TSTP Solution File: HEN009-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN009-3 : 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/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 : n005.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 10:42:18 EDT 2023

% Result   : Unsatisfiable 6.53s 2.63s
% Output   : CNFRefutation 6.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   89 (  55 unt;   8 typ;   0 def)
%            Number of atoms       :  114 (  70 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   68 (  35   ~;  33   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (;  68   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > d > c > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(f_84,axiom,
    b != d,
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X] : less_equal(zero,X),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ( divide(X,Y) = zero ) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ! [X] : less_equal(X,identity),
    file(unknown,unknown) ).

tff(f_82,axiom,
    divide(identity,c) = d,
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X,Y] : less_equal(divide(X,Y),X),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X,Y] :
      ( ( divide(X,Y) != zero )
      | less_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_81,axiom,
    divide(identity,b) = c,
    file(unknown,unknown) ).

tff(f_80,axiom,
    divide(identity,a) = b,
    file(unknown,unknown) ).

tff(c_24,plain,
    d != b,
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_10,plain,
    ! [X_10] : less_equal(zero,X_10),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_53,plain,
    ! [X_18,Y_19] :
      ( ( divide(X_18,Y_19) = zero )
      | ~ less_equal(X_18,Y_19) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_64,plain,
    ! [X_10] : ( divide(zero,X_10) = zero ),
    inference(resolution,[status(thm)],[c_10,c_53]) ).

tff(c_14,plain,
    ! [X_13] : less_equal(X_13,identity),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_65,plain,
    ! [X_13] : ( divide(X_13,identity) = zero ),
    inference(resolution,[status(thm)],[c_14,c_53]) ).

tff(c_22,plain,
    divide(identity,c) = d,
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_191,plain,
    ! [X_30,Z_31,Y_32] : less_equal(divide(divide(X_30,Z_31),divide(Y_32,Z_31)),divide(divide(X_30,Y_32),Z_31)),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_249,plain,
    ! [X_30] : less_equal(divide(divide(X_30,c),d),divide(divide(X_30,identity),c)),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_191]) ).

tff(c_308,plain,
    ! [X_35] : less_equal(divide(divide(X_35,c),d),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_249]) ).

tff(c_148,plain,
    ! [Y_26,X_27] :
      ( ( Y_26 = X_27 )
      | ~ less_equal(Y_26,X_27)
      | ~ less_equal(X_27,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_159,plain,
    ! [X_10] :
      ( ( zero = X_10 )
      | ~ less_equal(X_10,zero) ),
    inference(resolution,[status(thm)],[c_10,c_148]) ).

tff(c_328,plain,
    ! [X_35] : ( divide(divide(X_35,c),d) = zero ),
    inference(resolution,[status(thm)],[c_308,c_159]) ).

tff(c_6,plain,
    ! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_63,plain,
    ! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
    inference(resolution,[status(thm)],[c_6,c_53]) ).

tff(c_877,plain,
    ! [X_46,Y_47] : less_equal(divide(divide(X_46,X_46),divide(Y_47,X_46)),zero),
    inference(superposition,[status(thm),theory(equality)],[c_63,c_191]) ).

tff(c_968,plain,
    ! [X_48] : less_equal(divide(divide(X_48,X_48),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_63,c_877]) ).

tff(c_4,plain,
    ! [X_3,Y_4] :
      ( less_equal(X_3,Y_4)
      | ( divide(X_3,Y_4) != zero ) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_157,plain,
    ! [Y_4,X_3] :
      ( ( Y_4 = X_3 )
      | ~ less_equal(Y_4,X_3)
      | ( divide(X_3,Y_4) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_148]) ).

tff(c_971,plain,
    ! [X_48] :
      ( ( divide(divide(X_48,X_48),zero) = zero )
      | ( divide(zero,divide(divide(X_48,X_48),zero)) != zero ) ),
    inference(resolution,[status(thm)],[c_968,c_157]) ).

tff(c_1049,plain,
    ! [X_50] : ( divide(divide(X_50,X_50),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_971]) ).

tff(c_161,plain,
    ! [X_28] :
      ( ( zero = X_28 )
      | ~ less_equal(X_28,zero) ),
    inference(resolution,[status(thm)],[c_10,c_148]) ).

tff(c_174,plain,
    ! [X_3] :
      ( ( zero = X_3 )
      | ( divide(X_3,zero) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_161]) ).

tff(c_1102,plain,
    ! [X_50] : ( divide(X_50,X_50) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_1049,c_174]) ).

tff(c_20,plain,
    divide(identity,b) = c,
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_1390,plain,
    ! [Z_53] : less_equal(divide(divide(identity,Z_53),divide(b,Z_53)),divide(c,Z_53)),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_191]) ).

tff(c_1431,plain,
    less_equal(divide(d,divide(b,c)),divide(c,c)),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_1390]) ).

tff(c_1445,plain,
    less_equal(divide(d,divide(b,c)),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_1102,c_1431]) ).

tff(c_1448,plain,
    ( ( divide(d,divide(b,c)) = zero )
    | ( divide(zero,divide(d,divide(b,c))) != zero ) ),
    inference(resolution,[status(thm)],[c_1445,c_157]) ).

tff(c_1459,plain,
    divide(d,divide(b,c)) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_1448]) ).

tff(c_683,plain,
    ! [Y_41,X_42] :
      ( ( Y_41 = X_42 )
      | ~ less_equal(Y_41,X_42)
      | ( divide(X_42,Y_41) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_148]) ).

tff(c_4291,plain,
    ! [Y_76,X_77] :
      ( ( Y_76 = X_77 )
      | ( divide(Y_76,X_77) != zero )
      | ( divide(X_77,Y_76) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_683]) ).

tff(c_4311,plain,
    ( ( divide(b,c) = d )
    | ( divide(divide(b,c),d) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1459,c_4291]) ).

tff(c_4342,plain,
    divide(b,c) = d,
    inference(demodulation,[status(thm),theory(equality)],[c_328,c_4311]) ).

tff(c_4629,plain,
    divide(d,b) = zero,
    inference(superposition,[status(thm),theory(equality)],[c_4342,c_63]) ).

tff(c_18,plain,
    divide(identity,a) = b,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_258,plain,
    ! [X_30] : less_equal(divide(divide(X_30,a),b),divide(divide(X_30,identity),a)),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).

tff(c_336,plain,
    ! [X_36] : less_equal(divide(divide(X_36,a),b),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_258]) ).

tff(c_356,plain,
    ! [X_36] : ( divide(divide(X_36,a),b) = zero ),
    inference(resolution,[status(thm)],[c_336,c_159]) ).

tff(c_240,plain,
    ! [X_30] : less_equal(divide(divide(X_30,b),c),divide(divide(X_30,identity),b)),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_191]) ).

tff(c_543,plain,
    ! [X_39] : less_equal(divide(divide(X_39,b),c),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_65,c_240]) ).

tff(c_567,plain,
    ! [X_39] : ( divide(divide(X_39,b),c) = zero ),
    inference(resolution,[status(thm)],[c_543,c_159]) ).

tff(c_355,plain,
    less_equal(divide(b,b),zero),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_336]) ).

tff(c_411,plain,
    divide(b,b) = zero,
    inference(resolution,[status(thm)],[c_355,c_159]) ).

tff(c_783,plain,
    ! [Z_45] : less_equal(divide(divide(identity,Z_45),divide(a,Z_45)),divide(b,Z_45)),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).

tff(c_809,plain,
    less_equal(divide(c,divide(a,b)),divide(b,b)),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_783]) ).

tff(c_823,plain,
    less_equal(divide(c,divide(a,b)),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_809]) ).

tff(c_826,plain,
    ( ( divide(c,divide(a,b)) = zero )
    | ( divide(zero,divide(c,divide(a,b))) != zero ) ),
    inference(resolution,[status(thm)],[c_823,c_157]) ).

tff(c_837,plain,
    divide(c,divide(a,b)) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_826]) ).

tff(c_4315,plain,
    ( ( divide(a,b) = c )
    | ( divide(divide(a,b),c) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_837,c_4291]) ).

tff(c_4349,plain,
    divide(a,b) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_567,c_4315]) ).

tff(c_4421,plain,
    divide(c,a) = zero,
    inference(superposition,[status(thm),theory(equality)],[c_4349,c_63]) ).

tff(c_1009,plain,
    ! [Y_49] : less_equal(divide(b,divide(Y_49,a)),divide(divide(identity,Y_49),a)),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_191]) ).

tff(c_1035,plain,
    less_equal(divide(b,divide(c,a)),divide(d,a)),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_1009]) ).

tff(c_4476,plain,
    less_equal(divide(b,zero),divide(d,a)),
    inference(demodulation,[status(thm),theory(equality)],[c_4421,c_1035]) ).

tff(c_2,plain,
    ! [X_1,Y_2] :
      ( ( divide(X_1,Y_2) = zero )
      | ~ less_equal(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_4795,plain,
    divide(divide(b,zero),divide(d,a)) = zero,
    inference(resolution,[status(thm)],[c_4476,c_2]) ).

tff(c_12,plain,
    ! [Y_12,X_11] :
      ( ( Y_12 = X_11 )
      | ~ less_equal(Y_12,X_11)
      | ~ less_equal(X_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_262,plain,
    ! [X_30,Z_31,Y_32] :
      ( ( divide(divide(X_30,Z_31),divide(Y_32,Z_31)) = divide(divide(X_30,Y_32),Z_31) )
      | ~ less_equal(divide(divide(X_30,Y_32),Z_31),divide(divide(X_30,Z_31),divide(Y_32,Z_31))) ),
    inference(resolution,[status(thm)],[c_191,c_12]) ).

tff(c_4817,plain,
    ( ( divide(divide(b,divide(d,a)),divide(zero,divide(d,a))) = divide(divide(b,zero),divide(d,a)) )
    | ~ less_equal(zero,divide(divide(b,divide(d,a)),divide(zero,divide(d,a)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_4795,c_262]) ).

tff(c_4870,plain,
    divide(divide(b,divide(d,a)),zero) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_4795,c_64,c_4817]) ).

tff(c_700,plain,
    ! [Y_4,X_3] :
      ( ( Y_4 = X_3 )
      | ( divide(Y_4,X_3) != zero )
      | ( divide(X_3,Y_4) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_683]) ).

tff(c_5357,plain,
    ( ( divide(b,divide(d,a)) = zero )
    | ( divide(zero,divide(b,divide(d,a))) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4870,c_700]) ).

tff(c_5425,plain,
    divide(b,divide(d,a)) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_5357]) ).

tff(c_5452,plain,
    ( ( divide(d,a) = b )
    | ( divide(divide(d,a),b) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5425,c_700]) ).

tff(c_5515,plain,
    divide(d,a) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_356,c_5452]) ).

tff(c_701,plain,
    ! [X_5,Y_6] :
      ( ( divide(X_5,Y_6) = X_5 )
      | ( divide(X_5,divide(X_5,Y_6)) != zero ) ),
    inference(resolution,[status(thm)],[c_6,c_683]) ).

tff(c_5545,plain,
    ( ( divide(d,a) = d )
    | ( divide(d,b) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5515,c_701]) ).

tff(c_5602,plain,
    d = b,
    inference(demodulation,[status(thm),theory(equality)],[c_4629,c_5515,c_5545]) ).

tff(c_5604,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_5602]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HEN009-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.19/0.36  % Computer : n005.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Thu Aug  3 13:07:12 EDT 2023
% 0.21/0.36  % CPUTime  : 
% 6.53/2.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.53/2.64  
% 6.53/2.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/2.69  
% 6.77/2.69  Inference rules
% 6.77/2.69  ----------------------
% 6.77/2.69  #Ref     : 0
% 6.77/2.69  #Sup     : 1402
% 6.77/2.69  #Fact    : 0
% 6.77/2.69  #Define  : 0
% 6.77/2.69  #Split   : 4
% 6.77/2.69  #Chain   : 0
% 6.77/2.69  #Close   : 0
% 6.77/2.69  
% 6.77/2.69  Ordering : KBO
% 6.77/2.69  
% 6.77/2.69  Simplification rules
% 6.77/2.69  ----------------------
% 6.77/2.69  #Subsume      : 123
% 6.77/2.69  #Demod        : 1657
% 6.77/2.69  #Tautology    : 800
% 6.77/2.69  #SimpNegUnit  : 35
% 6.77/2.69  #BackRed      : 38
% 6.77/2.69  
% 6.77/2.69  #Partial instantiations: 0
% 6.77/2.69  #Strategies tried      : 1
% 6.77/2.69  
% 6.77/2.69  Timing (in seconds)
% 6.77/2.69  ----------------------
% 6.77/2.69  Preprocessing        : 0.47
% 6.77/2.69  Parsing              : 0.24
% 6.77/2.69  CNF conversion       : 0.03
% 6.77/2.69  Main loop            : 1.11
% 6.77/2.69  Inferencing          : 0.35
% 6.77/2.69  Reduction            : 0.47
% 6.77/2.69  Demodulation         : 0.36
% 6.77/2.69  BG Simplification    : 0.03
% 6.77/2.69  Subsumption          : 0.18
% 6.77/2.69  Abstraction          : 0.04
% 6.77/2.69  MUC search           : 0.00
% 6.77/2.69  Cooper               : 0.00
% 6.77/2.69  Total                : 1.65
% 6.77/2.70  Index Insertion      : 0.00
% 6.77/2.70  Index Deletion       : 0.00
% 6.77/2.70  Index Matching       : 0.00
% 6.77/2.70  BG Taut test         : 0.00
%------------------------------------------------------------------------------