TSTP Solution File: LCL015-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL015-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n026.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 10:47:11 EDT 2023

% Result   : Unsatisfiable 178.13s 152.40s
% Output   : CNFRefutation 178.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   57 (  18 unt;   5 typ;   0 def)
%            Number of atoms       :  110 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  121 (  63   ~;  58   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  139 (; 139   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > c > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff(f_35,axiom,
    ! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(Z,equivalent(equivalent(Y,Z),X)))),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [X,Y] :
      ( ~ is_a_theorem(equivalent(X,Y))
      | ~ is_a_theorem(X)
      | is_a_theorem(Y) ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(a,b)))),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(equivalent(X_3,Y_4),equivalent(Z_5,equivalent(equivalent(Y_4,Z_5),X_3)))),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_8,plain,
    ! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(equivalent(X_8,Y_9),equivalent(Z_10,equivalent(equivalent(Y_9,Z_10),X_8)))),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_2,plain,
    ! [Y_2,X_1] :
      ( is_a_theorem(Y_2)
      | ~ is_a_theorem(X_1)
      | ~ is_a_theorem(equivalent(X_1,Y_2)) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_12,plain,
    ! [Z_10,Y_9,X_8] :
      ( is_a_theorem(equivalent(Z_10,equivalent(equivalent(Y_9,Z_10),X_8)))
      | ~ is_a_theorem(equivalent(X_8,Y_9)) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_13,plain,
    ! [Z_11,Y_12,X_13] :
      ( is_a_theorem(equivalent(Z_11,equivalent(equivalent(Y_12,Z_11),X_13)))
      | ~ is_a_theorem(equivalent(X_13,Y_12)) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_18,plain,
    ! [Y_14,Z_15,X_16] :
      ( is_a_theorem(equivalent(equivalent(Y_14,Z_15),X_16))
      | ~ is_a_theorem(Z_15)
      | ~ is_a_theorem(equivalent(X_16,Y_14)) ),
    inference(resolution,[status(thm)],[c_13,c_2]) ).

tff(c_33,plain,
    ! [X_17,Y_18,Z_19] :
      ( is_a_theorem(X_17)
      | ~ is_a_theorem(equivalent(Y_18,Z_19))
      | ~ is_a_theorem(Z_19)
      | ~ is_a_theorem(equivalent(X_17,Y_18)) ),
    inference(resolution,[status(thm)],[c_18,c_2]) ).

tff(c_54,plain,
    ! [X_24,Z_25,Y_26,X_27] :
      ( is_a_theorem(X_24)
      | ~ is_a_theorem(equivalent(Z_25,equivalent(equivalent(Y_26,Z_25),X_27)))
      | ~ is_a_theorem(equivalent(X_24,equivalent(X_27,Y_26))) ),
    inference(resolution,[status(thm)],[c_4,c_33]) ).

tff(c_66,plain,
    ! [X_28,X_29,Y_30] :
      ( is_a_theorem(X_28)
      | ~ is_a_theorem(equivalent(X_28,equivalent(X_29,Y_30)))
      | ~ is_a_theorem(equivalent(X_29,Y_30)) ),
    inference(resolution,[status(thm)],[c_12,c_54]) ).

tff(c_94,plain,
    ! [X_34,Y_35,Z_36] :
      ( is_a_theorem(equivalent(X_34,Y_35))
      | ~ is_a_theorem(equivalent(Z_36,equivalent(equivalent(Y_35,Z_36),X_34))) ),
    inference(resolution,[status(thm)],[c_4,c_66]) ).

tff(c_108,plain,
    ! [Y_4,Y_35,X_3] : is_a_theorem(equivalent(equivalent(equivalent(Y_4,equivalent(Y_35,equivalent(X_3,Y_4))),X_3),Y_35)),
    inference(resolution,[status(thm)],[c_4,c_94]) ).

tff(c_17,plain,
    ! [Y_12,Z_11,X_13] :
      ( is_a_theorem(equivalent(equivalent(Y_12,Z_11),X_13))
      | ~ is_a_theorem(Z_11)
      | ~ is_a_theorem(equivalent(X_13,Y_12)) ),
    inference(resolution,[status(thm)],[c_13,c_2]) ).

tff(c_80,plain,
    ! [Z_31,Y_32,X_33] :
      ( is_a_theorem(Z_31)
      | ~ is_a_theorem(equivalent(equivalent(Y_32,Z_31),X_33))
      | ~ is_a_theorem(equivalent(X_33,Y_32)) ),
    inference(resolution,[status(thm)],[c_12,c_66]) ).

tff(c_176,plain,
    ! [Y_49,Z_50,X_51] :
      ( is_a_theorem(Y_49)
      | ~ is_a_theorem(equivalent(equivalent(Z_50,equivalent(equivalent(Y_49,Z_50),X_51)),X_51)) ),
    inference(resolution,[status(thm)],[c_4,c_80]) ).

tff(c_188,plain,
    ! [Y_55,Y_56,X_57] :
      ( is_a_theorem(Y_55)
      | ~ is_a_theorem(equivalent(equivalent(Y_55,Y_56),X_57))
      | ~ is_a_theorem(equivalent(X_57,Y_56)) ),
    inference(resolution,[status(thm)],[c_17,c_176]) ).

tff(c_294,plain,
    ! [Y_74,Y_75,X_76] :
      ( is_a_theorem(equivalent(Y_74,equivalent(Y_75,equivalent(X_76,Y_74))))
      | ~ is_a_theorem(equivalent(Y_75,X_76)) ),
    inference(resolution,[status(thm)],[c_108,c_188]) ).

tff(c_79,plain,
    ! [X_3,Y_4,Z_5] :
      ( is_a_theorem(equivalent(X_3,Y_4))
      | ~ is_a_theorem(equivalent(Z_5,equivalent(equivalent(Y_4,Z_5),X_3))) ),
    inference(resolution,[status(thm)],[c_4,c_66]) ).

tff(c_1191,plain,
    ! [X_121,Y_122,Y_123] :
      ( is_a_theorem(equivalent(equivalent(X_121,Y_122),Y_123))
      | ~ is_a_theorem(equivalent(equivalent(Y_123,Y_122),X_121)) ),
    inference(resolution,[status(thm)],[c_294,c_79]) ).

tff(c_5168,plain,
    ! [Z_305,Y_306,X_307] : is_a_theorem(equivalent(equivalent(equivalent(Z_305,equivalent(equivalent(Y_306,Z_305),X_307)),Y_306),X_307)),
    inference(resolution,[status(thm)],[c_4,c_1191]) ).

tff(c_109,plain,
    ! [X_37,Y_38,Z_39,X_40] :
      ( is_a_theorem(X_37)
      | ~ is_a_theorem(equivalent(equivalent(Y_38,Z_39),X_40))
      | ~ is_a_theorem(equivalent(X_37,Z_39))
      | ~ is_a_theorem(equivalent(X_40,Y_38)) ),
    inference(resolution,[status(thm)],[c_12,c_33]) ).

tff(c_117,plain,
    ! [X_37,Z_11,X_13,Y_12] :
      ( is_a_theorem(X_37)
      | ~ is_a_theorem(equivalent(X_37,Z_11))
      | ~ is_a_theorem(Z_11)
      | ~ is_a_theorem(equivalent(X_13,Y_12)) ),
    inference(resolution,[status(thm)],[c_17,c_109]) ).

tff(c_120,plain,
    ! [X_13,Y_12] : ~ is_a_theorem(equivalent(X_13,Y_12)),
    inference(splitLeft,[status(thm)],[c_117]) ).

tff(c_125,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_120,c_4]) ).

tff(c_126,plain,
    ! [X_37,Z_11] :
      ( is_a_theorem(X_37)
      | ~ is_a_theorem(equivalent(X_37,Z_11))
      | ~ is_a_theorem(Z_11) ),
    inference(splitRight,[status(thm)],[c_117]) ).

tff(c_603,plain,
    ! [Y_97,Y_98,X_99] :
      ( is_a_theorem(Y_97)
      | ~ is_a_theorem(equivalent(Y_98,equivalent(X_99,Y_97)))
      | ~ is_a_theorem(equivalent(Y_98,X_99)) ),
    inference(resolution,[status(thm)],[c_294,c_126]) ).

tff(c_638,plain,
    ! [Y_4,Z_5,X_3] :
      ( is_a_theorem(equivalent(equivalent(Y_4,Z_5),X_3))
      | ~ is_a_theorem(equivalent(equivalent(X_3,Y_4),Z_5)) ),
    inference(resolution,[status(thm)],[c_4,c_603]) ).

tff(c_132509,plain,
    ! [Y_2136,X_2137,Z_2138] : is_a_theorem(equivalent(equivalent(Y_2136,X_2137),equivalent(Z_2138,equivalent(equivalent(Y_2136,Z_2138),X_2137)))),
    inference(resolution,[status(thm)],[c_5168,c_638]) ).

tff(c_403397,plain,
    ! [Y_3351,Y_3352,X_3353] : is_a_theorem(equivalent(equivalent(equivalent(Y_3351,equivalent(Y_3352,equivalent(Y_3351,X_3353))),X_3353),Y_3352)),
    inference(resolution,[status(thm)],[c_132509,c_79]) ).

tff(c_404449,plain,
    ! [X_3353,Y_3352,Y_3351] : is_a_theorem(equivalent(equivalent(X_3353,Y_3352),equivalent(Y_3351,equivalent(Y_3352,equivalent(Y_3351,X_3353))))),
    inference(resolution,[status(thm)],[c_403397,c_638]) ).

tff(c_1228,plain,
    ! [Y_124,Z_125,X_126] :
      ( is_a_theorem(equivalent(equivalent(Y_124,Z_125),X_126))
      | ~ is_a_theorem(equivalent(equivalent(X_126,Y_124),Z_125)) ),
    inference(resolution,[status(thm)],[c_4,c_603]) ).

tff(c_1261,plain,
    ! [X_3,Y_35,Y_4] : is_a_theorem(equivalent(equivalent(X_3,Y_35),equivalent(Y_4,equivalent(Y_35,equivalent(X_3,Y_4))))),
    inference(resolution,[status(thm)],[c_108,c_1228]) ).

tff(c_140,plain,
    ! [Y_43,Y_44,X_45] : is_a_theorem(equivalent(equivalent(equivalent(Y_43,equivalent(Y_44,equivalent(X_45,Y_43))),X_45),Y_44)),
    inference(resolution,[status(thm)],[c_4,c_94]) ).

tff(c_206,plain,
    ! [Y_58,Y_59,X_60] :
      ( is_a_theorem(equivalent(equivalent(Y_58,equivalent(Y_59,equivalent(X_60,Y_58))),X_60))
      | ~ is_a_theorem(Y_59) ),
    inference(resolution,[status(thm)],[c_140,c_126]) ).

tff(c_508,plain,
    ! [Y_91,Y_92,X_93] :
      ( is_a_theorem(equivalent(Y_91,equivalent(Y_92,equivalent(X_93,Y_91))))
      | ~ is_a_theorem(X_93)
      | ~ is_a_theorem(Y_92) ),
    inference(resolution,[status(thm)],[c_206,c_126]) ).

tff(c_639,plain,
    ! [Y_100,X_101,Y_102] :
      ( is_a_theorem(equivalent(Y_100,equivalent(X_101,Y_102)))
      | ~ is_a_theorem(Y_102)
      | ~ is_a_theorem(X_101)
      | ~ is_a_theorem(Y_100) ),
    inference(resolution,[status(thm)],[c_508,c_2]) ).

tff(c_736,plain,
    ! [X_101,Y_102,Y_100] :
      ( is_a_theorem(equivalent(X_101,Y_102))
      | ~ is_a_theorem(Y_102)
      | ~ is_a_theorem(X_101)
      | ~ is_a_theorem(Y_100) ),
    inference(resolution,[status(thm)],[c_639,c_2]) ).

tff(c_808,plain,
    ! [Y_100] : ~ is_a_theorem(Y_100),
    inference(splitLeft,[status(thm)],[c_736]) ).

tff(c_840,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_808,c_108]) ).

tff(c_841,plain,
    ! [X_101,Y_102] :
      ( is_a_theorem(equivalent(X_101,Y_102))
      | ~ is_a_theorem(Y_102)
      | ~ is_a_theorem(X_101) ),
    inference(splitRight,[status(thm)],[c_736]) ).

tff(c_240,plain,
    ! [X_61,Y_62,Y_63,X_64] :
      ( is_a_theorem(X_61)
      | ~ is_a_theorem(equivalent(X_61,equivalent(equivalent(equivalent(Y_62,equivalent(Y_63,equivalent(X_64,Y_62))),X_64),Y_63))) ),
    inference(resolution,[status(thm)],[c_4,c_54]) ).

tff(c_10017,plain,
    ! [X_446,Y_444,Y_445,Z_448,Y_447] :
      ( is_a_theorem(equivalent(Y_444,Z_448))
      | ~ is_a_theorem(Z_448)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y_445,equivalent(Y_447,equivalent(X_446,Y_445))),X_446),Y_447),Y_444)) ),
    inference(resolution,[status(thm)],[c_17,c_240]) ).

tff(c_24409,plain,
    ! [X_772,Z_773,Y_775,Y_774,Z_776] :
      ( is_a_theorem(equivalent(equivalent(Z_773,equivalent(equivalent(Y_775,Z_773),equivalent(equivalent(Y_774,equivalent(Y_775,equivalent(X_772,Y_774))),X_772))),Z_776))
      | ~ is_a_theorem(Z_776) ),
    inference(resolution,[status(thm)],[c_4,c_10017]) ).

tff(c_162,plain,
    ! [Y_44,Y_43,X_45] :
      ( is_a_theorem(Y_44)
      | ~ is_a_theorem(equivalent(equivalent(Y_43,equivalent(Y_44,equivalent(X_45,Y_43))),X_45)) ),
    inference(resolution,[status(thm)],[c_140,c_2]) ).

tff(c_80014,plain,
    ! [Y_1778,X_1779,Y_1780] :
      ( is_a_theorem(equivalent(Y_1778,X_1779))
      | ~ is_a_theorem(equivalent(Y_1780,equivalent(Y_1778,equivalent(X_1779,Y_1780)))) ),
    inference(resolution,[status(thm)],[c_24409,c_162]) ).

tff(c_154471,plain,
    ! [Y_2287,X_2288,X_2289] :
      ( is_a_theorem(equivalent(Y_2287,X_2288))
      | ~ is_a_theorem(equivalent(Y_2287,equivalent(X_2288,X_2289)))
      | ~ is_a_theorem(X_2289) ),
    inference(resolution,[status(thm)],[c_841,c_80014]) ).

tff(c_263711,plain,
    ! [X_2837,Y_2838,Y_2839] :
      ( is_a_theorem(equivalent(equivalent(X_2837,Y_2838),Y_2839))
      | ~ is_a_theorem(equivalent(Y_2838,equivalent(X_2837,Y_2839))) ),
    inference(resolution,[status(thm)],[c_1261,c_154471]) ).

tff(c_6,plain,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(c,equivalent(a,b)))),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_266394,plain,
    ~ is_a_theorem(equivalent(equivalent(b,c),equivalent(a,equivalent(c,equivalent(a,b))))),
    inference(resolution,[status(thm)],[c_263711,c_6]) ).

tff(c_512819,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_404449,c_266394]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL015-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 13:58:46 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 178.13/152.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 178.13/152.41  
% 178.13/152.41  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 178.13/152.45  
% 178.13/152.45  Inference rules
% 178.13/152.45  ----------------------
% 178.13/152.45  #Ref     : 0
% 178.13/152.45  #Sup     : 117420
% 178.13/152.45  #Fact    : 0
% 178.13/152.45  #Define  : 0
% 178.13/152.45  #Split   : 27
% 178.13/152.45  #Chain   : 0
% 178.13/152.45  #Close   : 0
% 178.13/152.45  
% 178.13/152.45  Ordering : KBO
% 178.13/152.45  
% 178.13/152.45  Simplification rules
% 178.13/152.45  ----------------------
% 178.13/152.45  #Subsume      : 39264
% 178.13/152.45  #Demod        : 5403
% 178.13/152.45  #Tautology    : 4752
% 178.13/152.45  #SimpNegUnit  : 1896
% 178.13/152.45  #BackRed      : 191
% 178.13/152.45  
% 178.13/152.45  #Partial instantiations: 0
% 178.13/152.45  #Strategies tried      : 1
% 178.13/152.45  
% 178.13/152.45  Timing (in seconds)
% 178.13/152.45  ----------------------
% 178.13/152.46  Preprocessing        : 0.40
% 178.13/152.46  Parsing              : 0.22
% 178.13/152.46  CNF conversion       : 0.02
% 178.13/152.46  Main loop            : 150.96
% 178.13/152.46  Inferencing          : 7.78
% 178.13/152.46  Reduction            : 25.24
% 178.13/152.46  Demodulation         : 16.58
% 178.13/152.46  BG Simplification    : 0.54
% 178.13/152.46  Subsumption          : 109.25
% 178.13/152.46  Abstraction          : 0.80
% 178.13/152.46  MUC search           : 0.00
% 178.13/152.46  Cooper               : 0.00
% 178.13/152.46  Total                : 151.44
% 178.13/152.46  Index Insertion      : 0.00
% 178.13/152.46  Index Deletion       : 0.00
% 178.13/152.46  Index Matching       : 0.00
% 178.13/152.46  BG Taut test         : 0.00
%------------------------------------------------------------------------------