TSTP Solution File: LCL167-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL167-1 : 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 : 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 10:47:31 EDT 2023

% Result   : Unsatisfiable 158.47s 136.51s
% Output   : CNFRefutation 158.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :    8
% Syntax   : Number of formulae    :  112 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :  255 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  304 ( 156   ~; 148   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  282 (; 282   !;   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_34,axiom,
    ! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(X,Z),Y)))),
    file(unknown,unknown) ).

tff(f_31,axiom,
    ! [X,Y] :
      ( ~ is_a_theorem(equivalent(X,Y))
      | ~ is_a_theorem(X)
      | is_a_theorem(Y) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(c,b),a)))),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(X_3,equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(X_3,Z_5),Y_4)))),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_8,plain,
    ! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(X_8,equivalent(equivalent(Y_9,Z_10),equivalent(equivalent(X_8,Z_10),Y_9)))),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

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_31]) ).

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

tff(c_13,plain,
    ! [Y_11,Z_12,X_13] :
      ( is_a_theorem(equivalent(equivalent(Y_11,Z_12),equivalent(equivalent(X_13,Z_12),Y_11)))
      | ~ is_a_theorem(X_13) ),
    inference(resolution,[status(thm)],[c_8,c_2]) ).

tff(c_17,plain,
    ! [X_13,Z_12,Y_11] :
      ( is_a_theorem(equivalent(equivalent(X_13,Z_12),Y_11))
      | ~ is_a_theorem(equivalent(Y_11,Z_12))
      | ~ is_a_theorem(X_13) ),
    inference(resolution,[status(thm)],[c_13,c_2]) ).

tff(c_18,plain,
    ! [X_14,Z_15,Y_16] :
      ( is_a_theorem(equivalent(equivalent(X_14,Z_15),Y_16))
      | ~ is_a_theorem(equivalent(Y_16,Z_15))
      | ~ is_a_theorem(X_14) ),
    inference(resolution,[status(thm)],[c_13,c_2]) ).

tff(c_28,plain,
    ! [Y_17,X_18,Z_19] :
      ( is_a_theorem(Y_17)
      | ~ is_a_theorem(equivalent(X_18,Z_19))
      | ~ is_a_theorem(equivalent(Y_17,Z_19))
      | ~ is_a_theorem(X_18) ),
    inference(resolution,[status(thm)],[c_18,c_2]) ).

tff(c_97,plain,
    ! [Y_34,X_35,Z_36,Y_37] :
      ( is_a_theorem(Y_34)
      | ~ is_a_theorem(equivalent(Y_34,equivalent(equivalent(X_35,Z_36),Y_37)))
      | ~ is_a_theorem(equivalent(Y_37,Z_36))
      | ~ is_a_theorem(X_35) ),
    inference(resolution,[status(thm)],[c_12,c_28]) ).

tff(c_116,plain,
    ! [X_38,Z_39,Y_40] :
      ( is_a_theorem(X_38)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_38,Z_39),Y_40),Z_39))
      | ~ is_a_theorem(Y_40) ),
    inference(resolution,[status(thm)],[c_4,c_97]) ).

tff(c_126,plain,
    ! [X_41,Z_42,Y_43] :
      ( is_a_theorem(X_41)
      | ~ is_a_theorem(Z_42)
      | ~ is_a_theorem(equivalent(Y_43,Z_42))
      | ~ is_a_theorem(equivalent(X_41,Y_43)) ),
    inference(resolution,[status(thm)],[c_17,c_116]) ).

tff(c_165,plain,
    ! [X_53,Y_54,Z_55,X_56] :
      ( is_a_theorem(X_53)
      | ~ is_a_theorem(equivalent(equivalent(Y_54,Z_55),equivalent(equivalent(X_56,Z_55),Y_54)))
      | ~ is_a_theorem(equivalent(X_53,X_56)) ),
    inference(resolution,[status(thm)],[c_4,c_126]) ).

tff(c_173,plain,
    ! [X_57,X_58] :
      ( is_a_theorem(X_57)
      | ~ is_a_theorem(equivalent(X_57,X_58))
      | ~ is_a_theorem(X_58) ),
    inference(resolution,[status(thm)],[c_12,c_165]) ).

tff(c_213,plain,
    ! [Y_65,Z_66,X_67] :
      ( is_a_theorem(equivalent(Y_65,Z_66))
      | ~ is_a_theorem(equivalent(equivalent(X_67,Z_66),Y_65))
      | ~ is_a_theorem(X_67) ),
    inference(resolution,[status(thm)],[c_12,c_173]) ).

tff(c_2497,plain,
    ! [Y_249,Z_250,X_251,Z_252] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Y_249,Z_250),equivalent(equivalent(equivalent(X_251,Z_252),Z_250),Y_249)),Z_252))
      | ~ is_a_theorem(X_251) ),
    inference(resolution,[status(thm)],[c_4,c_213]) ).

tff(c_115,plain,
    ! [X_3,Z_5,Y_4] :
      ( is_a_theorem(X_3)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_3,Z_5),Y_4),Z_5))
      | ~ is_a_theorem(Y_4) ),
    inference(resolution,[status(thm)],[c_4,c_97]) ).

tff(c_2667,plain,
    ! [Y_253,X_254,Z_255] :
      ( is_a_theorem(Y_253)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_254,Z_255),Z_255),Y_253))
      | ~ is_a_theorem(X_254) ),
    inference(resolution,[status(thm)],[c_2497,c_115]) ).

tff(c_2760,plain,
    ! [X_259,Z_260,X_261] :
      ( is_a_theorem(equivalent(equivalent(X_259,Z_260),equivalent(X_261,Z_260)))
      | ~ is_a_theorem(X_261)
      | ~ is_a_theorem(X_259) ),
    inference(resolution,[status(thm)],[c_12,c_2667]) ).

tff(c_188,plain,
    ! [Y_9,Z_10,X_8] :
      ( is_a_theorem(equivalent(Y_9,Z_10))
      | ~ is_a_theorem(equivalent(equivalent(X_8,Z_10),Y_9))
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_173]) ).

tff(c_2930,plain,
    ! [X_261,Z_260,X_259] :
      ( is_a_theorem(equivalent(equivalent(X_261,Z_260),Z_260))
      | ~ is_a_theorem(X_261)
      | ~ is_a_theorem(X_259) ),
    inference(resolution,[status(thm)],[c_2760,c_188]) ).

tff(c_2943,plain,
    ! [X_259] : ~ is_a_theorem(X_259),
    inference(splitLeft,[status(thm)],[c_2930]) ).

tff(c_3007,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2943,c_4]) ).

tff(c_3008,plain,
    ! [X_261,Z_260] :
      ( is_a_theorem(equivalent(equivalent(X_261,Z_260),Z_260))
      | ~ is_a_theorem(X_261) ),
    inference(splitRight,[status(thm)],[c_2930]) ).

tff(c_3201,plain,
    ! [X_267,Z_268] :
      ( is_a_theorem(equivalent(equivalent(X_267,Z_268),Z_268))
      | ~ is_a_theorem(X_267) ),
    inference(splitRight,[status(thm)],[c_2930]) ).

tff(c_137,plain,
    ! [X_41,X_8,Z_10,Y_9] :
      ( is_a_theorem(X_41)
      | ~ is_a_theorem(equivalent(equivalent(X_8,Z_10),Y_9))
      | ~ is_a_theorem(equivalent(X_41,equivalent(Y_9,Z_10)))
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_126]) ).

tff(c_3350,plain,
    ! [X_41,Z_268,X_267] :
      ( is_a_theorem(X_41)
      | ~ is_a_theorem(equivalent(X_41,equivalent(Z_268,Z_268)))
      | ~ is_a_theorem(X_267) ),
    inference(resolution,[status(thm)],[c_3201,c_137]) ).

tff(c_3718,plain,
    ! [X_267] : ~ is_a_theorem(X_267),
    inference(splitLeft,[status(thm)],[c_3350]) ).

tff(c_3365,plain,
    ! [Z_268,X_267] :
      ( is_a_theorem(equivalent(Z_268,Z_268))
      | ~ is_a_theorem(X_267) ),
    inference(resolution,[status(thm)],[c_3201,c_188]) ).

tff(c_3376,plain,
    ! [X_267] : ~ is_a_theorem(X_267),
    inference(splitLeft,[status(thm)],[c_3365]) ).

tff(c_3442,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3376,c_4]) ).

tff(c_3443,plain,
    ! [Z_268] : is_a_theorem(equivalent(Z_268,Z_268)),
    inference(splitRight,[status(thm)],[c_3365]) ).

tff(c_3787,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3718,c_3443]) ).

tff(c_3789,plain,
    ! [X_276,Z_277] :
      ( is_a_theorem(X_276)
      | ~ is_a_theorem(equivalent(X_276,equivalent(Z_277,Z_277))) ),
    inference(splitRight,[status(thm)],[c_3350]) ).

tff(c_3844,plain,
    ! [X_261,Z_277] :
      ( is_a_theorem(equivalent(X_261,equivalent(Z_277,Z_277)))
      | ~ is_a_theorem(X_261) ),
    inference(resolution,[status(thm)],[c_3008,c_3789]) ).

tff(c_3923,plain,
    ! [X_283,Z_284] :
      ( is_a_theorem(equivalent(X_283,equivalent(Z_284,Z_284)))
      | ~ is_a_theorem(X_283) ),
    inference(resolution,[status(thm)],[c_3008,c_3789]) ).

tff(c_8084,plain,
    ! [Z_376,Z_377,X_378] :
      ( is_a_theorem(equivalent(equivalent(Z_376,Z_376),Z_377))
      | ~ is_a_theorem(X_378)
      | ~ is_a_theorem(equivalent(X_378,Z_377)) ),
    inference(resolution,[status(thm)],[c_3923,c_188]) ).

tff(c_8154,plain,
    ! [Z_376,Z_277,X_261] :
      ( is_a_theorem(equivalent(equivalent(Z_376,Z_376),equivalent(Z_277,Z_277)))
      | ~ is_a_theorem(X_261) ),
    inference(resolution,[status(thm)],[c_3844,c_8084]) ).

tff(c_8171,plain,
    ! [X_261] : ~ is_a_theorem(X_261),
    inference(splitLeft,[status(thm)],[c_8154]) ).

tff(c_8375,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8171,c_3443]) ).

tff(c_8377,plain,
    ! [Z_385,Z_386] : is_a_theorem(equivalent(equivalent(Z_385,Z_385),equivalent(Z_386,Z_386))),
    inference(splitRight,[status(thm)],[c_8154]) ).

tff(c_48,plain,
    ! [Y_24,Y_25,Z_26,X_27] :
      ( is_a_theorem(Y_24)
      | ~ is_a_theorem(equivalent(Y_24,equivalent(equivalent(Y_25,Z_26),equivalent(equivalent(X_27,Z_26),Y_25))))
      | ~ is_a_theorem(X_27) ),
    inference(resolution,[status(thm)],[c_4,c_28]) ).

tff(c_61,plain,
    ! [X_27,Z_10,X_8] :
      ( is_a_theorem(equivalent(equivalent(equivalent(X_27,Z_10),X_8),Z_10))
      | ~ is_a_theorem(X_27)
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_48]) ).

tff(c_231,plain,
    ! [X_68,Z_69,X_70] :
      ( is_a_theorem(equivalent(equivalent(X_68,Z_69),X_70))
      | ~ is_a_theorem(Z_69)
      | ~ is_a_theorem(X_68)
      | ~ is_a_theorem(X_70) ),
    inference(resolution,[status(thm)],[c_61,c_173]) ).

tff(c_278,plain,
    ! [X_70,Z_69,X_68] :
      ( is_a_theorem(equivalent(X_70,Z_69))
      | ~ is_a_theorem(Z_69)
      | ~ is_a_theorem(X_68)
      | ~ is_a_theorem(X_70) ),
    inference(resolution,[status(thm)],[c_231,c_188]) ).

tff(c_294,plain,
    ! [X_68] : ~ is_a_theorem(X_68),
    inference(splitLeft,[status(thm)],[c_278]) ).

tff(c_315,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_294,c_4]) ).

tff(c_338,plain,
    ! [X_76,Z_77] :
      ( is_a_theorem(equivalent(X_76,Z_77))
      | ~ is_a_theorem(Z_77)
      | ~ is_a_theorem(X_76) ),
    inference(splitRight,[status(thm)],[c_278]) ).

tff(c_189,plain,
    ! [X_3,Y_4,Z_5] :
      ( is_a_theorem(X_3)
      | ~ is_a_theorem(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(X_3,Z_5),Y_4))) ),
    inference(resolution,[status(thm)],[c_4,c_173]) ).

tff(c_392,plain,
    ! [X_3,Z_5,Y_4] :
      ( is_a_theorem(X_3)
      | ~ is_a_theorem(equivalent(equivalent(X_3,Z_5),Y_4))
      | ~ is_a_theorem(equivalent(Y_4,Z_5)) ),
    inference(resolution,[status(thm)],[c_338,c_189]) ).

tff(c_8651,plain,
    ! [Z_387,Z_388] :
      ( is_a_theorem(Z_387)
      | ~ is_a_theorem(equivalent(equivalent(Z_388,Z_388),Z_387)) ),
    inference(resolution,[status(thm)],[c_8377,c_392]) ).

tff(c_8795,plain,
    ! [Y_389,Z_390,Z_391] : is_a_theorem(equivalent(equivalent(Y_389,Z_390),equivalent(equivalent(equivalent(Z_391,Z_391),Z_390),Y_389))),
    inference(resolution,[status(thm)],[c_4,c_8651]) ).

tff(c_8626,plain,
    ! [Z_385,Z_386] :
      ( is_a_theorem(Z_385)
      | ~ is_a_theorem(equivalent(equivalent(Z_386,Z_386),Z_385)) ),
    inference(resolution,[status(thm)],[c_8377,c_392]) ).

tff(c_8948,plain,
    ! [Z_391,Z_390] : is_a_theorem(equivalent(equivalent(equivalent(Z_391,Z_391),Z_390),Z_390)),
    inference(resolution,[status(thm)],[c_8795,c_8626]) ).

tff(c_172,plain,
    ! [X_53,X_8] :
      ( is_a_theorem(X_53)
      | ~ is_a_theorem(equivalent(X_53,X_8))
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_165]) ).

tff(c_18295,plain,
    ! [Y_558,Z_559,Z_560] :
      ( is_a_theorem(equivalent(Y_558,Z_559))
      | ~ is_a_theorem(equivalent(equivalent(equivalent(Z_560,Z_560),Z_559),Y_558)) ),
    inference(resolution,[status(thm)],[c_8795,c_172]) ).

tff(c_18517,plain,
    ! [Y_4,Z_5,Z_560,Z_559] : is_a_theorem(equivalent(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(equivalent(equivalent(Z_560,Z_560),Z_559),Z_5),Y_4)),Z_559)),
    inference(resolution,[status(thm)],[c_4,c_18295]) ).

tff(c_230,plain,
    ! [Y_4,Z_5,X_67,Z_66] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(equivalent(X_67,Z_66),Z_5),Y_4)),Z_66))
      | ~ is_a_theorem(X_67) ),
    inference(resolution,[status(thm)],[c_4,c_213]) ).

tff(c_37424,plain,
    ! [Z_773,X_774,Z_775] :
      ( is_a_theorem(equivalent(Z_773,equivalent(equivalent(equivalent(X_774,Z_773),Z_775),Z_775)))
      | ~ is_a_theorem(X_774) ),
    inference(resolution,[status(thm)],[c_230,c_18295]) ).

tff(c_561,plain,
    ! [X_94,Z_95,Y_96] :
      ( is_a_theorem(X_94)
      | ~ is_a_theorem(equivalent(equivalent(X_94,Z_95),Y_96))
      | ~ is_a_theorem(equivalent(Y_96,Z_95)) ),
    inference(resolution,[status(thm)],[c_338,c_189]) ).

tff(c_586,plain,
    ! [Y_9,X_8,Z_10] :
      ( is_a_theorem(Y_9)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,Z_10),Y_9),Z_10))
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_561]) ).

tff(c_4523,plain,
    ! [X_291,Z_292,Y_293] :
      ( is_a_theorem(equivalent(equivalent(equivalent(X_291,Z_292),Z_292),Y_293))
      | ~ is_a_theorem(Y_293)
      | ~ is_a_theorem(X_291) ),
    inference(resolution,[status(thm)],[c_2497,c_586]) ).

tff(c_4726,plain,
    ! [X_3,Z_292,X_291] :
      ( is_a_theorem(X_3)
      | ~ is_a_theorem(equivalent(equivalent(X_3,Z_292),equivalent(X_291,Z_292)))
      | ~ is_a_theorem(X_291) ),
    inference(resolution,[status(thm)],[c_4523,c_189]) ).

tff(c_48283,plain,
    ! [X_882,X_883,Z_884] :
      ( is_a_theorem(X_882)
      | ~ is_a_theorem(equivalent(equivalent(X_883,equivalent(X_882,Z_884)),Z_884))
      | ~ is_a_theorem(X_883) ),
    inference(resolution,[status(thm)],[c_37424,c_4726]) ).

tff(c_68226,plain,
    ! [Z_1022,Z_1023,Z_1024] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Z_1022,Z_1022),Z_1023),Z_1024))
      | ~ is_a_theorem(equivalent(Z_1023,Z_1024)) ),
    inference(resolution,[status(thm)],[c_18517,c_48283]) ).

tff(c_68678,plain,
    ! [X_41,Z_1024,Z_1023,Z_1022] :
      ( is_a_theorem(X_41)
      | ~ is_a_theorem(equivalent(X_41,equivalent(Z_1024,Z_1023)))
      | ~ is_a_theorem(equivalent(Z_1022,Z_1022))
      | ~ is_a_theorem(equivalent(Z_1023,Z_1024)) ),
    inference(resolution,[status(thm)],[c_68226,c_137]) ).

tff(c_79344,plain,
    ! [X_1098,Z_1099,Z_1100] :
      ( is_a_theorem(X_1098)
      | ~ is_a_theorem(equivalent(X_1098,equivalent(Z_1099,Z_1100)))
      | ~ is_a_theorem(equivalent(Z_1100,Z_1099)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3443,c_68678]) ).

tff(c_117429,plain,
    ! [Z_1354,Z_1355,Z_1356] :
      ( is_a_theorem(equivalent(equivalent(Z_1354,Z_1354),equivalent(Z_1355,Z_1356)))
      | ~ is_a_theorem(equivalent(Z_1356,Z_1355)) ),
    inference(resolution,[status(thm)],[c_8948,c_79344]) ).

tff(c_8794,plain,
    ! [Y_4,Z_5,Z_388] : is_a_theorem(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(equivalent(Z_388,Z_388),Z_5),Y_4))),
    inference(resolution,[status(thm)],[c_4,c_8651]) ).

tff(c_512,plain,
    ! [Y_87,Z_89,X_88,X_90,Z_91] :
      ( is_a_theorem(equivalent(X_88,Z_91))
      | ~ is_a_theorem(equivalent(Y_87,Z_89))
      | ~ is_a_theorem(X_90)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_90,Z_89),Y_87),Z_91))
      | ~ is_a_theorem(X_88) ),
    inference(resolution,[status(thm)],[c_17,c_97]) ).

tff(c_532,plain,
    ! [X_88,Z_10,X_8,X_27] :
      ( is_a_theorem(equivalent(X_88,Z_10))
      | ~ is_a_theorem(equivalent(X_8,Z_10))
      | ~ is_a_theorem(X_88)
      | ~ is_a_theorem(X_27)
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_61,c_512]) ).

tff(c_739,plain,
    ! [X_27] : ~ is_a_theorem(X_27),
    inference(splitLeft,[status(thm)],[c_532]) ).

tff(c_773,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_739,c_4]) ).

tff(c_775,plain,
    ! [X_121,Z_122,X_123] :
      ( is_a_theorem(equivalent(X_121,Z_122))
      | ~ is_a_theorem(equivalent(X_123,Z_122))
      | ~ is_a_theorem(X_121)
      | ~ is_a_theorem(X_123) ),
    inference(splitRight,[status(thm)],[c_532]) ).

tff(c_794,plain,
    ! [X_124,Y_125,Z_126,X_127] :
      ( is_a_theorem(equivalent(X_124,equivalent(equivalent(Y_125,Z_126),equivalent(equivalent(X_127,Z_126),Y_125))))
      | ~ is_a_theorem(X_124)
      | ~ is_a_theorem(X_127) ),
    inference(resolution,[status(thm)],[c_4,c_775]) ).

tff(c_63,plain,
    ! [X_28,Z_29,X_30] :
      ( is_a_theorem(equivalent(equivalent(equivalent(X_28,Z_29),X_30),Z_29))
      | ~ is_a_theorem(X_28)
      | ~ is_a_theorem(X_30) ),
    inference(resolution,[status(thm)],[c_12,c_48]) ).

tff(c_79,plain,
    ! [Z_31,X_32,X_33] :
      ( is_a_theorem(Z_31)
      | ~ is_a_theorem(equivalent(equivalent(X_32,Z_31),X_33))
      | ~ is_a_theorem(X_32)
      | ~ is_a_theorem(X_33) ),
    inference(resolution,[status(thm)],[c_63,c_2]) ).

tff(c_96,plain,
    ! [Z_31,X_32,Y_4,Z_5] :
      ( is_a_theorem(Z_31)
      | ~ is_a_theorem(X_32)
      | ~ is_a_theorem(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(equivalent(X_32,Z_31),Z_5),Y_4))) ),
    inference(resolution,[status(thm)],[c_4,c_79]) ).

tff(c_1704,plain,
    ! [Z_196,X_197,X_198,Z_199] :
      ( is_a_theorem(Z_196)
      | ~ is_a_theorem(X_197)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(X_198,Z_199),equivalent(X_197,Z_196)),Z_199))
      | ~ is_a_theorem(X_198) ),
    inference(resolution,[status(thm)],[c_794,c_96]) ).

tff(c_1964,plain,
    ! [Z_213,X_214,X_215,Y_216] :
      ( is_a_theorem(Z_213)
      | ~ is_a_theorem(X_214)
      | ~ is_a_theorem(X_215)
      | ~ is_a_theorem(equivalent(Y_216,equivalent(X_214,Z_213)))
      | ~ is_a_theorem(equivalent(X_215,Y_216)) ),
    inference(resolution,[status(thm)],[c_17,c_1704]) ).

tff(c_1998,plain,
    ! [X_3,Z_5,Y_4,X_215] :
      ( is_a_theorem(equivalent(equivalent(X_3,Z_5),Y_4))
      | ~ is_a_theorem(equivalent(Y_4,Z_5))
      | ~ is_a_theorem(X_215)
      | ~ is_a_theorem(equivalent(X_215,X_3)) ),
    inference(resolution,[status(thm)],[c_4,c_1964]) ).

tff(c_8435,plain,
    ! [Z_386,Z_5,Y_4,Z_385] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Z_386,Z_386),Z_5),Y_4))
      | ~ is_a_theorem(equivalent(Y_4,Z_5))
      | ~ is_a_theorem(equivalent(Z_385,Z_385)) ),
    inference(resolution,[status(thm)],[c_8377,c_1998]) ).

tff(c_8567,plain,
    ! [Z_386,Z_5,Y_4] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Z_386,Z_386),Z_5),Y_4))
      | ~ is_a_theorem(equivalent(Y_4,Z_5)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3443,c_8435]) ).

tff(c_2721,plain,
    ! [X_8,Z_10,X_254] :
      ( is_a_theorem(equivalent(equivalent(X_8,Z_10),equivalent(X_254,Z_10)))
      | ~ is_a_theorem(X_254)
      | ~ is_a_theorem(X_8) ),
    inference(resolution,[status(thm)],[c_12,c_2667]) ).

tff(c_12329,plain,
    ! [Z_465,Z_466,Y_467] :
      ( is_a_theorem(equivalent(equivalent(equivalent(Z_465,Z_465),Z_466),Y_467))
      | ~ is_a_theorem(equivalent(Y_467,Z_466)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3443,c_8435]) ).

tff(c_587,plain,
    ! [X_94,Y_4,Z_5,Z_95] :
      ( is_a_theorem(X_94)
      | ~ is_a_theorem(equivalent(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(equivalent(X_94,Z_95),Z_5),Y_4)),Z_95)) ),
    inference(resolution,[status(thm)],[c_4,c_561]) ).

tff(c_13362,plain,
    ! [X_487,Y_488,Z_489] :
      ( is_a_theorem(X_487)
      | ~ is_a_theorem(equivalent(Y_488,equivalent(equivalent(equivalent(X_487,Y_488),Z_489),Z_489))) ),
    inference(resolution,[status(thm)],[c_12329,c_587]) ).

tff(c_15000,plain,
    ! [X_515,X_516,Z_517] :
      ( is_a_theorem(X_515)
      | ~ is_a_theorem(equivalent(equivalent(X_515,equivalent(X_516,Z_517)),Z_517))
      | ~ is_a_theorem(X_516) ),
    inference(resolution,[status(thm)],[c_2721,c_13362]) ).

tff(c_29507,plain,
    ! [Z_694,Z_695,X_696] :
      ( is_a_theorem(equivalent(Z_694,Z_695))
      | ~ is_a_theorem(equivalent(equivalent(X_696,Z_694),Z_695))
      | ~ is_a_theorem(X_696) ),
    inference(resolution,[status(thm)],[c_230,c_15000]) ).

tff(c_29579,plain,
    ! [Z_5,Y_4,Z_386] :
      ( is_a_theorem(equivalent(Z_5,Y_4))
      | ~ is_a_theorem(equivalent(Z_386,Z_386))
      | ~ is_a_theorem(equivalent(Y_4,Z_5)) ),
    inference(resolution,[status(thm)],[c_8567,c_29507]) ).

tff(c_29764,plain,
    ! [Z_697,Y_698] :
      ( is_a_theorem(equivalent(Z_697,Y_698))
      | ~ is_a_theorem(equivalent(Y_698,Z_697)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3443,c_29579]) ).

tff(c_61805,plain,
    ! [Z_985,Z_986,Y_987] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z_985,Z_985),Z_986),Y_987),equivalent(Y_987,Z_986))),
    inference(resolution,[status(thm)],[c_8794,c_29764]) ).

tff(c_62336,plain,
    ! [Y_987,Z_986,Z_985] :
      ( is_a_theorem(equivalent(equivalent(Y_987,Z_986),Y_987))
      | ~ is_a_theorem(equivalent(equivalent(Z_985,Z_985),Z_986)) ),
    inference(resolution,[status(thm)],[c_61805,c_188]) ).

tff(c_193012,plain,
    ! [Y_1830,Z_1831,Z_1832] :
      ( is_a_theorem(equivalent(equivalent(Y_1830,equivalent(Z_1831,Z_1832)),Y_1830))
      | ~ is_a_theorem(equivalent(Z_1832,Z_1831)) ),
    inference(resolution,[status(thm)],[c_117429,c_62336]) ).

tff(c_72211,plain,
    ! [X_1047,Z_1048,Z_1049] :
      ( is_a_theorem(equivalent(equivalent(X_1047,Z_1048),Z_1049))
      | ~ is_a_theorem(equivalent(Z_1048,Z_1049))
      | ~ is_a_theorem(X_1047) ),
    inference(resolution,[status(thm)],[c_230,c_48283]) ).

tff(c_29725,plain,
    ! [Z_5,Y_4] :
      ( is_a_theorem(equivalent(Z_5,Y_4))
      | ~ is_a_theorem(equivalent(Y_4,Z_5)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3443,c_29579]) ).

tff(c_99726,plain,
    ! [Z_1260,X_1261,Z_1262] :
      ( is_a_theorem(equivalent(Z_1260,equivalent(X_1261,Z_1262)))
      | ~ is_a_theorem(equivalent(Z_1262,Z_1260))
      | ~ is_a_theorem(X_1261) ),
    inference(resolution,[status(thm)],[c_72211,c_29725]) ).

tff(c_30993,plain,
    ! [Y_713,Z_714,X_715] : is_a_theorem(equivalent(equivalent(equivalent(Y_713,Z_714),equivalent(equivalent(X_715,Z_714),Y_713)),X_715)),
    inference(resolution,[status(thm)],[c_4,c_29764]) ).

tff(c_31365,plain,
    ! [Y_713,Z_714,X_715] :
      ( is_a_theorem(equivalent(Y_713,Z_714))
      | ~ is_a_theorem(equivalent(X_715,equivalent(equivalent(X_715,Z_714),Y_713))) ),
    inference(resolution,[status(thm)],[c_30993,c_392]) ).

tff(c_106824,plain,
    ! [Z_1305,Z_1306,Z_1307] :
      ( is_a_theorem(equivalent(Z_1305,Z_1306))
      | ~ is_a_theorem(equivalent(Z_1305,Z_1307))
      | ~ is_a_theorem(equivalent(Z_1307,Z_1306)) ),
    inference(resolution,[status(thm)],[c_99726,c_31365]) ).

tff(c_107190,plain,
    ! [X_3,Z_1306,Y_4,Z_5] :
      ( is_a_theorem(equivalent(X_3,Z_1306))
      | ~ is_a_theorem(equivalent(equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(X_3,Z_5),Y_4)),Z_1306)) ),
    inference(resolution,[status(thm)],[c_4,c_106824]) ).

tff(c_533443,plain,
    ! [X_3197,Z_3198,Z_3199] :
      ( is_a_theorem(equivalent(X_3197,equivalent(Z_3198,Z_3199)))
      | ~ is_a_theorem(equivalent(Z_3198,equivalent(X_3197,Z_3199))) ),
    inference(resolution,[status(thm)],[c_193012,c_107190]) ).

tff(c_534497,plain,
    ! [Y_4,Z_5,X_3] : is_a_theorem(equivalent(equivalent(Y_4,Z_5),equivalent(X_3,equivalent(equivalent(X_3,Z_5),Y_4)))),
    inference(resolution,[status(thm)],[c_4,c_533443]) ).

tff(c_6,plain,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(c,b),a)))),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_535224,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_534497,c_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : LCL167-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % 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
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 14:19:57 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 158.47/136.51  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.47/136.53  
% 158.47/136.53  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 158.47/136.58  
% 158.47/136.58  Inference rules
% 158.47/136.58  ----------------------
% 158.47/136.58  #Ref     : 0
% 158.47/136.58  #Sup     : 119380
% 158.47/136.58  #Fact    : 0
% 158.47/136.58  #Define  : 0
% 158.47/136.58  #Split   : 54
% 158.47/136.58  #Chain   : 0
% 158.47/136.58  #Close   : 0
% 158.47/136.58  
% 158.47/136.58  Ordering : KBO
% 158.47/136.58  
% 158.47/136.58  Simplification rules
% 158.47/136.58  ----------------------
% 158.47/136.58  #Subsume      : 49758
% 158.47/136.58  #Demod        : 20784
% 158.47/136.58  #Tautology    : 15996
% 158.47/136.58  #SimpNegUnit  : 15528
% 158.47/136.58  #BackRed      : 1921
% 158.47/136.58  
% 158.47/136.58  #Partial instantiations: 0
% 158.47/136.58  #Strategies tried      : 1
% 158.47/136.58  
% 158.47/136.58  Timing (in seconds)
% 158.47/136.58  ----------------------
% 158.85/136.59  Preprocessing        : 0.39
% 158.85/136.59  Parsing              : 0.21
% 158.85/136.59  CNF conversion       : 0.02
% 158.85/136.59  Main loop            : 135.13
% 158.85/136.59  Inferencing          : 6.48
% 158.85/136.59  Reduction            : 22.05
% 158.85/136.59  Demodulation         : 19.04
% 158.85/136.59  BG Simplification    : 0.41
% 158.85/136.59  Subsumption          : 99.32
% 158.85/136.59  Abstraction          : 0.75
% 158.85/136.59  MUC search           : 0.00
% 158.85/136.59  Cooper               : 0.00
% 158.85/136.59  Total                : 135.60
% 158.85/136.59  Index Insertion      : 0.00
% 158.85/136.59  Index Deletion       : 0.00
% 158.85/136.59  Index Matching       : 0.00
% 158.85/136.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------