TSTP Solution File: LCL036-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL036-1 : 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 : 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 10:47:13 EDT 2023

% Result   : Unsatisfiable 9.72s 3.41s
% Output   : CNFRefutation 10.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   64 (  40 unt;   4 typ;   0 def)
%            Number of atoms       :   83 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   51 (  28   ~;  23   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    7 (   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    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  193 (; 193   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > falsehood > a

%Foreground sorts:

%Background operators:

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

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

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

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

tff(f_36,axiom,
    ! [U,Z,X,Y,V] : is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))),
    file(unknown,unknown) ).

tff(f_34,axiom,
    ! [X,Y] :
      ( ~ is_a_theorem(implies(X,Y))
      | ~ is_a_theorem(X)
      | is_a_theorem(Y) ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [V_7,Z_4,Y_6,U_3,X_5] : is_a_theorem(implies(implies(implies(implies(implies(X_5,Y_6),implies(Z_4,falsehood)),U_3),V_7),implies(implies(V_7,X_5),implies(Z_4,X_5)))),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_8,plain,
    ! [U_13,X_14,Y_12,V_10,Z_11] : is_a_theorem(implies(implies(implies(implies(implies(X_14,Y_12),implies(Z_11,falsehood)),U_13),V_10),implies(implies(V_10,X_14),implies(Z_11,X_14)))),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_2,plain,
    ! [Y_2,X_1] :
      ( is_a_theorem(Y_2)
      | ~ is_a_theorem(X_1)
      | ~ is_a_theorem(implies(X_1,Y_2)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_13,plain,
    ! [Y_16,V_18,U_15,Z_19,X_17] :
      ( is_a_theorem(implies(implies(V_18,X_17),implies(Z_19,X_17)))
      | ~ is_a_theorem(implies(implies(implies(implies(X_17,Y_16),implies(Z_19,falsehood)),U_15),V_18)) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_18,plain,
    ! [Z_21,Z_24,Y_22,V_20,X_23] : is_a_theorem(implies(implies(implies(implies(V_20,X_23),implies(Z_21,X_23)),implies(X_23,Y_22)),implies(Z_24,implies(X_23,Y_22)))),
    inference(resolution,[status(thm)],[c_4,c_13]) ).

tff(c_12,plain,
    ! [U_13,X_14,Y_12,V_10,Z_11] :
      ( is_a_theorem(implies(implies(V_10,X_14),implies(Z_11,X_14)))
      | ~ is_a_theorem(implies(implies(implies(implies(X_14,Y_12),implies(Z_11,falsehood)),U_13),V_10)) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_27,plain,
    ! [Z_25,Y_26,V_27,Z_28] : is_a_theorem(implies(implies(implies(Z_25,implies(falsehood,Y_26)),V_27),implies(Z_28,V_27))),
    inference(resolution,[status(thm)],[c_18,c_12]) ).

tff(c_36,plain,
    ! [Z_29,V_30,X_31] : is_a_theorem(implies(implies(implies(Z_29,V_30),X_31),implies(falsehood,X_31))),
    inference(resolution,[status(thm)],[c_27,c_12]) ).

tff(c_43,plain,
    ! [X_31,X_14,Z_11] : is_a_theorem(implies(implies(implies(falsehood,X_31),X_14),implies(Z_11,X_14))),
    inference(resolution,[status(thm)],[c_36,c_12]) ).

tff(c_80,plain,
    ! [Z_43,V_47,X_46,Y_45,Z_44] :
      ( is_a_theorem(implies(Z_44,implies(X_46,Y_45)))
      | ~ is_a_theorem(implies(implies(implies(V_47,X_46),implies(Z_43,X_46)),implies(X_46,Y_45))) ),
    inference(resolution,[status(thm)],[c_18,c_2]) ).

tff(c_126,plain,
    ! [Z_50,Z_51,Z_52] : is_a_theorem(implies(Z_50,implies(Z_51,implies(Z_52,Z_51)))),
    inference(resolution,[status(thm)],[c_43,c_80]) ).

tff(c_150,plain,
    ! [Z_51,Z_52,Z_50] :
      ( is_a_theorem(implies(Z_51,implies(Z_52,Z_51)))
      | ~ is_a_theorem(Z_50) ),
    inference(resolution,[status(thm)],[c_126,c_2]) ).

tff(c_151,plain,
    ! [Z_50] : ~ is_a_theorem(Z_50),
    inference(splitLeft,[status(thm)],[c_150]) ).

tff(c_93,plain,
    ! [Z_44,Z_11,Z_43] : is_a_theorem(implies(Z_44,implies(Z_11,implies(Z_43,Z_11)))),
    inference(resolution,[status(thm)],[c_43,c_80]) ).

tff(c_164,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_151,c_93]) ).

tff(c_166,plain,
    ! [Z_53,Z_54] : is_a_theorem(implies(Z_53,implies(Z_54,Z_53))),
    inference(splitRight,[status(thm)],[c_150]) ).

tff(c_1509,plain,
    ! [X_180,Z_179,Y_178,Z_181,U_177] : is_a_theorem(implies(implies(implies(Z_179,implies(implies(implies(X_180,Y_178),implies(Z_181,falsehood)),U_177)),X_180),implies(Z_181,X_180))),
    inference(resolution,[status(thm)],[c_166,c_12]) ).

tff(c_3648,plain,
    ! [Z_289,X_290,X_291,Y_292] : is_a_theorem(implies(implies(implies(Z_289,X_290),X_291),implies(implies(implies(X_290,Y_292),implies(Z_289,falsehood)),X_291))),
    inference(resolution,[status(thm)],[c_1509,c_12]) ).

tff(c_368,plain,
    ! [Z_69,V_70,Z_71,Y_72] :
      ( is_a_theorem(implies(Z_69,V_70))
      | ~ is_a_theorem(implies(implies(Z_71,implies(falsehood,Y_72)),V_70)) ),
    inference(resolution,[status(thm)],[c_27,c_2]) ).

tff(c_470,plain,
    ! [Z_80,Y_81,X_82,Z_83] : is_a_theorem(implies(Z_80,implies(implies(implies(falsehood,Y_81),X_82),implies(Z_83,X_82)))),
    inference(resolution,[status(thm)],[c_4,c_368]) ).

tff(c_675,plain,
    ! [Z_104,Z_108,X_106,Y_105,X_107] : is_a_theorem(implies(implies(implies(implies(implies(falsehood,Y_105),X_106),implies(Z_104,X_106)),X_107),implies(Z_108,X_107))),
    inference(resolution,[status(thm)],[c_470,c_12]) ).

tff(c_701,plain,
    ! [Z_104,Z_108,X_106,Y_105,X_107] :
      ( is_a_theorem(implies(Z_108,X_107))
      | ~ is_a_theorem(implies(implies(implies(implies(falsehood,Y_105),X_106),implies(Z_104,X_106)),X_107)) ),
    inference(resolution,[status(thm)],[c_675,c_2]) ).

tff(c_9201,plain,
    ! [Z_466,Y_468,X_470,Z_469,Y_467] : is_a_theorem(implies(Z_469,implies(implies(implies(X_470,Y_468),implies(implies(falsehood,Y_467),falsehood)),implies(Z_466,X_470)))),
    inference(resolution,[status(thm)],[c_3648,c_701]) ).

tff(c_9360,plain,
    ! [Z_466,Y_468,X_470,Z_469,Y_467] :
      ( is_a_theorem(implies(implies(implies(X_470,Y_468),implies(implies(falsehood,Y_467),falsehood)),implies(Z_466,X_470)))
      | ~ is_a_theorem(Z_469) ),
    inference(resolution,[status(thm)],[c_9201,c_2]) ).

tff(c_9617,plain,
    ! [Z_469] : ~ is_a_theorem(Z_469),
    inference(splitLeft,[status(thm)],[c_9360]) ).

tff(c_3704,plain,
    ! [Z_104,Z_108,X_290,Y_105,Y_292] : is_a_theorem(implies(Z_108,implies(implies(implies(X_290,Y_292),implies(implies(falsehood,Y_105),falsehood)),implies(Z_104,X_290)))),
    inference(resolution,[status(thm)],[c_3648,c_701]) ).

tff(c_9715,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9617,c_3704]) ).

tff(c_9717,plain,
    ! [X_485,Y_486,Y_487,Z_488] : is_a_theorem(implies(implies(implies(X_485,Y_486),implies(implies(falsehood,Y_487),falsehood)),implies(Z_488,X_485))),
    inference(splitRight,[status(thm)],[c_9360]) ).

tff(c_9787,plain,
    ! [Z_492,X_493,Y_494,Z_495] : is_a_theorem(implies(implies(implies(Z_492,implies(X_493,Y_494)),X_493),implies(Z_495,X_493))),
    inference(resolution,[status(thm)],[c_9717,c_12]) ).

tff(c_9905,plain,
    ! [Z_496,X_497,X_498] : is_a_theorem(implies(implies(implies(Z_496,X_497),X_498),implies(X_497,X_498))),
    inference(resolution,[status(thm)],[c_9787,c_12]) ).

tff(c_15354,plain,
    ! [Z_600,X_601,X_602] : is_a_theorem(implies(implies(implies(implies(Z_600,falsehood),X_601),X_602),implies(Z_600,X_602))),
    inference(resolution,[status(thm)],[c_9905,c_12]) ).

tff(c_9903,plain,
    ! [Z_495,X_493,X_14] : is_a_theorem(implies(implies(implies(Z_495,X_493),X_14),implies(X_493,X_14))),
    inference(resolution,[status(thm)],[c_9787,c_12]) ).

tff(c_3710,plain,
    ! [X_290,Y_292,Z_289,X_291] :
      ( is_a_theorem(implies(implies(implies(X_290,Y_292),implies(Z_289,falsehood)),X_291))
      | ~ is_a_theorem(implies(implies(Z_289,X_290),X_291)) ),
    inference(resolution,[status(thm)],[c_3648,c_2]) ).

tff(c_11630,plain,
    ! [Z_534,X_535,Z_536,Y_537] :
      ( is_a_theorem(implies(Z_534,X_535))
      | ~ is_a_theorem(implies(implies(Z_536,implies(X_535,Y_537)),X_535)) ),
    inference(resolution,[status(thm)],[c_9787,c_2]) ).

tff(c_11794,plain,
    ! [Z_538,X_539,X_540] :
      ( is_a_theorem(implies(Z_538,X_539))
      | ~ is_a_theorem(implies(implies(X_539,X_540),X_539)) ),
    inference(resolution,[status(thm)],[c_3710,c_11630]) ).

tff(c_12045,plain,
    ! [Z_541,X_542] : is_a_theorem(implies(Z_541,implies(X_542,X_542))),
    inference(resolution,[status(thm)],[c_9903,c_11794]) ).

tff(c_5113,plain,
    ! [X_343,Y_344,Z_345,X_346] :
      ( is_a_theorem(implies(implies(implies(X_343,Y_344),implies(Z_345,falsehood)),X_346))
      | ~ is_a_theorem(implies(implies(Z_345,X_343),X_346)) ),
    inference(resolution,[status(thm)],[c_3648,c_2]) ).

tff(c_5174,plain,
    ! [X_346,X_343,Y_344,Z_345] :
      ( is_a_theorem(X_346)
      | ~ is_a_theorem(implies(implies(X_343,Y_344),implies(Z_345,falsehood)))
      | ~ is_a_theorem(implies(implies(Z_345,X_343),X_346)) ),
    inference(resolution,[status(thm)],[c_5113,c_2]) ).

tff(c_10018,plain,
    ! [X_346,X_497,Z_496] :
      ( is_a_theorem(X_346)
      | ~ is_a_theorem(implies(implies(X_497,implies(Z_496,X_497)),X_346)) ),
    inference(resolution,[status(thm)],[c_9905,c_5174]) ).

tff(c_12355,plain,
    ! [X_543] : is_a_theorem(implies(X_543,X_543)),
    inference(resolution,[status(thm)],[c_12045,c_10018]) ).

tff(c_12504,plain,
    ! [X_346,X_343] :
      ( is_a_theorem(X_346)
      | ~ is_a_theorem(implies(implies(X_343,X_343),X_346)) ),
    inference(resolution,[status(thm)],[c_12355,c_5174]) ).

tff(c_15527,plain,
    ! [Z_603,X_604] : is_a_theorem(implies(Z_603,implies(implies(Z_603,falsehood),X_604))),
    inference(resolution,[status(thm)],[c_15354,c_12504]) ).

tff(c_499,plain,
    ! [Z_84,Z_85,X_86,Z_87] : is_a_theorem(implies(implies(implies(Z_84,implies(Z_85,Z_84)),X_86),implies(Z_87,X_86))),
    inference(resolution,[status(thm)],[c_126,c_12]) ).

tff(c_516,plain,
    ! [Z_87,X_86,Z_84,Z_85] :
      ( is_a_theorem(implies(Z_87,X_86))
      | ~ is_a_theorem(implies(implies(Z_84,implies(Z_85,Z_84)),X_86)) ),
    inference(resolution,[status(thm)],[c_499,c_2]) ).

tff(c_8745,plain,
    ! [X_446,Y_444,Z_443,Z_442,Z_445] : is_a_theorem(implies(Z_443,implies(implies(implies(X_446,Y_444),implies(Z_442,falsehood)),implies(Z_445,implies(Z_442,X_446))))),
    inference(resolution,[status(thm)],[c_3648,c_516]) ).

tff(c_8904,plain,
    ! [X_446,Y_444,Z_443,Z_442,Z_445] :
      ( is_a_theorem(implies(implies(implies(X_446,Y_444),implies(Z_442,falsehood)),implies(Z_445,implies(Z_442,X_446))))
      | ~ is_a_theorem(Z_443) ),
    inference(resolution,[status(thm)],[c_8745,c_2]) ).

tff(c_8917,plain,
    ! [Z_443] : ~ is_a_theorem(Z_443),
    inference(splitLeft,[status(thm)],[c_8904]) ).

tff(c_3705,plain,
    ! [Z_87,X_290,Y_292,Z_289,Z_85] : is_a_theorem(implies(Z_87,implies(implies(implies(X_290,Y_292),implies(Z_289,falsehood)),implies(Z_85,implies(Z_289,X_290))))),
    inference(resolution,[status(thm)],[c_3648,c_516]) ).

tff(c_9008,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8917,c_3705]) ).

tff(c_9015,plain,
    ! [X_453,Y_454,Z_455,Z_456] : is_a_theorem(implies(implies(implies(X_453,Y_454),implies(Z_455,falsehood)),implies(Z_456,implies(Z_455,X_453)))),
    inference(splitRight,[status(thm)],[c_8904]) ).

tff(c_9082,plain,
    ! [Z_456,Z_455,X_453,Y_454] :
      ( is_a_theorem(implies(Z_456,implies(Z_455,X_453)))
      | ~ is_a_theorem(implies(implies(X_453,Y_454),implies(Z_455,falsehood))) ),
    inference(resolution,[status(thm)],[c_9015,c_2]) ).

tff(c_19535,plain,
    ! [Z_680,X_681,Y_682] : is_a_theorem(implies(Z_680,implies(implies(implies(X_681,Y_682),falsehood),X_681))),
    inference(resolution,[status(thm)],[c_15527,c_9082]) ).

tff(c_14098,plain,
    ! [X_575,X_576,Z_577] : is_a_theorem(implies(implies(implies(X_575,X_575),X_576),implies(Z_577,X_576))),
    inference(resolution,[status(thm)],[c_12045,c_12]) ).

tff(c_14243,plain,
    ! [X_346,Z_577,X_575] :
      ( is_a_theorem(X_346)
      | ~ is_a_theorem(implies(implies(Z_577,implies(X_575,X_575)),X_346)) ),
    inference(resolution,[status(thm)],[c_14098,c_5174]) ).

tff(c_19700,plain,
    ! [X_681,Y_682] : is_a_theorem(implies(implies(implies(X_681,Y_682),falsehood),X_681)),
    inference(resolution,[status(thm)],[c_19535,c_14243]) ).

tff(c_6,plain,
    ~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_19769,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_19700,c_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL036-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.16/0.34  % Computer : n026.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Thu Aug  3 14:26:01 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 9.72/3.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.72/3.42  
% 9.72/3.42  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.11/3.46  
% 10.11/3.46  Inference rules
% 10.11/3.46  ----------------------
% 10.11/3.46  #Ref     : 0
% 10.11/3.46  #Sup     : 4025
% 10.11/3.46  #Fact    : 0
% 10.11/3.46  #Define  : 0
% 10.11/3.46  #Split   : 21
% 10.11/3.46  #Chain   : 0
% 10.11/3.46  #Close   : 0
% 10.11/3.46  
% 10.11/3.46  Ordering : KBO
% 10.11/3.46  
% 10.11/3.46  Simplification rules
% 10.11/3.46  ----------------------
% 10.11/3.46  #Subsume      : 1431
% 10.11/3.46  #Demod        : 2079
% 10.11/3.46  #Tautology    : 2092
% 10.11/3.46  #SimpNegUnit  : 569
% 10.11/3.46  #BackRed      : 261
% 10.11/3.46  
% 10.11/3.46  #Partial instantiations: 0
% 10.11/3.46  #Strategies tried      : 1
% 10.11/3.46  
% 10.11/3.46  Timing (in seconds)
% 10.11/3.46  ----------------------
% 10.11/3.47  Preprocessing        : 0.38
% 10.11/3.47  Parsing              : 0.21
% 10.11/3.47  CNF conversion       : 0.02
% 10.11/3.47  Main loop            : 2.01
% 10.11/3.47  Inferencing          : 0.65
% 10.11/3.47  Reduction            : 0.69
% 10.11/3.47  Demodulation         : 0.53
% 10.11/3.47  BG Simplification    : 0.03
% 10.11/3.47  Subsumption          : 0.50
% 10.11/3.47  Abstraction          : 0.05
% 10.11/3.47  MUC search           : 0.00
% 10.11/3.47  Cooper               : 0.00
% 10.11/3.47  Total                : 2.46
% 10.11/3.47  Index Insertion      : 0.00
% 10.11/3.47  Index Deletion       : 0.00
% 10.11/3.47  Index Matching       : 0.00
% 10.11/3.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------