
    ! [X_688,U_689] :
      ( ~ sum(X_688,v,U_689)
      | ~ less_or_equal(X_688,a)
      | less_or_equal(U_689,b) ),
    inference(resolution,[status(thm)],[c_64,c_39512]) ).

tff(c_39586,plain,
    ( ~ less_or_equal(a,a)
    | less_or_equal(b,b) ),
    inference(resolution,[status(thm)],[c_64,c_39549]) ).

tff(c_39631,plain,
    ~ less_or_equal(a,a),
    inference(splitLeft,[status(thm)],[c_39586]) ).

tff(c_39634,plain,
    ~ defined(a),
    inference(resolution,[status(thm)],[c_39377,c_39631]) ).

tff(c_39640,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_39634]) ).

tff(c_39642,plain,
    less_or_equal(a,a),
    inference(splitRight,[status(thm)],[c_39586]) ).

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_39700,plain,
    ! [X_707,W_708,Y_704,U_706,V_705,Z_703] :
      ( ~ sum(U_706,Z_703,W_708)
      | ~ sum(Y_704,Z_703,V_705)
      | ~ sum(X_707,Y_704,U_706)
      | sum(X_707,V_705,W_708) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_40195,plain,
    ! [Y_739,V_740,X_741] :
      ( ~ sum(Y_739,v,V_740)
      | ~ sum(X_741,Y_739,a)
      | sum(X_741,V_740,b) ),
    inference(resolution,[status(thm)],[c_64,c_39700]) ).

tff(c_40277,plain,
    ! [X_744] :
      ( ~ sum(X_744,a,a)
      | sum(X_744,b,b) ),
    inference(resolution,[status(thm)],[c_64,c_40195]) ).

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_40317,plain,
    ! [X_746] :
      ( sum(b,X_746,b)
      | ~ sum(X_746,a,a) ),
    inference(resolution,[status(thm)],[c_40277,c_10]) ).

tff(c_40320,plain,
    ( sum(b,additive_identity,b)
    | ~ less_or_equal(a,a) ),
    inference(resolution,[status(thm)],[c_42,c_40317]) ).

tff(c_40326,plain,
    sum(b,additive_identity,b),
    inference(demodulation,[status(thm),theory(equality)],[c_39642,c_40320]) ).

tff(c_40376,plain,
    sum(additive_identity,b,b),
    inference(resolution,[status(thm)],[c_40326,c_10]) ).

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_62,plain,
    sum(a,u,b),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_73,plain,
    ! [X_82,Y_83,Z_84] :
      ( ~ sum(X_82,Y_83,Z_84)
      | sum(Y_83,X_82,Z_84) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_85,plain,
    sum(u,a,b),
    inference(resolution,[status(thm)],[c_62,c_73]) ).

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

tff(c_42343,plain,
    ! [Y_800,X_801,V_802,X_803] :
      ( ~ sum(Y_800,X_801,V_802)
      | ~ sum(X_803,Y_800,additive_identity)
      | sum(X_803,V_802,X_801)
      | ~ defined(X_801) ),
    inference(resolution,[status(thm)],[c_6,c_39700]) ).

tff(c_42415,plain,
    ! [X_803] :
      ( ~ sum(X_803,u,additive_identity)
      | sum(X_803,b,a)
      | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_85,c_42343]) ).

tff(c_42513,plain,
    ! [X_804] :
      ( ~ sum(X_804,u,additive_identity)
      | sum(X_804,b,a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_42415]) ).

tff(c_42521,plain,
    ( sum(additive_inverse(u),b,a)
    | ~ defined(u) ),
    inference(resolution,[status(thm)],[c_8,c_42513]) ).

tff(c_42527,plain,
    sum(additive_inverse(u),b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_42521]) ).

tff(c_42563,plain,
    sum(b,additive_inverse(u),a),
    inference(resolution,[status(thm)],[c_42527,c_10]) ).

tff(c_39759,plain,
    ! [X_713,W_710,V_712,Z_709,U_711,Y_714] :
      ( ~ sum(X_713,V_712,W_710)
      | ~ sum(Y_714,Z_709,V_712)
      | ~ sum(X_713,Y_714,U_711)
      | sum(U_711,Z_709,W_710) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_39793,plain,
    ! [Y_714,Z_709,X_13,U_711] :
      ( ~ sum(Y_714,Z_709,X_13)
      | ~ sum(additive_identity,Y_714,U_711)
      | sum(U_711,Z_709,X_13)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_6,c_39759]) ).

tff(c_42567,plain,
    ! [U_711] :
      ( ~ sum(additive_identity,b,U_711)
      | sum(U_711,additive_inverse(u),a)
      | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_42563,c_39793]) ).

tff(c_57207,plain,
    ! [U_1054] :
      ( ~ sum(additive_identity,b,U_1054)
      | sum(U_1054,additive_inverse(u),a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_42567]) ).

tff(c_57292,plain,
    ! [U_1054] :
      ( sum(additive_inverse(u),U_1054,a)
      | ~ sum(additive_identity,b,U_1054) ),
    inference(resolution,[status(thm)],[c_57207,c_10]) ).

tff(c_42423,plain,
    ! [X_803] :
      ( ~ sum(X_803,a,additive_identity)
      | sum(X_803,b,v)
      | ~ defined(v) ),
    inference(resolution,[status(thm)],[c_64,c_42343]) ).

tff(c_42848,plain,
    ! [X_810] :
      ( ~ sum(X_810,a,additive_identity)
      | sum(X_810,b,v) ),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_42423]) ).

tff(c_42928,plain,
    ! [X_812] :
      ( sum(b,X_812,v)
      | ~ sum(X_812,a,additive_identity) ),
    inference(resolution,[status(thm)],[c_42848,c_10]) ).

tff(c_42934,plain,
    ( sum(b,additive_inverse(a),v)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_8,c_42928]) ).

tff(c_42940,plain,
    sum(b,additive_inverse(a),v),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_42934]) ).

tff(c_82,plain,
    ! [X_14] :
      ( sum(X_14,additive_inverse(X_14),additive_identity)
      | ~ defined(X_14) ),
    inference(resolution,[status(thm)],[c_8,c_73]) ).

tff(c_117560,plain,
    ! [Y_1495,X_1496,V_1497,X_1498] :
      ( ~ sum(Y_1495,additive_inverse(X_1496),V_1497)
      | ~ sum(X_1498,Y_1495,X_1496)
      | sum(X_1498,V_1497,additive_identity)
      | ~ defined(X_1496) ),
    inference(resolution,[status(thm)],[c_82,c_39700]) ).

tff(c_117736,plain,
    ! [X_1498] :
      ( ~ sum(X_1498,b,a)
      | sum(X_1498,v,additive_identity)
      | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_42940,c_117560]) ).

tff(c_192193,plain,
    ! [X_1873] :
      ( ~ sum(X_1873,b,a)
      | sum(X_1873,v,additive_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_117736]) ).

tff(c_192438,plain,
    ! [X_1874] :
      ( sum(v,X_1874,additive_identity)
      | ~ sum(X_1874,b,a) ),
    inference(resolution,[status(thm)],[c_192193,c_10]) ).

tff(c_192450,plain,
    ( sum(v,additive_inverse(u),additive_identity)
    | ~ sum(additive_identity,b,b) ),
    inference(resolution,[status(thm)],[c_57292,c_192438]) ).

tff(c_192475,plain,
    sum(v,additive_inverse(u),additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_40376,c_192450]) ).

tff(c_42505,plain,
    ! [X_803,X_14] :
      ( ~ sum(X_803,additive_inverse(X_14),additive_identity)
      | sum(X_803,additive_identity,X_14)
      | ~ defined(X_14) ),
    inference(resolution,[status(thm)],[c_8,c_42343]) ).

tff(c_193100,plain,
    ( sum(v,additive_identity,u)
    | ~ defined(u) ),
    inference(resolution,[status(thm)],[c_192475,c_42505]) ).

tff(c_193185,plain,
    sum(v,additive_identity,u),
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_193100]) ).

tff(c_193903,plain,
    sum(additive_identity,v,u),
    inference(resolution,[status(thm)],[c_193185,c_10]) ).

tff(c_83,plain,
    ! [X_13] :
      ( sum(X_13,additive_identity,X_13)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_6,c_73]) ).

tff(c_41780,plain,
    ! [Y_787,Z_788,X_789,U_790] :
      ( ~ sum(Y_787,Z_788,X_789)
      | ~ sum(additive_identity,Y_787,U_790)
      | sum(U_790,Z_788,X_789)
      | ~ defined(X_789) ),
    inference(resolution,[status(thm)],[c_6,c_39759]) ).

tff(c_41917,plain,
    ! [X_13,U_790] :
      ( ~ sum(additive_identity,X_13,U_790)
      | sum(U_790,additive_identity,X_13)
      | ~ defined(X_13) ),
    inference(resolution,[status(thm)],[c_83,c_41780]) ).

tff(c_193930,plain,
    ( sum(u,additive_identity,v)
    | ~ defined(v) ),
    inference(resolution,[status(thm)],[c_193903,c_41917]) ).

tff(c_194003,plain,
    sum(u,additive_identity,v),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_193930]) ).

tff(c_194116,plain,
    sum(additive_identity,u,v),
    inference(resolution,[status(thm)],[c_194003,c_10]) ).

tff(c_194189,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_66,c_194116]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD016-3 : 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 : n022.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 19:54:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 69.96/56.98  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.97/57.00  
% 69.97/57.00  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.97/57.04  
% 69.97/57.04  Inference rules
% 69.97/57.04  ----------------------
% 69.97/57.04  #Ref     : 0
% 69.97/57.04  #Sup     : 42826
% 69.97/57.04  #Fact    : 22
% 69.97/57.04  #Define  : 0
% 69.97/57.04  #Split   : 184
% 69.97/57.04  #Chain   : 0
% 69.97/57.04  #Close   : 0
% 69.97/57.04  
% 69.97/57.04  Ordering : KBO
% 69.97/57.04  
% 69.97/57.04  Simplification rules
% 69.97/57.04  ----------------------
% 69.97/57.04  #Subsume      : 11902
% 69.97/57.04  #Demod        : 29150
% 69.97/57.04  #Tautology    : 5572
% 69.97/57.04  #SimpNegUnit  : 1535
% 69.97/57.04  #BackRed      : 0
% 69.97/57.04  
% 69.97/57.04  #Partial instantiations: 0
% 69.97/57.04  #Strategies tried      : 1
% 69.97/57.04  
% 69.97/57.04  Timing (in seconds)
% 69.97/57.04  ----------------------
% 69.97/57.05  Preprocessing        : 0.51
% 69.97/57.05  Parsing              : 0.27
% 69.97/57.05  CNF conversion       : 0.03
% 69.97/57.05  Main loop            : 55.44
% 69.97/57.05  Inferencing          : 5.12
% 69.97/57.05  Reduction            : 28.95
% 69.97/57.05  Demodulation         : 23.84
% 69.97/57.05  BG Simplification    : 0.20
% 69.97/57.05  Subsumption          : 17.80
% 69.97/57.05  Abstraction          : 0.30
% 69.97/57.05  MUC search           : 0.00
% 69.97/57.05  Cooper               : 0.00
% 69.97/57.05  Total                : 56.02
% 69.97/57.05  Index Insertion      : 0.00
% 69.97/57.05  Index Deletion       : 0.00
% 69.97/57.05  Index Matching       : 0.00
% 69.97/57.05  BG Taut test         : 0.00
%------------------------------------------------------------------------------