TSTP Solution File: GRP059-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP059-1 : 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 : n024.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 10:39:45 EDT 2023

% Result   : Unsatisfiable 28.04s 10.83s
% Output   : CNFRefutation 28.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  126 ( 114 unt;   9 typ;   0 def)
%            Number of atoms       :  122 ( 119 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   17 (  12   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :   10 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :  286 (; 286   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > c3 > b3 > b2 > b1 > a3 > a2 > a1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a1,type,
    a1: $i ).

tff(a3,type,
    a3: $i ).

tff(c3,type,
    c3: $i ).

tff(b2,type,
    b2: $i ).

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

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

tff(b1,type,
    b1: $i ).

tff(b3,type,
    b3: $i ).

tff(a2,type,
    a2: $i ).

tff(f_24,axiom,
    ! [X,Y,Z,U] : ( inverse(multiply(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(U,inverse(U)))) = Z ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
    file(unknown,unknown) ).

tff(c_5,plain,
    ! [X_5,Y_6,Z_7,U_8] : ( inverse(multiply(multiply(multiply(inverse(multiply(multiply(X_5,Y_6),Z_7)),X_5),Y_6),multiply(U_8,inverse(U_8)))) = Z_7 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_2,plain,
    ! [X_1,Y_2,Z_3,U_4] : ( inverse(multiply(multiply(multiply(inverse(multiply(multiply(X_1,Y_2),Z_3)),X_1),Y_2),multiply(U_4,inverse(U_4)))) = Z_3 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_26,plain,
    ! [Y_12,Z_10,X_13,U_9,U_11] : ( multiply(U_9,inverse(U_9)) = inverse(multiply(multiply(multiply(Z_10,multiply(inverse(multiply(multiply(X_13,Y_12),Z_10)),X_13)),Y_12),multiply(U_11,inverse(U_11)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_8,plain,
    ! [U_4,Y_6,U_8,X_5,Z_7] : ( multiply(U_8,inverse(U_8)) = inverse(multiply(multiply(multiply(Z_7,multiply(inverse(multiply(multiply(X_5,Y_6),Z_7)),X_5)),Y_6),multiply(U_4,inverse(U_4)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_95,plain,
    ! [U_15,U_14] : ( multiply(U_15,inverse(U_15)) = multiply(U_14,inverse(U_14)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_8]) ).

tff(c_57741,plain,
    ! [U_421,X_422,Y_423,U_424] : ( inverse(multiply(multiply(multiply(inverse(multiply(U_421,inverse(U_421))),X_422),Y_423),multiply(U_424,inverse(U_424)))) = inverse(multiply(X_422,Y_423)) ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_128,plain,
    ! [U_15,Z_3,U_14,U_4] : ( inverse(multiply(multiply(multiply(inverse(multiply(multiply(U_15,inverse(U_15)),Z_3)),U_14),inverse(U_14)),multiply(U_4,inverse(U_4)))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_57908,plain,
    ! [X_425,U_426] : ( inverse(multiply(X_425,inverse(X_425))) = inverse(multiply(U_426,inverse(U_426))) ),
    inference(superposition,[status(thm),theory(equality)],[c_57741,c_128]) ).

tff(c_37,plain,
    ! [U_9,U_8] : ( multiply(U_9,inverse(U_9)) = multiply(U_8,inverse(U_8)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_8]) ).

tff(c_57993,plain,
    ! [U_426,X_425,U_8] : ( multiply(multiply(U_426,inverse(U_426)),inverse(multiply(X_425,inverse(X_425)))) = multiply(U_8,inverse(U_8)) ),
    inference(superposition,[status(thm),theory(equality)],[c_57908,c_37]) ).

tff(c_57777,plain,
    ! [X_422,U_15] : ( inverse(multiply(X_422,inverse(X_422))) = inverse(multiply(U_15,inverse(U_15))) ),
    inference(superposition,[status(thm),theory(equality)],[c_57741,c_128]) ).

tff(c_59186,plain,
    ! [U_440,X_441,Y_442,U_443] : ( multiply(U_440,inverse(U_440)) = inverse(multiply(multiply(inverse(multiply(multiply(X_441,Y_442),inverse(multiply(U_443,inverse(U_443))))),X_441),Y_442)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_57741]) ).

tff(c_59577,plain,
    ! [U_444,X_445,X_446] : ( multiply(U_444,inverse(U_444)) = inverse(multiply(multiply(inverse(multiply(X_445,inverse(X_445))),X_446),inverse(X_446))) ),
    inference(superposition,[status(thm),theory(equality)],[c_57777,c_59186]) ).

tff(c_60399,plain,
    ! [U_454,X_455,X_456,U_457] : ( inverse(multiply(multiply(multiply(multiply(U_454,inverse(U_454)),inverse(multiply(X_455,inverse(X_455)))),X_456),multiply(U_457,inverse(U_457)))) = inverse(X_456) ),
    inference(superposition,[status(thm),theory(equality)],[c_59577,c_2]) ).

tff(c_60643,plain,
    ! [U_8,X_455,X_456,U_457] : ( inverse(multiply(multiply(multiply(multiply(U_8,inverse(U_8)),inverse(multiply(X_455,inverse(X_455)))),X_456),multiply(U_457,inverse(U_457)))) = inverse(X_456) ),
    inference(superposition,[status(thm),theory(equality)],[c_57993,c_60399]) ).

tff(c_60789,plain,
    ! [U_458,X_459,U_460] : ( inverse(multiply(multiply(multiply(U_458,inverse(U_458)),X_459),multiply(U_460,inverse(U_460)))) = inverse(X_459) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57993,c_60643]) ).

tff(c_141,plain,
    ! [U_14,X_1,Y_2,U_4] : ( inverse(multiply(multiply(multiply(inverse(multiply(U_14,inverse(U_14))),X_1),Y_2),multiply(U_4,inverse(U_4)))) = inverse(multiply(X_1,Y_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_60881,plain,
    ! [U_14,X_459] : ( inverse(multiply(inverse(inverse(multiply(U_14,inverse(U_14)))),X_459)) = inverse(X_459) ),
    inference(superposition,[status(thm),theory(equality)],[c_60789,c_141]) ).

tff(c_60904,plain,
    ! [U_15,Z_3] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_15,inverse(U_15)),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_60789,c_128]) ).

tff(c_59777,plain,
    ! [U_444,X_445,X_446,U_4] : ( inverse(multiply(multiply(multiply(multiply(U_444,inverse(U_444)),inverse(multiply(X_445,inverse(X_445)))),X_446),multiply(U_4,inverse(U_4)))) = inverse(X_446) ),
    inference(superposition,[status(thm),theory(equality)],[c_59577,c_2]) ).

tff(c_61399,plain,
    ! [U_463,Z_464] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_463,inverse(U_463)),Z_464))))) = Z_464 ),
    inference(superposition,[status(thm),theory(equality)],[c_60789,c_128]) ).

tff(c_61533,plain,
    ! [U_4,U_444,X_445] : ( multiply(U_4,inverse(U_4)) = inverse(inverse(inverse(inverse(inverse(multiply(multiply(U_444,inverse(U_444)),inverse(multiply(X_445,inverse(X_445))))))))) ),
    inference(superposition,[status(thm),theory(equality)],[c_59777,c_61399]) ).

tff(c_61654,plain,
    ! [U_465,X_466] : ( multiply(U_465,inverse(U_465)) = inverse(inverse(multiply(X_466,inverse(X_466)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_60904,c_61533]) ).

tff(c_61675,plain,
    ! [X_466,Z_3] : ( inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X_466,inverse(X_466)))),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_61654,c_60904]) ).

tff(c_62123,plain,
    ! [Z_467] : ( inverse(inverse(inverse(inverse(Z_467)))) = Z_467 ),
    inference(demodulation,[status(thm),theory(equality)],[c_60881,c_61675]) ).

tff(c_62147,plain,
    ! [U_15,Z_3] : ( multiply(multiply(U_15,inverse(U_15)),Z_3) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_62123,c_60904]) ).

tff(c_62111,plain,
    ! [Z_3] : ( inverse(inverse(inverse(inverse(Z_3)))) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_60881,c_61675]) ).

tff(c_60778,plain,
    ! [U_8,X_456,U_457] : ( inverse(multiply(multiply(multiply(U_8,inverse(U_8)),X_456),multiply(U_457,inverse(U_457)))) = inverse(X_456) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57993,c_60643]) ).

tff(c_63613,plain,
    ! [X_477,U_478] : ( inverse(multiply(X_477,multiply(U_478,inverse(U_478)))) = inverse(X_477) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62147,c_60778]) ).

tff(c_63638,plain,
    ! [X_477,U_478] : ( multiply(X_477,multiply(U_478,inverse(U_478))) = inverse(inverse(inverse(inverse(X_477)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_63613,c_62111]) ).

tff(c_63891,plain,
    ! [X_479,U_480] : ( multiply(X_479,multiply(U_480,inverse(U_480))) = X_479 ),
    inference(demodulation,[status(thm),theory(equality)],[c_62111,c_63638]) ).

tff(c_63932,plain,
    ! [X_479,U_15] : ( multiply(X_479,inverse(multiply(U_15,inverse(U_15)))) = X_479 ),
    inference(superposition,[status(thm),theory(equality)],[c_62147,c_63891]) ).

tff(c_63869,plain,
    ! [X_477,U_478] : ( multiply(X_477,multiply(U_478,inverse(U_478))) = X_477 ),
    inference(demodulation,[status(thm),theory(equality)],[c_62111,c_63638]) ).

tff(c_64152,plain,
    ! [X_483,Y_484,Z_485] : ( inverse(multiply(multiply(inverse(multiply(multiply(X_483,Y_484),Z_485)),X_483),Y_484)) = Z_485 ),
    inference(superposition,[status(thm),theory(equality)],[c_63613,c_2]) ).

tff(c_64269,plain,
    ! [U_8,Z_485,U_426,X_425] : ( inverse(multiply(multiply(inverse(multiply(multiply(U_8,inverse(U_8)),Z_485)),multiply(U_426,inverse(U_426))),inverse(multiply(X_425,inverse(X_425))))) = Z_485 ),
    inference(superposition,[status(thm),theory(equality)],[c_57993,c_64152]) ).

tff(c_64329,plain,
    ! [Z_486] : ( inverse(inverse(Z_486)) = Z_486 ),
    inference(demodulation,[status(thm),theory(equality)],[c_63932,c_63869,c_62147,c_64269]) ).

tff(c_64347,plain,
    ! [Z_486,Z_3] : ( multiply(multiply(inverse(Z_486),Z_486),Z_3) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_64329,c_62147]) ).

tff(c_14005,plain,
    ! [U_157,X_158,Y_159,U_160] : ( inverse(multiply(multiply(multiply(inverse(multiply(U_157,inverse(U_157))),X_158),Y_159),multiply(U_160,inverse(U_160)))) = inverse(multiply(X_158,Y_159)) ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_14163,plain,
    ! [X_161,U_162] : ( inverse(multiply(X_161,inverse(X_161))) = inverse(multiply(U_162,inverse(U_162))) ),
    inference(superposition,[status(thm),theory(equality)],[c_14005,c_128]) ).

tff(c_14242,plain,
    ! [U_162,X_161,U_8] : ( multiply(multiply(U_162,inverse(U_162)),inverse(multiply(X_161,inverse(X_161)))) = multiply(U_8,inverse(U_8)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14163,c_37]) ).

tff(c_14038,plain,
    ! [X_158,U_15] : ( inverse(multiply(X_158,inverse(X_158))) = inverse(multiply(U_15,inverse(U_15))) ),
    inference(superposition,[status(thm),theory(equality)],[c_14005,c_128]) ).

tff(c_15519,plain,
    ! [U_181,X_182,Y_183,U_184] : ( multiply(U_181,inverse(U_181)) = inverse(multiply(multiply(inverse(multiply(multiply(X_182,Y_183),inverse(multiply(U_184,inverse(U_184))))),X_182),Y_183)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_14005]) ).

tff(c_15916,plain,
    ! [U_185,X_186,X_187] : ( multiply(U_185,inverse(U_185)) = inverse(multiply(multiply(inverse(multiply(X_186,inverse(X_186))),X_187),inverse(X_187))) ),
    inference(superposition,[status(thm),theory(equality)],[c_14038,c_15519]) ).

tff(c_16337,plain,
    ! [U_188,X_189,X_190,U_191] : ( inverse(multiply(multiply(multiply(multiply(U_188,inverse(U_188)),inverse(multiply(X_189,inverse(X_189)))),X_190),multiply(U_191,inverse(U_191)))) = inverse(X_190) ),
    inference(superposition,[status(thm),theory(equality)],[c_15916,c_2]) ).

tff(c_16566,plain,
    ! [U_8,X_189,X_190,U_191] : ( inverse(multiply(multiply(multiply(multiply(U_8,inverse(U_8)),inverse(multiply(X_189,inverse(X_189)))),X_190),multiply(U_191,inverse(U_191)))) = inverse(X_190) ),
    inference(superposition,[status(thm),theory(equality)],[c_14242,c_16337]) ).

tff(c_16704,plain,
    ! [U_192,X_193,U_194] : ( inverse(multiply(multiply(multiply(U_192,inverse(U_192)),X_193),multiply(U_194,inverse(U_194)))) = inverse(X_193) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14242,c_16566]) ).

tff(c_16793,plain,
    ! [U_14,X_193] : ( inverse(multiply(inverse(inverse(multiply(U_14,inverse(U_14)))),X_193)) = inverse(X_193) ),
    inference(superposition,[status(thm),theory(equality)],[c_16704,c_141]) ).

tff(c_16813,plain,
    ! [U_15,Z_3] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_15,inverse(U_15)),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_16704,c_128]) ).

tff(c_16131,plain,
    ! [U_185,X_186,X_187,U_4] : ( inverse(multiply(multiply(multiply(multiply(U_185,inverse(U_185)),inverse(multiply(X_186,inverse(X_186)))),X_187),multiply(U_4,inverse(U_4)))) = inverse(X_187) ),
    inference(superposition,[status(thm),theory(equality)],[c_15916,c_2]) ).

tff(c_17285,plain,
    ! [U_197,Z_198] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_197,inverse(U_197)),Z_198))))) = Z_198 ),
    inference(superposition,[status(thm),theory(equality)],[c_16704,c_128]) ).

tff(c_17413,plain,
    ! [U_4,U_185,X_186] : ( multiply(U_4,inverse(U_4)) = inverse(inverse(inverse(inverse(inverse(multiply(multiply(U_185,inverse(U_185)),inverse(multiply(X_186,inverse(X_186))))))))) ),
    inference(superposition,[status(thm),theory(equality)],[c_16131,c_17285]) ).

tff(c_17527,plain,
    ! [U_199,X_200] : ( multiply(U_199,inverse(U_199)) = inverse(inverse(multiply(X_200,inverse(X_200)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16813,c_17413]) ).

tff(c_17548,plain,
    ! [X_200,Z_3] : ( inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X_200,inverse(X_200)))),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_17527,c_16813]) ).

tff(c_17971,plain,
    ! [Z_201] : ( inverse(inverse(inverse(inverse(Z_201)))) = Z_201 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16793,c_17548]) ).

tff(c_17995,plain,
    ! [U_15,Z_3] : ( multiply(multiply(U_15,inverse(U_15)),Z_3) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_17971,c_16813]) ).

tff(c_17958,plain,
    ! [Z_3] : ( inverse(inverse(inverse(inverse(Z_3)))) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16793,c_17548]) ).

tff(c_16691,plain,
    ! [U_8,X_190,U_191] : ( inverse(multiply(multiply(multiply(U_8,inverse(U_8)),X_190),multiply(U_191,inverse(U_191)))) = inverse(X_190) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14242,c_16566]) ).

tff(c_19520,plain,
    ! [X_212,U_213] : ( inverse(multiply(X_212,multiply(U_213,inverse(U_213)))) = inverse(X_212) ),
    inference(demodulation,[status(thm),theory(equality)],[c_17995,c_16691]) ).

tff(c_19549,plain,
    ! [X_212,U_213] : ( multiply(X_212,multiply(U_213,inverse(U_213))) = inverse(inverse(inverse(inverse(X_212)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_19520,c_17958]) ).

tff(c_19771,plain,
    ! [X_214,U_215] : ( multiply(X_214,multiply(U_215,inverse(U_215))) = X_214 ),
    inference(demodulation,[status(thm),theory(equality)],[c_17958,c_19549]) ).

tff(c_19812,plain,
    ! [X_214,U_15] : ( multiply(X_214,inverse(multiply(U_15,inverse(U_15)))) = X_214 ),
    inference(superposition,[status(thm),theory(equality)],[c_17995,c_19771]) ).

tff(c_19751,plain,
    ! [X_212,U_213] : ( multiply(X_212,multiply(U_213,inverse(U_213))) = X_212 ),
    inference(demodulation,[status(thm),theory(equality)],[c_17958,c_19549]) ).

tff(c_20032,plain,
    ! [X_218,Y_219,Z_220] : ( inverse(multiply(multiply(inverse(multiply(multiply(X_218,Y_219),Z_220)),X_218),Y_219)) = Z_220 ),
    inference(superposition,[status(thm),theory(equality)],[c_19520,c_2]) ).

tff(c_20149,plain,
    ! [U_8,Z_220,U_162,X_161] : ( inverse(multiply(multiply(inverse(multiply(multiply(U_8,inverse(U_8)),Z_220)),multiply(U_162,inverse(U_162))),inverse(multiply(X_161,inverse(X_161))))) = Z_220 ),
    inference(superposition,[status(thm),theory(equality)],[c_14242,c_20032]) ).

tff(c_20192,plain,
    ! [Z_220] : ( inverse(inverse(Z_220)) = Z_220 ),
    inference(demodulation,[status(thm),theory(equality)],[c_19812,c_19751,c_17995,c_20149]) ).

tff(c_20115,plain,
    ! [U_213,Y_219,Z_220] : ( inverse(multiply(inverse(multiply(multiply(multiply(U_213,inverse(U_213)),Y_219),Z_220)),Y_219)) = Z_220 ),
    inference(superposition,[status(thm),theory(equality)],[c_19751,c_20032]) ).

tff(c_20184,plain,
    ! [Y_219,Z_220] : ( inverse(multiply(inverse(multiply(Y_219,Z_220)),Y_219)) = Z_220 ),
    inference(demodulation,[status(thm),theory(equality)],[c_17995,c_20115]) ).

tff(c_20877,plain,
    ! [Y_230,Z_231] : ( inverse(multiply(inverse(multiply(Y_230,Z_231)),Y_230)) = Z_231 ),
    inference(demodulation,[status(thm),theory(equality)],[c_17995,c_20115]) ).

tff(c_21233,plain,
    ! [Z_234,Y_235] : ( inverse(multiply(Z_234,inverse(multiply(Y_235,Z_234)))) = Y_235 ),
    inference(superposition,[status(thm),theory(equality)],[c_20184,c_20877]) ).

tff(c_21264,plain,
    ! [Z_234,Y_235] : ( multiply(Z_234,inverse(multiply(Y_235,Z_234))) = inverse(Y_235) ),
    inference(superposition,[status(thm),theory(equality)],[c_21233,c_20192]) ).

tff(c_18169,plain,
    ! [X_1,Y_2,Z_3,U_4] : ( multiply(multiply(multiply(inverse(multiply(multiply(X_1,Y_2),Z_3)),X_1),Y_2),multiply(U_4,inverse(U_4))) = inverse(inverse(inverse(Z_3))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_17971]) ).

tff(c_28823,plain,
    ! [X_291,Y_292,Z_293,U_294] : ( multiply(multiply(multiply(inverse(multiply(multiply(X_291,Y_292),Z_293)),X_291),Y_292),multiply(U_294,inverse(U_294))) = inverse(Z_293) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20192,c_18169]) ).

tff(c_29035,plain,
    ! [Y_235,X_291,Y_292,U_294] : ( multiply(multiply(multiply(inverse(inverse(Y_235)),X_291),Y_292),multiply(U_294,inverse(U_294))) = inverse(inverse(multiply(Y_235,multiply(X_291,Y_292)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_21264,c_28823]) ).

tff(c_29295,plain,
    ! [Y_235,X_291,Y_292] : ( multiply(multiply(Y_235,X_291),Y_292) = multiply(Y_235,multiply(X_291,Y_292)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20192,c_19751,c_20192,c_29035]) ).

tff(c_287,plain,
    ! [U_20,X_21,Y_22,U_23] : ( inverse(multiply(multiply(multiply(inverse(multiply(U_20,inverse(U_20))),X_21),Y_22),multiply(U_23,inverse(U_23)))) = inverse(multiply(X_21,Y_22)) ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_426,plain,
    ! [X_24,U_25] : ( inverse(multiply(X_24,inverse(X_24))) = inverse(multiply(U_25,inverse(U_25))) ),
    inference(superposition,[status(thm),theory(equality)],[c_287,c_128]) ).

tff(c_500,plain,
    ! [X_24,U_25,U_9] : ( multiply(multiply(X_24,inverse(X_24)),inverse(multiply(U_25,inverse(U_25)))) = multiply(U_9,inverse(U_9)) ),
    inference(superposition,[status(thm),theory(equality)],[c_426,c_37]) ).

tff(c_313,plain,
    ! [X_21,U_15] : ( inverse(multiply(X_21,inverse(X_21))) = inverse(multiply(U_15,inverse(U_15))) ),
    inference(superposition,[status(thm),theory(equality)],[c_287,c_128]) ).

tff(c_1399,plain,
    ! [U_39,X_40,Y_41,U_42] : ( multiply(U_39,inverse(U_39)) = inverse(multiply(multiply(inverse(multiply(multiply(X_40,Y_41),inverse(multiply(U_42,inverse(U_42))))),X_40),Y_41)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_287]) ).

tff(c_2075,plain,
    ! [U_48,X_49,X_50] : ( multiply(U_48,inverse(U_48)) = inverse(multiply(multiply(inverse(multiply(X_49,inverse(X_49))),X_50),inverse(X_50))) ),
    inference(superposition,[status(thm),theory(equality)],[c_313,c_1399]) ).

tff(c_2899,plain,
    ! [U_54,X_55,X_56,U_57] : ( inverse(multiply(multiply(multiply(multiply(U_54,inverse(U_54)),inverse(multiply(X_55,inverse(X_55)))),X_56),multiply(U_57,inverse(U_57)))) = inverse(X_56) ),
    inference(superposition,[status(thm),theory(equality)],[c_2075,c_2]) ).

tff(c_3156,plain,
    ! [U_9,X_55,X_56,U_57] : ( inverse(multiply(multiply(multiply(multiply(U_9,inverse(U_9)),inverse(multiply(X_55,inverse(X_55)))),X_56),multiply(U_57,inverse(U_57)))) = inverse(X_56) ),
    inference(superposition,[status(thm),theory(equality)],[c_500,c_2899]) ).

tff(c_3285,plain,
    ! [U_58,X_59,U_60] : ( inverse(multiply(multiply(multiply(U_58,inverse(U_58)),X_59),multiply(U_60,inverse(U_60)))) = inverse(X_59) ),
    inference(demodulation,[status(thm),theory(equality)],[c_500,c_3156]) ).

tff(c_132,plain,
    ! [U_15,X_1,Y_2,U_4] : ( inverse(multiply(multiply(multiply(inverse(multiply(U_15,inverse(U_15))),X_1),Y_2),multiply(U_4,inverse(U_4)))) = inverse(multiply(X_1,Y_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_95,c_2]) ).

tff(c_3383,plain,
    ! [U_15,X_59] : ( inverse(multiply(inverse(inverse(multiply(U_15,inverse(U_15)))),X_59)) = inverse(X_59) ),
    inference(superposition,[status(thm),theory(equality)],[c_3285,c_132]) ).

tff(c_3400,plain,
    ! [U_15,Z_3] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_15,inverse(U_15)),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_3285,c_128]) ).

tff(c_2285,plain,
    ! [U_48,X_49,X_50,U_4] : ( inverse(multiply(multiply(multiply(multiply(U_48,inverse(U_48)),inverse(multiply(X_49,inverse(X_49)))),X_50),multiply(U_4,inverse(U_4)))) = inverse(X_50) ),
    inference(superposition,[status(thm),theory(equality)],[c_2075,c_2]) ).

tff(c_3897,plain,
    ! [U_63,Z_64] : ( inverse(inverse(inverse(inverse(multiply(multiply(U_63,inverse(U_63)),Z_64))))) = Z_64 ),
    inference(superposition,[status(thm),theory(equality)],[c_3285,c_128]) ).

tff(c_4031,plain,
    ! [U_4,U_48,X_49] : ( multiply(U_4,inverse(U_4)) = inverse(inverse(inverse(inverse(inverse(multiply(multiply(U_48,inverse(U_48)),inverse(multiply(X_49,inverse(X_49))))))))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2285,c_3897]) ).

tff(c_4155,plain,
    ! [U_65,X_66] : ( multiply(U_65,inverse(U_65)) = inverse(inverse(multiply(X_66,inverse(X_66)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3400,c_4031]) ).

tff(c_4176,plain,
    ! [X_66,Z_3] : ( inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X_66,inverse(X_66)))),Z_3))))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_4155,c_3400]) ).

tff(c_4612,plain,
    ! [Z_67] : ( inverse(inverse(inverse(inverse(Z_67)))) = Z_67 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3383,c_4176]) ).

tff(c_4636,plain,
    ! [U_15,Z_3] : ( multiply(multiply(U_15,inverse(U_15)),Z_3) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_4612,c_3400]) ).

tff(c_4598,plain,
    ! [Z_3] : ( inverse(inverse(inverse(inverse(Z_3)))) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3383,c_4176]) ).

tff(c_3272,plain,
    ! [U_9,X_56,U_57] : ( inverse(multiply(multiply(multiply(U_9,inverse(U_9)),X_56),multiply(U_57,inverse(U_57)))) = inverse(X_56) ),
    inference(demodulation,[status(thm),theory(equality)],[c_500,c_3156]) ).

tff(c_6684,plain,
    ! [X_85,U_86] : ( inverse(multiply(X_85,multiply(U_86,inverse(U_86)))) = inverse(X_85) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4636,c_3272]) ).

tff(c_6710,plain,
    ! [X_85,U_86] : ( multiply(X_85,multiply(U_86,inverse(U_86))) = inverse(inverse(inverse(inverse(X_85)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_6684,c_4598]) ).

tff(c_6913,plain,
    ! [X_87,U_88] : ( multiply(X_87,multiply(U_88,inverse(U_88))) = X_87 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4598,c_6710]) ).

tff(c_6974,plain,
    ! [X_87,U_15] : ( multiply(X_87,inverse(multiply(U_15,inverse(U_15)))) = X_87 ),
    inference(superposition,[status(thm),theory(equality)],[c_4636,c_6913]) ).

tff(c_6896,plain,
    ! [X_85,U_86] : ( multiply(X_85,multiply(U_86,inverse(U_86))) = X_85 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4598,c_6710]) ).

tff(c_7232,plain,
    ! [X_91,Y_92,Z_93] : ( inverse(multiply(multiply(inverse(multiply(multiply(X_91,Y_92),Z_93)),X_91),Y_92)) = Z_93 ),
    inference(superposition,[status(thm),theory(equality)],[c_6684,c_2]) ).

tff(c_7365,plain,
    ! [U_9,Z_93,X_24,U_25] : ( inverse(multiply(multiply(inverse(multiply(multiply(U_9,inverse(U_9)),Z_93)),multiply(X_24,inverse(X_24))),inverse(multiply(U_25,inverse(U_25))))) = Z_93 ),
    inference(superposition,[status(thm),theory(equality)],[c_500,c_7232]) ).

tff(c_7417,plain,
    ! [Z_94] : ( inverse(inverse(Z_94)) = Z_94 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6974,c_6896,c_4636,c_7365]) ).

tff(c_7468,plain,
    ! [Z_94,U_9] : ( multiply(inverse(Z_94),Z_94) = multiply(U_9,inverse(U_9)) ),
    inference(superposition,[status(thm),theory(equality)],[c_7417,c_37]) ).

tff(c_8889,plain,
    ! [X_113,Z_114] : ( multiply(X_113,inverse(multiply(inverse(Z_114),Z_114))) = X_113 ),
    inference(superposition,[status(thm),theory(equality)],[c_7417,c_6974]) ).

tff(c_9655,plain,
    ! [Z_120,Z_119] : ( multiply(inverse(Z_120),Z_120) = multiply(inverse(Z_119),Z_119) ),
    inference(superposition,[status(thm),theory(equality)],[c_7468,c_8889]) ).

tff(c_4,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_286,plain,
    multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
    inference(splitLeft,[status(thm)],[c_4]) ).

tff(c_9769,plain,
    ! [Z_120] : ( multiply(inverse(a1),a1) != multiply(inverse(Z_120),Z_120) ),
    inference(superposition,[status(thm),theory(equality)],[c_9655,c_286]) ).

tff(c_13920,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_9769]) ).

tff(c_13921,plain,
    ( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
    inference(splitRight,[status(thm)],[c_4]) ).

tff(c_13933,plain,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    inference(splitLeft,[status(thm)],[c_13921]) ).

tff(c_57585,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29295,c_13933]) ).

tff(c_57586,plain,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    inference(splitRight,[status(thm)],[c_13921]) ).

tff(c_64492,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_64347,c_57586]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP059-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12  % 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
% 0.11/0.33  % Computer : n024.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu Aug  3 22:00:45 EDT 2023
% 0.11/0.34  % CPUTime  : 
% 28.04/10.83  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.04/10.85  
% 28.04/10.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.16/10.89  
% 28.16/10.89  Inference rules
% 28.16/10.89  ----------------------
% 28.16/10.89  #Ref     : 1
% 28.16/10.89  #Sup     : 17855
% 28.16/10.89  #Fact    : 0
% 28.16/10.89  #Define  : 0
% 28.16/10.89  #Split   : 2
% 28.16/10.89  #Chain   : 0
% 28.16/10.89  #Close   : 0
% 28.16/10.89  
% 28.16/10.89  Ordering : KBO
% 28.16/10.89  
% 28.16/10.89  Simplification rules
% 28.16/10.89  ----------------------
% 28.16/10.89  #Subsume      : 2919
% 28.16/10.89  #Demod        : 15484
% 28.16/10.89  #Tautology    : 2923
% 28.16/10.89  #SimpNegUnit  : 0
% 28.16/10.89  #BackRed      : 95
% 28.16/10.89  
% 28.16/10.89  #Partial instantiations: 0
% 28.16/10.89  #Strategies tried      : 1
% 28.16/10.89  
% 28.16/10.89  Timing (in seconds)
% 28.16/10.89  ----------------------
% 28.16/10.89  Preprocessing        : 0.42
% 28.16/10.89  Parsing              : 0.21
% 28.16/10.89  CNF conversion       : 0.02
% 28.16/10.89  Main loop            : 9.31
% 28.16/10.89  Inferencing          : 2.30
% 28.16/10.89  Reduction            : 5.31
% 28.16/10.89  Demodulation         : 4.95
% 28.16/10.89  BG Simplification    : 0.32
% 28.16/10.89  Subsumption          : 0.84
% 28.16/10.89  Abstraction          : 0.66
% 28.16/10.89  MUC search           : 0.00
% 28.16/10.89  Cooper               : 0.00
% 28.16/10.89  Total                : 9.81
% 28.16/10.89  Index Insertion      : 0.00
% 28.16/10.89  Index Deletion       : 0.00
% 28.16/10.89  Index Matching       : 0.00
% 28.16/10.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------