TSTP Solution File: CAT003-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : CAT003-1 : 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 : n012.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 10:34:35 EDT 2023

% Result   : Unsatisfiable 84.29s 70.33s
% Output   : CNFRefutation 84.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   86 (  28 unt;  12 typ;   0 def)
%            Number of atoms       :  161 (  14 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  176 (  89   ~;  87   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  127 (; 127   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > defined > identity_map > compose > #nlpp > domain > codomain > h > g > d > c > b > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(h,type,
    h: $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_185,axiom,
    h != g,
    file(unknown,unknown) ).

tff(f_182,axiom,
    product(h,a,d),
    file(unknown,unknown) ).

tff(f_138,axiom,
    ! [X] : defined(X,domain(X)),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ! [X] : identity_map(domain(X)),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X,Y,Xy,Z] :
      ( ~ product(X,Y,Xy)
      | ~ defined(Xy,Z)
      | defined(Y,Z) ),
    file(unknown,unknown) ).

tff(f_161,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | ~ identity_map(Y)
      | product(X,Y,X) ),
    file(unknown,unknown) ).

tff(f_173,axiom,
    product(a,b,c),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | defined(X,Y) ),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ! [X,Y,Z] :
      ( ~ defined(X,Y)
      | ~ defined(Y,Z)
      | ~ identity_map(Y)
      | defined(X,Z) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [X] : identity_map(codomain(X)),
    file(unknown,unknown) ).

tff(f_140,axiom,
    ! [X] : defined(codomain(X),X),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ! [Y,Z,Yz,X] :
      ( ~ product(Y,Z,Yz)
      | ~ defined(X,Yz)
      | defined(X,Y) ),
    file(unknown,unknown) ).

tff(f_153,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | ~ identity_map(X)
      | product(X,Y,Y) ),
    file(unknown,unknown) ).

tff(f_183,axiom,
    product(g,a,d),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | product(X,Y,compose(X,Y)) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [Xyz,Z,Yz,X,Y,Xy] :
      ( ~ product(Y,Z,Yz)
      | ~ product(X,Yz,Xyz)
      | ~ product(X,Y,Xy)
      | product(Xy,Z,Xyz) ),
    file(unknown,unknown) ).

tff(f_170,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | ( Z = W ) ),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ! [Xyz,Z,Yz,X,Y,Xy] :
      ( ~ product(X,Y,Xy)
      | ~ product(Xy,Z,Xyz)
      | ~ product(Y,Z,Yz)
      | product(X,Yz,Xyz) ),
    file(unknown,unknown) ).

tff(f_181,axiom,
    ! [X,W,Y] :
      ( ~ product(X,c,W)
      | ~ product(Y,c,W)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(c_46,plain,
    h != g,
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_42,plain,
    product(h,a,d),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_24,plain,
    ! [X_41] : defined(X_41,domain(X_41)),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_20,plain,
    ! [X_39] : identity_map(domain(X_39)),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_232,plain,
    ! [Y_85,Z_86,Xy_87,X_88] :
      ( defined(Y_85,Z_86)
      | ~ defined(Xy_87,Z_86)
      | ~ product(X_88,Y_85,Xy_87) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_949,plain,
    ! [Y_143,X_144,X_145] :
      ( defined(Y_143,domain(X_144))
      | ~ product(X_145,Y_143,X_144) ),
    inference(resolution,[status(thm)],[c_24,c_232]) ).

tff(c_974,plain,
    defined(a,domain(d)),
    inference(resolution,[status(thm)],[c_42,c_949]) ).

tff(c_34,plain,
    ! [X_47,Y_48] :
      ( product(X_47,Y_48,X_47)
      | ~ identity_map(Y_48)
      | ~ defined(X_47,Y_48) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_38,plain,
    product(a,b,c),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_53,plain,
    ! [X_62,Y_63,Z_64] :
      ( defined(X_62,Y_63)
      | ~ product(X_62,Y_63,Z_64) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_74,plain,
    defined(a,b),
    inference(resolution,[status(thm)],[c_38,c_53]) ).

tff(c_800,plain,
    ! [Y_135,X_136] :
      ( defined(Y_135,b)
      | ~ product(X_136,Y_135,a) ),
    inference(resolution,[status(thm)],[c_74,c_232]) ).

tff(c_1528,plain,
    ! [Y_170] :
      ( defined(Y_170,b)
      | ~ identity_map(Y_170)
      | ~ defined(a,Y_170) ),
    inference(resolution,[status(thm)],[c_34,c_800]) ).

tff(c_1533,plain,
    ( defined(domain(d),b)
    | ~ identity_map(domain(d)) ),
    inference(resolution,[status(thm)],[c_974,c_1528]) ).

tff(c_1546,plain,
    defined(domain(d),b),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_1533]) ).

tff(c_18,plain,
    ! [X_36,Z_38,Y_37] :
      ( defined(X_36,Z_38)
      | ~ identity_map(Y_37)
      | ~ defined(Y_37,Z_38)
      | ~ defined(X_36,Y_37) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_1559,plain,
    ! [X_36] :
      ( defined(X_36,b)
      | ~ identity_map(domain(d))
      | ~ defined(X_36,domain(d)) ),
    inference(resolution,[status(thm)],[c_1546,c_18]) ).

tff(c_1571,plain,
    ! [X_171] :
      ( defined(X_171,b)
      | ~ defined(X_171,domain(d)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_1559]) ).

tff(c_1596,plain,
    defined(d,b),
    inference(resolution,[status(thm)],[c_24,c_1571]) ).

tff(c_22,plain,
    ! [X_40] : identity_map(codomain(X_40)),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_26,plain,
    ! [X_42] : defined(codomain(X_42),X_42),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_188,plain,
    ! [X_80,Y_81,Yz_82,Z_83] :
      ( defined(X_80,Y_81)
      | ~ defined(X_80,Yz_82)
      | ~ product(Y_81,Z_83,Yz_82) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_1307,plain,
    ! [X_159,Y_160,Z_161] :
      ( defined(codomain(X_159),Y_160)
      | ~ product(Y_160,Z_161,X_159) ),
    inference(resolution,[status(thm)],[c_26,c_188]) ).

tff(c_1341,plain,
    defined(codomain(c),a),
    inference(resolution,[status(thm)],[c_38,c_1307]) ).

tff(c_32,plain,
    ! [X_45,Y_46] :
      ( product(X_45,Y_46,Y_46)
      | ~ identity_map(X_45)
      | ~ defined(X_45,Y_46) ),
    inference(cnfTransformation,[status(thm)],[f_153]) ).

tff(c_44,plain,
    product(g,a,d),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_75,plain,
    defined(g,a),
    inference(resolution,[status(thm)],[c_44,c_53]) ).

tff(c_840,plain,
    ! [Y_137,Z_138] :
      ( defined(g,Y_137)
      | ~ product(Y_137,Z_138,a) ),
    inference(resolution,[status(thm)],[c_75,c_188]) ).

tff(c_1788,plain,
    ! [X_181] :
      ( defined(g,X_181)
      | ~ identity_map(X_181)
      | ~ defined(X_181,a) ),
    inference(resolution,[status(thm)],[c_32,c_840]) ).

tff(c_1790,plain,
    ( defined(g,codomain(c))
    | ~ identity_map(codomain(c)) ),
    inference(resolution,[status(thm)],[c_1341,c_1788]) ).

tff(c_1804,plain,
    defined(g,codomain(c)),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1790]) ).

tff(c_294,plain,
    ! [X_90,Z_91,Y_92] :
      ( defined(X_90,Z_91)
      | ~ identity_map(Y_92)
      | ~ defined(Y_92,Z_91)
      | ~ defined(X_90,Y_92) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_304,plain,
    ! [X_90,X_42] :
      ( defined(X_90,X_42)
      | ~ identity_map(codomain(X_42))
      | ~ defined(X_90,codomain(X_42)) ),
    inference(resolution,[status(thm)],[c_26,c_294]) ).

tff(c_311,plain,
    ! [X_90,X_42] :
      ( defined(X_90,X_42)
      | ~ defined(X_90,codomain(X_42)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_304]) ).

tff(c_1839,plain,
    defined(g,c),
    inference(resolution,[status(thm)],[c_1804,c_311]) ).

tff(c_2,plain,
    ! [X_1,Y_2] :
      ( product(X_1,Y_2,compose(X_1,Y_2))
      | ~ defined(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_735,plain,
    ! [Xy_128,Yz_129,Xyz_131,X_130,Y_132,Z_127] :
      ( product(Xy_128,Z_127,Xyz_131)
      | ~ product(X_130,Y_132,Xy_128)
      | ~ product(X_130,Yz_129,Xyz_131)
      | ~ product(Y_132,Z_127,Yz_129) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_3634,plain,
    ! [Z_268,Xyz_269,Yz_270] :
      ( product(d,Z_268,Xyz_269)
      | ~ product(g,Yz_270,Xyz_269)
      | ~ product(a,Z_268,Yz_270) ),
    inference(resolution,[status(thm)],[c_44,c_735]) ).

tff(c_28246,plain,
    ! [Z_707,Y_708] :
      ( product(d,Z_707,compose(g,Y_708))
      | ~ product(a,Z_707,Y_708)
      | ~ defined(g,Y_708) ),
    inference(resolution,[status(thm)],[c_2,c_3634]) ).

tff(c_125,plain,
    ! [Z_75,W_76,X_77,Y_78] :
      ( ( Z_75 = W_76 )
      | ~ product(X_77,Y_78,W_76)
      | ~ product(X_77,Y_78,Z_75) ),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_143,plain,
    ! [X_1,Y_2,Z_75] :
      ( ( compose(X_1,Y_2) = Z_75 )
      | ~ product(X_1,Y_2,Z_75)
      | ~ defined(X_1,Y_2) ),
    inference(resolution,[status(thm)],[c_2,c_125]) ).

tff(c_408601,plain,
    ! [Y_2732,Z_2733] :
      ( ( compose(g,Y_2732) = compose(d,Z_2733) )
      | ~ defined(d,Z_2733)
      | ~ product(a,Z_2733,Y_2732)
      | ~ defined(g,Y_2732) ),
    inference(resolution,[status(thm)],[c_28246,c_143]) ).

tff(c_408851,plain,
    ( ( compose(g,c) = compose(d,b) )
    | ~ defined(d,b)
    | ~ defined(g,c) ),
    inference(resolution,[status(thm)],[c_38,c_408601]) ).

tff(c_408983,plain,
    compose(g,c) = compose(d,b),
    inference(demodulation,[status(thm),theory(equality)],[c_1839,c_1596,c_408851]) ).

tff(c_409257,plain,
    ( product(g,c,compose(d,b))
    | ~ defined(g,c) ),
    inference(superposition,[status(thm),theory(equality)],[c_408983,c_2]) ).

tff(c_409442,plain,
    product(g,c,compose(d,b)),
    inference(demodulation,[status(thm),theory(equality)],[c_1839,c_409257]) ).

tff(c_562,plain,
    ! [X_119,Yz_118,Xy_116,Xyz_120,Z_117,Y_121] :
      ( product(X_119,Yz_118,Xyz_120)
      | ~ product(Y_121,Z_117,Yz_118)
      | ~ product(Xy_116,Z_117,Xyz_120)
      | ~ product(X_119,Y_121,Xy_116) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_4037,plain,
    ! [X_285,Xyz_286,Xy_287] :
      ( product(X_285,c,Xyz_286)
      | ~ product(Xy_287,b,Xyz_286)
      | ~ product(X_285,a,Xy_287) ),
    inference(resolution,[status(thm)],[c_38,c_562]) ).

tff(c_17612,plain,
    ! [X_577,X_578] :
      ( product(X_577,c,compose(X_578,b))
      | ~ product(X_577,a,X_578)
      | ~ defined(X_578,b) ),
    inference(resolution,[status(thm)],[c_2,c_4037]) ).

tff(c_40,plain,
    ! [Y_55,X_53,W_54] :
      ( ( Y_55 = X_53 )
      | ~ product(Y_55,c,W_54)
      | ~ product(X_53,c,W_54) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_17734,plain,
    ! [X_577,X_53,X_578] :
      ( ( X_577 = X_53 )
      | ~ product(X_53,c,compose(X_578,b))
      | ~ product(X_577,a,X_578)
      | ~ defined(X_578,b) ),
    inference(resolution,[status(thm)],[c_17612,c_40]) ).

tff(c_409455,plain,
    ! [X_577] :
      ( ( g = X_577 )
      | ~ product(X_577,a,d)
      | ~ defined(d,b) ),
    inference(resolution,[status(thm)],[c_409442,c_17734]) ).

tff(c_409717,plain,
    ! [X_2734] :
      ( ( g = X_2734 )
      | ~ product(X_2734,a,d) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1596,c_409455]) ).

tff(c_409772,plain,
    h = g,
    inference(resolution,[status(thm)],[c_42,c_409717]) ).

tff(c_409794,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_409772]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : CAT003-1 : 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
% 0.14/0.35  % Computer : n012.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 17:43:07 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 84.29/70.33  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.29/70.34  
% 84.29/70.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 84.50/70.39  
% 84.50/70.39  Inference rules
% 84.50/70.39  ----------------------
% 84.50/70.39  #Ref     : 0
% 84.50/70.39  #Sup     : 84326
% 84.50/70.39  #Fact    : 0
% 84.50/70.39  #Define  : 0
% 84.50/70.39  #Split   : 66
% 84.50/70.39  #Chain   : 0
% 84.50/70.39  #Close   : 0
% 84.50/70.39  
% 84.50/70.39  Ordering : KBO
% 84.50/70.39  
% 84.50/70.39  Simplification rules
% 84.50/70.39  ----------------------
% 84.50/70.39  #Subsume      : 46395
% 84.50/70.39  #Demod        : 68262
% 84.50/70.39  #Tautology    : 9543
% 84.50/70.39  #SimpNegUnit  : 4194
% 84.50/70.39  #BackRed      : 100
% 84.50/70.39  
% 84.50/70.39  #Partial instantiations: 0
% 84.50/70.39  #Strategies tried      : 1
% 84.50/70.39  
% 84.50/70.39  Timing (in seconds)
% 84.50/70.39  ----------------------
% 84.50/70.39  Preprocessing        : 0.49
% 84.50/70.39  Parsing              : 0.26
% 84.50/70.39  CNF conversion       : 0.03
% 84.50/70.39  Main loop            : 68.82
% 84.50/70.39  Inferencing          : 6.61
% 84.50/70.39  Reduction            : 20.50
% 84.50/70.39  Demodulation         : 13.50
% 84.50/70.39  BG Simplification    : 0.27
% 84.50/70.39  Subsumption          : 35.72
% 84.50/70.39  Abstraction          : 0.56
% 84.50/70.39  MUC search           : 0.00
% 84.50/70.39  Cooper               : 0.00
% 84.50/70.39  Total                : 69.37
% 84.50/70.39  Index Insertion      : 0.00
% 84.50/70.39  Index Deletion       : 0.00
% 84.50/70.39  Index Matching       : 0.00
% 84.50/70.39  BG Taut test         : 0.00
%------------------------------------------------------------------------------