%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP237-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n014.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 10:40:35 EDT 2023

% Result   : Unsatisfiable 13.93s 5.01s
% Output   : CNFRefutation 13.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  696 ( 558 unt;  12 typ;   0 def)
%            Number of atoms       :  906 ( 875 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  485 ( 263   ~; 222   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   2 avg)
%            Maximal term depth    :    4 (   1 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    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :  284 (; 284   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c9 > sk_c8 > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(sk_c4,type,
    sk_c4: $i ).

tff(sk_c7,type,
    sk_c7: $i ).

tff(sk_c5,type,
    sk_c5: $i ).

tff(sk_c2,type,
    sk_c2: $i ).

tff(sk_c3,type,
    sk_c3: $i ).

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

tff(sk_c8,type,
    sk_c8: $i ).

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

tff(sk_c9,type,
    sk_c9: $i ).

tff(sk_c6,type,
    sk_c6: $i ).

tff(sk_c1,type,
    sk_c1: $i ).

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

tff(f_57,axiom,
    ! [X] : ( multiply(inverse(X),X) = identity ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_170,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_146,axiom,
    ( ( multiply(sk_c2,sk_c9) = sk_c3 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_206,axiom,
    ! [X5,X6,X3,X7,X1,X2,X4] :
      ( ( inverse(sk_c9) != sk_c8 )
      | ( inverse(X4) != sk_c9 )
      | ( multiply(X4,sk_c8) != sk_c9 )
      | ( multiply(sk_c9,X5) != sk_c8 )
      | ( multiply(X6,sk_c9) != X5 )
      | ( inverse(X6) != sk_c9 )
      | ( multiply(X2,X1) != sk_c9 )
      | ( inverse(X2) != X1 )
      | ( multiply(X1,sk_c8) != sk_c9 )
      | ( multiply(sk_c9,X3) != sk_c8 )
      | ( multiply(X7,sk_c9) != X3 )
      | ( inverse(X7) != sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_140,axiom,
    ( ( multiply(sk_c2,sk_c9) = sk_c3 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c9 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_152,axiom,
    ( ( multiply(sk_c2,sk_c9) = sk_c3 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_149,axiom,
    ( ( multiply(sk_c2,sk_c9) = sk_c3 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c9 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c9 )
    | ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c9 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_119,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_125,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ( ( multiply(sk_c9,sk_c3) = sk_c8 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c9 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_164,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_167,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_161,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_158,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_155,axiom,
    ( ( inverse(sk_c2) = sk_c9 )
    | ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( inverse(sk_c6) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ( ( inverse(sk_c1) = sk_c9 )
    | ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_65,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( inverse(sk_c4) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ( ( inverse(sk_c9) = sk_c8 )
    | ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_30493,plain,
    ! [X_359,Y_360,Z_361] : ( multiply(multiply(X_359,Y_360),Z_361) = multiply(X_359,multiply(Y_360,Z_361)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_30532,plain,
    ! [X_2,Z_361] : ( multiply(inverse(X_2),multiply(X_2,Z_361)) = multiply(identity,Z_361) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_30493]) ).

tff(c_30544,plain,
    ! [X_2,Z_361] : ( multiply(inverse(X_2),multiply(X_2,Z_361)) = Z_361 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30532]) ).

tff(c_32492,plain,
    ! [X_399,Z_400] : ( multiply(inverse(X_399),multiply(X_399,Z_400)) = Z_400 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30532]) ).

tff(c_32768,plain,
    ! [X_403,Z_404] : ( multiply(inverse(inverse(X_403)),Z_404) = multiply(X_403,Z_404) ),
    inference(superposition,[status(thm),theory(equality)],[c_30544,c_32492]) ).

tff(c_32534,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_32492]) ).

tff(c_32775,plain,
    ! [X_403] : ( multiply(X_403,identity) = X_403 ),
    inference(superposition,[status(thm),theory(equality)],[c_32768,c_32534]) ).

tff(c_7607,plain,
    ! [X_156,Y_157,Z_158] : ( multiply(multiply(X_156,Y_157),Z_158) = multiply(X_156,multiply(Y_157,Z_158)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_7646,plain,
    ! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = multiply(identity,Z_158) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7607]) ).

tff(c_7658,plain,
    ! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = Z_158 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7646]) ).

tff(c_9757,plain,
    ! [X_198,Z_199] : ( multiply(inverse(X_198),multiply(X_198,Z_199)) = Z_199 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7646]) ).

tff(c_10070,plain,
    ! [X_203,Z_204] : ( multiply(inverse(inverse(X_203)),Z_204) = multiply(X_203,Z_204) ),
    inference(superposition,[status(thm),theory(equality)],[c_7658,c_9757]) ).

tff(c_9796,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_9757]) ).

tff(c_10077,plain,
    ! [X_203] : ( multiply(X_203,identity) = X_203 ),
    inference(superposition,[status(thm),theory(equality)],[c_10070,c_9796]) ).

tff(c_22,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_110,plain,
    inverse(sk_c1) = sk_c9,
    inference(splitLeft,[status(thm)],[c_22]) ).

tff(c_114,plain,
    multiply(sk_c9,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_110,c_4]) ).

tff(c_18,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_97,plain,
    inverse(sk_c9) = sk_c8,
    inference(splitLeft,[status(thm)],[c_18]) ).

tff(c_101,plain,
    multiply(sk_c8,sk_c9) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_97,c_4]) ).

tff(c_7643,plain,
    ! [Z_158] : ( multiply(sk_c8,multiply(sk_c9,Z_158)) = multiply(identity,Z_158) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_7607]) ).

tff(c_7673,plain,
    ! [Z_160] : ( multiply(sk_c8,multiply(sk_c9,Z_160)) = Z_160 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7643]) ).

tff(c_7694,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_7673]) ).

tff(c_4593,plain,
    ! [X_97,Y_98,Z_99] : ( multiply(multiply(X_97,Y_98),Z_99) = multiply(X_97,multiply(Y_98,Z_99)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_4635,plain,
    ! [Z_99] : ( multiply(sk_c8,multiply(sk_c9,Z_99)) = multiply(identity,Z_99) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_4593]) ).

tff(c_4679,plain,
    ! [Z_102] : ( multiply(sk_c8,multiply(sk_c9,Z_102)) = Z_102 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4635]) ).

tff(c_4709,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_4679]) ).

tff(c_78,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_123,plain,
    inverse(sk_c2) = sk_c9,
    inference(splitLeft,[status(thm)],[c_78]) ).

tff(c_127,plain,
    multiply(sk_c9,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_123,c_4]) ).

tff(c_4706,plain,
    multiply(sk_c8,identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_127,c_4679]) ).

tff(c_4731,plain,
    sk_c2 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_4709,c_4706]) ).

tff(c_46,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_136,plain,
    multiply(sk_c9,sk_c3) = sk_c8,
    inference(splitLeft,[status(thm)],[c_46]) ).

tff(c_62,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_3795,plain,
    multiply(sk_c2,sk_c9) = sk_c3,
    inference(splitLeft,[status(thm)],[c_62]) ).

tff(c_3815,plain,
    ! [X_87,Y_88,Z_89] : ( multiply(multiply(X_87,Y_88),Z_89) = multiply(X_87,multiply(Y_88,Z_89)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_3854,plain,
    ! [Z_89] : ( multiply(sk_c9,multiply(sk_c2,Z_89)) = multiply(identity,Z_89) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_3815]) ).

tff(c_3878,plain,
    ! [Z_90] : ( multiply(sk_c9,multiply(sk_c2,Z_90)) = Z_90 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3854]) ).

tff(c_3890,plain,
    multiply(sk_c9,sk_c3) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_3795,c_3878]) ).

tff(c_3894,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_136,c_3890]) ).

tff(c_80,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 )
      | ( inverse(sk_c9) != sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_3922,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_9,sk_c8)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c8 )
      | ( inverse(X4_12) != sk_c8 )
      | ( inverse(sk_c8) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_3894,c_80]) ).

tff(c_3923,plain,
    inverse(sk_c8) != sk_c8,
    inference(splitLeft,[status(thm)],[c_3922]) ).

tff(c_3910,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_97]) ).

tff(c_3931,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3923,c_3910]) ).

tff(c_3933,plain,
    inverse(sk_c8) = sk_c8,
    inference(splitRight,[status(thm)],[c_3922]) ).

tff(c_3465,plain,
    ! [X_79,Y_80,Z_81] : ( multiply(multiply(X_79,Y_80),Z_81) = multiply(X_79,multiply(Y_80,Z_81)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_3510,plain,
    ! [Z_81] : ( multiply(sk_c8,multiply(sk_c9,Z_81)) = multiply(identity,Z_81) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_3465]) ).

tff(c_3637,plain,
    ! [Z_85] : ( multiply(sk_c8,multiply(sk_c9,Z_85)) = Z_85 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3510]) ).

tff(c_3664,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_3637]) ).

tff(c_3661,plain,
    multiply(sk_c8,identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_127,c_3637]) ).

tff(c_3708,plain,
    sk_c2 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_3664,c_3661]) ).

tff(c_178,plain,
    ! [X_15,Y_16,Z_17] : ( multiply(multiply(X_15,Y_16),Z_17) = multiply(X_15,multiply(Y_16,Z_17)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_211,plain,
    ! [X_2,Z_17] : ( multiply(inverse(X_2),multiply(X_2,Z_17)) = multiply(identity,Z_17) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_178]) ).

tff(c_222,plain,
    ! [X_2,Z_17] : ( multiply(inverse(X_2),multiply(X_2,Z_17)) = Z_17 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_211]) ).

tff(c_1769,plain,
    ! [X_47,Z_48] : ( multiply(inverse(X_47),multiply(X_47,Z_48)) = Z_48 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_211]) ).

tff(c_2038,plain,
    ! [X_51,Z_52] : ( multiply(inverse(inverse(X_51)),Z_52) = multiply(X_51,Z_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_222,c_1769]) ).

tff(c_2076,plain,
    ! [X_51] : ( multiply(X_51,inverse(X_51)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2038]) ).

tff(c_58,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_156,plain,
    multiply(sk_c2,sk_c9) = sk_c3,
    inference(splitLeft,[status(thm)],[c_58]) ).

tff(c_202,plain,
    ! [Z_17] : ( multiply(sk_c9,multiply(sk_c2,Z_17)) = multiply(identity,Z_17) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_178]) ).

tff(c_224,plain,
    ! [Z_18] : ( multiply(sk_c9,multiply(sk_c2,Z_18)) = Z_18 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_202]) ).

tff(c_236,plain,
    multiply(sk_c9,sk_c3) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_156,c_224]) ).

tff(c_240,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_136,c_236]) ).

tff(c_455,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_101]) ).

tff(c_454,plain,
    inverse(sk_c1) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_110]) ).

tff(c_42,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_150,plain,
    multiply(sk_c1,sk_c8) = sk_c9,
    inference(splitLeft,[status(thm)],[c_42]) ).

tff(c_449,plain,
    multiply(sk_c1,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_150]) ).

tff(c_1787,plain,
    multiply(inverse(sk_c1),sk_c8) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_449,c_1769]) ).

tff(c_1821,plain,
    multiply(sk_c8,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_454,c_1787]) ).

tff(c_1872,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_455,c_1821]) ).

tff(c_1814,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_1769]) ).

tff(c_2045,plain,
    ! [X_51] : ( multiply(X_51,identity) = X_51 ),
    inference(superposition,[status(thm),theory(equality)],[c_2038,c_1814]) ).

tff(c_585,plain,
    ! [X_22,Z_23] : ( multiply(inverse(X_22),multiply(X_22,Z_23)) = Z_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_211]) ).

tff(c_761,plain,
    ! [X_25,Z_26] : ( multiply(inverse(inverse(X_25)),Z_26) = multiply(X_25,Z_26) ),
    inference(superposition,[status(thm),theory(equality)],[c_222,c_585]) ).

tff(c_612,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_585]) ).

tff(c_768,plain,
    ! [X_25] : ( multiply(X_25,identity) = X_25 ),
    inference(superposition,[status(thm),theory(equality)],[c_761,c_612]) ).

tff(c_205,plain,
    ! [Z_17] : ( multiply(sk_c9,multiply(sk_c1,Z_17)) = multiply(identity,Z_17) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_178]) ).

tff(c_220,plain,
    ! [Z_17] : ( multiply(sk_c9,multiply(sk_c1,Z_17)) = Z_17 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_205]) ).

tff(c_533,plain,
    ! [Z_21] : ( multiply(sk_c8,multiply(sk_c1,Z_21)) = Z_21 ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_220]) ).

tff(c_545,plain,
    multiply(sk_c8,sk_c8) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_449,c_533]) ).

tff(c_549,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_455,c_545]) ).

tff(c_363,plain,
    multiply(sk_c8,sk_c3) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_136]) ).

tff(c_365,plain,
    inverse(sk_c2) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_123]) ).

tff(c_361,plain,
    multiply(sk_c2,sk_c8) = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_156]) ).

tff(c_251,plain,
    inverse(sk_c1) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_110]) ).

tff(c_246,plain,
    multiply(sk_c1,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_150]) ).

tff(c_242,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_97,c_80]) ).

tff(c_243,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(splitLeft,[status(thm)],[c_242]) ).

tff(c_286,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c8 )
      | ( inverse(X4_12) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_240,c_243]) ).

tff(c_348,plain,
    inverse(sk_c1) != sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_246,c_286]) ).

tff(c_357,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_251,c_348]) ).

tff(c_358,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_242]) ).

tff(c_359,plain,
    ! [X7_9] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_358]) ).

tff(c_427,plain,
    ! [X7_20] :
      ( ( inverse(X7_20) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_20,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_240,c_240,c_359]) ).

tff(c_430,plain,
    ( ( inverse(sk_c2) != sk_c8 )
    | ( multiply(sk_c8,sk_c3) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_361,c_427]) ).

tff(c_445,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_363,c_365,c_430]) ).

tff(c_446,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_358]) ).

tff(c_513,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_240,c_240,c_240,c_240,c_446]) ).

tff(c_514,plain,
    ! [X6_7] :
      ( ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_513]) ).

tff(c_1758,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_768,c_549,c_549,c_2,c_549,c_549,c_514]) ).

tff(c_456,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_240,c_97]) ).

tff(c_558,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_549,c_549,c_456]) ).

tff(c_1760,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1758,c_558]) ).

tff(c_1761,plain,
    ! [X2_11] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_513]) ).

tff(c_3405,plain,
    ! [X2_11] : ( inverse(X2_11) != identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_2076,c_1872,c_2045,c_1872,c_1872,c_1761]) ).

tff(c_1880,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1872,c_1872,c_456]) ).

tff(c_3407,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3405,c_1880]) ).

tff(c_3409,plain,
    multiply(sk_c2,sk_c9) != sk_c3,
    inference(splitRight,[status(thm)],[c_58]) ).

tff(c_3721,plain,
    multiply(sk_c1,sk_c9) != sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_3708,c_3409]) ).

tff(c_66,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_3422,plain,
    inverse(sk_c6) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_3409,c_66]) ).

tff(c_3426,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3422,c_4]) ).

tff(c_3655,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_3426,c_3637]) ).

tff(c_3746,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_3664,c_3655]) ).

tff(c_3658,plain,
    multiply(sk_c8,sk_c8) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_136,c_3637]) ).

tff(c_3453,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_3409,c_62]) ).

tff(c_3652,plain,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_3453,c_3637]) ).

tff(c_3730,plain,
    sk_c7 = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_3658,c_3652]) ).

tff(c_64,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_3437,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_3409,c_64]) ).

tff(c_3732,plain,
    multiply(sk_c6,sk_c9) = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_3730,c_3437]) ).

tff(c_3747,plain,
    multiply(sk_c1,sk_c9) = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_3746,c_3732]) ).

tff(c_3751,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3721,c_3747]) ).

tff(c_3752,plain,
    inverse(sk_c6) = sk_c9,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_3757,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3752,c_4]) ).

tff(c_3901,plain,
    multiply(sk_c8,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_3757]) ).

tff(c_3863,plain,
    ! [X_2,Z_89] : ( multiply(inverse(X_2),multiply(X_2,Z_89)) = multiply(identity,Z_89) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_3815]) ).

tff(c_3876,plain,
    ! [X_2,Z_89] : ( multiply(inverse(X_2),multiply(X_2,Z_89)) = Z_89 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3863]) ).

tff(c_4093,plain,
    multiply(inverse(sk_c8),identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_3901,c_3876]) ).

tff(c_4099,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_3933,c_4093]) ).

tff(c_3904,plain,
    multiply(sk_c8,sk_c3) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_136]) ).

tff(c_4029,plain,
    multiply(inverse(sk_c8),sk_c8) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_3904,c_3876]) ).

tff(c_4035,plain,
    sk_c3 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4029]) ).

tff(c_4037,plain,
    multiply(sk_c8,identity) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_4035,c_3904]) ).

tff(c_4204,plain,
    sk_c8 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4099,c_4037]) ).

tff(c_3907,plain,
    multiply(sk_c8,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_114]) ).

tff(c_4058,plain,
    multiply(inverse(sk_c8),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_3907,c_3876]) ).

tff(c_4064,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_3933,c_4058]) ).

tff(c_4372,plain,
    multiply(sk_c6,identity) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_4204,c_4064]) ).

tff(c_3903,plain,
    inverse(sk_c6) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_3752]) ).

tff(c_4266,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4204,c_3903]) ).

tff(c_3945,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3933,c_4]) ).

tff(c_4265,plain,
    multiply(sk_c6,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4204,c_4204,c_3945]) ).

tff(c_4395,plain,
    multiply(inverse(sk_c6),identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_4265,c_3876]) ).

tff(c_4402,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_4372,c_4266,c_4395]) ).

tff(c_4415,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_4402,c_4204]) ).

tff(c_3753,plain,
    multiply(sk_c1,sk_c8) != sk_c9,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_34,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_3761,plain,
    inverse(sk_c4) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_3753,c_34]) ).

tff(c_32,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c9 )
    | ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_3790,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_3753,c_32]) ).

tff(c_3899,plain,
    multiply(sk_c4,sk_c5) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_3790]) ).

tff(c_4071,plain,
    multiply(inverse(sk_c4),sk_c8) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_3899,c_3876]) ).

tff(c_4077,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_3761,c_4071]) ).

tff(c_4484,plain,
    multiply(sk_c5,sk_c1) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4415,c_4077]) ).

tff(c_4491,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_4484,c_3876]) ).

tff(c_4498,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4491]) ).

tff(c_3902,plain,
    multiply(sk_c1,sk_c8) != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_3894,c_3753]) ).

tff(c_4260,plain,
    multiply(sk_c1,sk_c6) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4204,c_4204,c_3902]) ).

tff(c_4572,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4498,c_4260]) ).

tff(c_4574,plain,
    multiply(sk_c2,sk_c9) != sk_c3,
    inference(splitRight,[status(thm)],[c_62]) ).

tff(c_4757,plain,
    multiply(sk_c1,sk_c9) != sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_4731,c_4574]) ).

tff(c_4700,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_3757,c_4679]) ).

tff(c_4782,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_4709,c_4700]) ).

tff(c_4703,plain,
    multiply(sk_c8,sk_c8) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_136,c_4679]) ).

tff(c_4573,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(splitRight,[status(thm)],[c_62]) ).

tff(c_4697,plain,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_4573,c_4679]) ).

tff(c_4767,plain,
    sk_c7 = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_4703,c_4697]) ).

tff(c_40,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_3783,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_3753,c_40]) ).

tff(c_4769,plain,
    multiply(sk_c6,sk_c9) = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_4767,c_3783]) ).

tff(c_4783,plain,
    multiply(sk_c1,sk_c9) = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_4782,c_4769]) ).

tff(c_4787,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4757,c_4783]) ).

tff(c_4789,plain,
    multiply(sk_c9,sk_c3) != sk_c8,
    inference(splitRight,[status(thm)],[c_46]) ).

tff(c_44,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c9 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_5306,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_44]) ).

tff(c_4788,plain,
    inverse(sk_c4) = sk_c5,
    inference(splitRight,[status(thm)],[c_46]) ).

tff(c_48,plain,
    ( ( multiply(sk_c5,sk_c8) = sk_c9 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_6720,plain,
    multiply(sk_c5,sk_c8) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_48]) ).

tff(c_6742,plain,
    ! [X_140,Y_141,Z_142] : ( multiply(multiply(X_140,Y_141),Z_142) = multiply(X_140,multiply(Y_141,Z_142)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_6781,plain,
    ! [Z_142] : ( multiply(sk_c8,multiply(sk_c9,Z_142)) = multiply(identity,Z_142) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_6742]) ).

tff(c_6825,plain,
    ! [Z_145] : ( multiply(sk_c8,multiply(sk_c9,Z_145)) = Z_145 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6781]) ).

tff(c_6852,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_6825]) ).

tff(c_5342,plain,
    ! [X_114,Y_115,Z_116] : ( multiply(multiply(X_114,Y_115),Z_116) = multiply(X_114,multiply(Y_115,Z_116)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_5384,plain,
    ! [Z_116] : ( multiply(sk_c8,multiply(sk_c9,Z_116)) = multiply(identity,Z_116) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_5342]) ).

tff(c_5438,plain,
    ! [Z_119] : ( multiply(sk_c8,multiply(sk_c9,Z_119)) = Z_119 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5384]) ).

tff(c_5468,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_5438]) ).

tff(c_4810,plain,
    multiply(sk_c2,sk_c9) = sk_c3,
    inference(splitLeft,[status(thm)],[c_66]) ).

tff(c_4865,plain,
    ! [X_104,Y_105,Z_106] : ( multiply(multiply(X_104,Y_105),Z_106) = multiply(X_104,multiply(Y_105,Z_106)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_4904,plain,
    ! [Z_106] : ( multiply(sk_c9,multiply(sk_c2,Z_106)) = multiply(identity,Z_106) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_4865]) ).

tff(c_4928,plain,
    ! [Z_107] : ( multiply(sk_c9,multiply(sk_c2,Z_107)) = Z_107 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4904]) ).

tff(c_4940,plain,
    multiply(sk_c9,sk_c3) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_4810,c_4928]) ).

tff(c_4944,plain,
    sk_c9 != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_4940,c_4789]) ).

tff(c_50,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_4860,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_50]) ).

tff(c_4910,plain,
    ! [Z_106] : ( multiply(sk_c8,multiply(sk_c9,Z_106)) = multiply(identity,Z_106) ),
    inference(superposition,[status(thm),theory(equality)],[c_101,c_4865]) ).

tff(c_5142,plain,
    ! [Z_112] : ( multiply(sk_c8,multiply(sk_c9,Z_112)) = Z_112 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4910]) ).

tff(c_5175,plain,
    multiply(sk_c8,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_114,c_5142]) ).

tff(c_54,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_4824,plain,
    inverse(sk_c6) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_54]) ).

tff(c_4828,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_4824,c_4]) ).

tff(c_5169,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_4828,c_5142]) ).

tff(c_5261,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5175,c_5169]) ).

tff(c_52,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_4848,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_52]) ).

tff(c_5262,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_5261,c_4848]) ).

tff(c_4907,plain,
    ! [Z_106] : ( multiply(sk_c9,multiply(sk_c1,Z_106)) = multiply(identity,Z_106) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_4865]) ).

tff(c_4924,plain,
    ! [Z_106] : ( multiply(sk_c9,multiply(sk_c1,Z_106)) = Z_106 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4907]) ).

tff(c_5275,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_5262,c_4924]) ).

tff(c_5281,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_4860,c_5275]) ).

tff(c_5283,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4944,c_5281]) ).

tff(c_5285,plain,
    multiply(sk_c2,sk_c9) != sk_c3,
    inference(splitRight,[status(thm)],[c_66]) ).

tff(c_5324,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_5285,c_62]) ).

tff(c_5284,plain,
    inverse(sk_c6) = sk_c9,
    inference(splitRight,[status(thm)],[c_66]) ).

tff(c_5289,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5284,c_4]) ).

tff(c_5462,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5289,c_5438]) ).

tff(c_6110,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_5462]) ).

tff(c_5330,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_4789,c_52]) ).

tff(c_6111,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_6110,c_5330]) ).

tff(c_5381,plain,
    ! [Z_116] : ( multiply(sk_c9,multiply(sk_c1,Z_116)) = multiply(identity,Z_116) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_5342]) ).

tff(c_5398,plain,
    ! [Z_116] : ( multiply(sk_c9,multiply(sk_c1,Z_116)) = Z_116 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5381]) ).

tff(c_6252,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_6111,c_5398]) ).

tff(c_6258,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5324,c_6252]) ).

tff(c_6270,plain,
    inverse(sk_c1) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6258,c_110]) ).

tff(c_6271,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6258,c_101]) ).

tff(c_5459,plain,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_5324,c_5438]) ).

tff(c_6312,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6271,c_5459]) ).

tff(c_6260,plain,
    multiply(sk_c1,sk_c8) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_6258,c_6111]) ).

tff(c_6341,plain,
    multiply(sk_c1,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6312,c_6260]) ).

tff(c_5387,plain,
    ! [X_2,Z_116] : ( multiply(inverse(X_2),multiply(X_2,Z_116)) = multiply(identity,Z_116) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5342]) ).

tff(c_6351,plain,
    ! [X_133,Z_134] : ( multiply(inverse(X_133),multiply(X_133,Z_134)) = Z_134 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5387]) ).

tff(c_6369,plain,
    multiply(inverse(sk_c1),identity) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_6341,c_6351]) ).

tff(c_6406,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_6270,c_6369]) ).

tff(c_6272,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6258,c_97]) ).

tff(c_6300,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_6272,c_4]) ).

tff(c_6429,plain,
    multiply(sk_c1,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6406,c_6406,c_6300]) ).

tff(c_6418,plain,
    sk_c9 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6406,c_6258]) ).

tff(c_38,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_5314,plain,
    multiply(sk_c1,sk_c8) = sk_c9,
    inference(splitLeft,[status(thm)],[c_38]) ).

tff(c_5415,plain,
    ! [Z_118] : ( multiply(sk_c9,multiply(sk_c1,Z_118)) = Z_118 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5381]) ).

tff(c_5427,plain,
    multiply(sk_c9,sk_c9) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_5314,c_5415]) ).

tff(c_5450,plain,
    multiply(sk_c8,sk_c8) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_5427,c_5438]) ).

tff(c_6477,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6429,c_6418,c_6406,c_6406,c_5450]) ).

tff(c_6415,plain,
    inverse(sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6406,c_6406,c_6272]) ).

tff(c_6480,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6477,c_6477,c_6415]) ).

tff(c_6483,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6477,c_6406]) ).

tff(c_6125,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_6111,c_5398]) ).

tff(c_6131,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5324,c_6125]) ).

tff(c_6145,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6131,c_97]) ).

tff(c_6144,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6131,c_101]) ).

tff(c_5871,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_5462]) ).

tff(c_5872,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_5871,c_5330]) ).

tff(c_5911,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_5872,c_5398]) ).

tff(c_5917,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5324,c_5911]) ).

tff(c_5932,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5917,c_97]) ).

tff(c_5947,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5932,c_4]) ).

tff(c_6024,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5947,c_5917,c_5450]) ).

tff(c_6034,plain,
    multiply(identity,identity) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6024,c_5468]) ).

tff(c_6037,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6034]) ).

tff(c_5495,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_5462]) ).

tff(c_5496,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_5495,c_5330]) ).

tff(c_5534,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_5496,c_5398]) ).

tff(c_5540,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5324,c_5534]) ).

tff(c_5553,plain,
    inverse(sk_c1) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5540,c_110]) ).

tff(c_5555,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_5540,c_97]) ).

tff(c_5570,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5555,c_4]) ).

tff(c_5611,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5570,c_5459]) ).

tff(c_5542,plain,
    multiply(sk_c1,sk_c8) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_5540,c_5496]) ).

tff(c_5631,plain,
    multiply(sk_c1,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5611,c_5542]) ).

tff(c_5646,plain,
    ! [X_122,Z_123] : ( multiply(inverse(X_122),multiply(X_122,Z_123)) = Z_123 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5387]) ).

tff(c_5664,plain,
    multiply(inverse(sk_c1),identity) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_5631,c_5646]) ).

tff(c_5698,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_5553,c_5664]) ).

tff(c_5473,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_97,c_80]) ).

tff(c_5474,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(splitLeft,[status(thm)],[c_5473]) ).

tff(c_5583,plain,
    ! [X4_121] :
      ( ( multiply(X4_121,sk_c8) != sk_c8 )
      | ( inverse(X4_121) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5540,c_5540,c_5474]) ).

tff(c_5591,plain,
    ( ( sk_c8 != identity )
    | ( inverse(inverse(sk_c8)) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5583]) ).

tff(c_5597,plain,
    sk_c8 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5555,c_5555,c_5591]) ).

tff(c_5706,plain,
    sk_c1 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5698,c_5597]) ).

tff(c_5711,plain,
    sk_c9 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5698,c_5540]) ).

tff(c_5563,plain,
    multiply(sk_c8,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5553,c_4]) ).

tff(c_5718,plain,
    multiply(sk_c1,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5698,c_5563]) ).

tff(c_5847,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5711,c_5718,c_5698,c_5698,c_5450]) ).

tff(c_5848,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5706,c_5847]) ).

tff(c_5849,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_5473]) ).

tff(c_5858,plain,
    ! [X7_9] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_5849]) ).

tff(c_5952,plain,
    ! [X7_127] :
      ( ( inverse(X7_127) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_127,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5917,c_5917,c_5917,c_5858]) ).

tff(c_5960,plain,
    ( ( inverse(inverse(sk_c8)) != sk_c8 )
    | ( multiply(sk_c8,identity) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5952]) ).

tff(c_5966,plain,
    sk_c8 != sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_5932,c_5932,c_5960]) ).

tff(c_6029,plain,
    sk_c1 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6024,c_5966]) ).

tff(c_6096,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6037,c_6029]) ).

tff(c_6097,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_5849]) ).

tff(c_6120,plain,
    ! [X6_7] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_6097]) ).

tff(c_6212,plain,
    ! [X6_131] :
      ( ( inverse(X6_131) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_131,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6131,c_6131,c_6131,c_6120]) ).

tff(c_6215,plain,
    ( ( inverse(sk_c8) != sk_c8 )
    | ( multiply(sk_c8,identity) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_6144,c_6212]) ).

tff(c_6229,plain,
    sk_c8 != sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_6145,c_6215]) ).

tff(c_6193,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6144,c_5459]) ).

tff(c_6137,plain,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6131,c_5324]) ).

tff(c_6245,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_5468,c_6193,c_6137]) ).

tff(c_6246,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6229,c_6245]) ).

tff(c_6247,plain,
    ! [X2_11] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 ) ),
    inference(splitRight,[status(thm)],[c_6097]) ).

tff(c_6285,plain,
    ! [X2_132] :
      ( ( multiply(inverse(X2_132),sk_c8) != sk_c8 )
      | ( multiply(X2_132,inverse(X2_132)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6258,c_6258,c_6247]) ).

tff(c_6292,plain,
    ( ( sk_c8 != identity )
    | ( multiply(sk_c8,inverse(sk_c8)) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_6285]) ).

tff(c_6713,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6480,c_6483,c_6483,c_2,c_6483,c_6483,c_6292]) ).

tff(c_6714,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(splitRight,[status(thm)],[c_38]) ).

tff(c_6846,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5289,c_6825]) ).

tff(c_7273,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_6846]) ).

tff(c_6715,plain,
    multiply(sk_c1,sk_c8) != sk_c9,
    inference(splitRight,[status(thm)],[c_38]) ).

tff(c_6727,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_6715,c_40]) ).

tff(c_7274,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_7273,c_6727]) ).

tff(c_6778,plain,
    ! [Z_142] : ( multiply(sk_c9,multiply(sk_c1,Z_142)) = multiply(identity,Z_142) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_6742]) ).

tff(c_6795,plain,
    ! [Z_142] : ( multiply(sk_c9,multiply(sk_c1,Z_142)) = Z_142 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6778]) ).

tff(c_7287,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_7274,c_6795]) ).

tff(c_7293,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6714,c_7287]) ).

tff(c_7422,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_97]) ).

tff(c_7308,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_97]) ).

tff(c_6913,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_6846]) ).

tff(c_6914,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_6913,c_6727]) ).

tff(c_6927,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_6914,c_6795]) ).

tff(c_6933,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6714,c_6927]) ).

tff(c_6947,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6933,c_97]) ).

tff(c_6946,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6933,c_101]) ).

tff(c_6784,plain,
    ! [X_2,Z_142] : ( multiply(inverse(X_2),multiply(X_2,Z_142)) = multiply(identity,Z_142) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_6742]) ).

tff(c_7012,plain,
    ! [X_148,Z_149] : ( multiply(inverse(X_148),multiply(X_148,Z_149)) = Z_149 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6784]) ).

tff(c_7030,plain,
    multiply(inverse(sk_c8),identity) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_6946,c_7012]) ).

tff(c_7061,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_6947,c_7030]) ).

tff(c_6865,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_97,c_80]) ).

tff(c_6866,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(splitLeft,[status(thm)],[c_6865]) ).

tff(c_6952,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c8 )
      | ( inverse(X4_12) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6933,c_6933,c_6866]) ).

tff(c_6996,plain,
    ( ( sk_c8 != identity )
    | ( inverse(sk_c8) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_6946,c_6952]) ).

tff(c_7003,plain,
    sk_c8 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6947,c_6996]) ).

tff(c_7064,plain,
    sk_c1 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_7003]) ).

tff(c_6980,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_6947,c_4]) ).

tff(c_7081,plain,
    multiply(sk_c1,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_7061,c_6980]) ).

tff(c_6939,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6933,c_6720]) ).

tff(c_7202,plain,
    multiply(sk_c5,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_7061,c_6939]) ).

tff(c_6942,plain,
    multiply(sk_c4,sk_c5) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_6933,c_5306]) ).

tff(c_7105,plain,
    multiply(sk_c4,sk_c5) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7061,c_6942]) ).

tff(c_6797,plain,
    ! [X_2,Z_142] : ( multiply(inverse(X_2),multiply(X_2,Z_142)) = Z_142 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6784]) ).

tff(c_7109,plain,
    multiply(inverse(sk_c4),sk_c1) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_7105,c_6797]) ).

tff(c_7115,plain,
    multiply(sk_c5,sk_c1) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4788,c_7109]) ).

tff(c_7218,plain,
    sk_c5 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7202,c_7115]) ).

tff(c_7219,plain,
    multiply(sk_c1,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7218,c_7202]) ).

tff(c_7223,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_7081,c_7219]) ).

tff(c_7225,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7064,c_7223]) ).

tff(c_7226,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_6865]) ).

tff(c_7295,plain,
    ! [X7_9] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_7226]) ).

tff(c_7351,plain,
    ! [X7_153] :
      ( ( inverse(X7_153) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_153,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_7293,c_7293,c_7295]) ).

tff(c_7362,plain,
    ( ( inverse(inverse(sk_c8)) != sk_c8 )
    | ( multiply(sk_c8,identity) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7351]) ).

tff(c_7370,plain,
    sk_c8 != sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_7308,c_7308,c_7362]) ).

tff(c_7323,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_7308,c_4]) ).

tff(c_6843,plain,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_6714,c_6825]) ).

tff(c_7327,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_7323,c_6843]) ).

tff(c_7302,plain,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_6714]) ).

tff(c_7406,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_7327,c_7302]) ).

tff(c_7407,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7370,c_7406]) ).

tff(c_7408,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_7226]) ).

tff(c_7409,plain,
    ! [X6_7] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_7408]) ).

tff(c_7465,plain,
    ! [X6_154] :
      ( ( inverse(X6_154) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_154,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_7293,c_7293,c_7409]) ).

tff(c_7476,plain,
    ( ( inverse(inverse(sk_c8)) != sk_c8 )
    | ( multiply(sk_c8,identity) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7465]) ).

tff(c_7484,plain,
    sk_c8 != sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_7422,c_7422,c_7476]) ).

tff(c_7437,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_7422,c_4]) ).

tff(c_7441,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_7437,c_6843]) ).

tff(c_7416,plain,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7293,c_6714]) ).

tff(c_7520,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6852,c_7441,c_7416]) ).

tff(c_7521,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7484,c_7520]) ).

tff(c_7523,plain,
    ! [X2_155] :
      ( ( multiply(inverse(X2_155),sk_c8) != sk_c9 )
      | ( multiply(X2_155,inverse(X2_155)) != sk_c9 ) ),
    inference(splitRight,[status(thm)],[c_7408]) ).

tff(c_7525,plain,
    ( ( multiply(sk_c5,sk_c8) != sk_c9 )
    | ( multiply(sk_c4,inverse(sk_c4)) != sk_c9 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4788,c_7523]) ).

tff(c_7535,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5306,c_4788,c_6720,c_7525]) ).

tff(c_7537,plain,
    inverse(sk_c2) != sk_c9,
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_74,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_164]) ).

tff(c_7575,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_7537,c_74]) ).

tff(c_7536,plain,
    inverse(sk_c6) = sk_c9,
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_7541,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_7536,c_4]) ).

tff(c_7691,plain,
    multiply(sk_c8,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_7541,c_7673]) ).

tff(c_8027,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7694,c_7691]) ).

tff(c_76,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_7569,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_7537,c_76]) ).

tff(c_8052,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_8027,c_7569]) ).

tff(c_7640,plain,
    ! [Z_158] : ( multiply(sk_c9,multiply(sk_c1,Z_158)) = multiply(identity,Z_158) ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_7607]) ).

tff(c_7656,plain,
    ! [Z_158] : ( multiply(sk_c9,multiply(sk_c1,Z_158)) = Z_158 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7640]) ).

tff(c_8064,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_8052,c_7656]) ).

tff(c_8070,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7575,c_8064]) ).

tff(c_8083,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_97]) ).

tff(c_8082,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_101]) ).

tff(c_9775,plain,
    multiply(inverse(sk_c8),identity) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_8082,c_9757]) ).

tff(c_9803,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7694,c_8083,c_9775]) ).

tff(c_9744,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_8083,c_4]) ).

tff(c_9823,plain,
    multiply(sk_c1,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9803,c_9803,c_9744]) ).

tff(c_72,plain,
    ( ( multiply(sk_c5,sk_c8) = sk_c9 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_7582,plain,
    multiply(sk_c5,sk_c8) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_7537,c_72]) ).

tff(c_8077,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_7582]) ).

tff(c_9896,plain,
    multiply(sk_c5,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_9803,c_9803,c_8077]) ).

tff(c_70,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_7549,plain,
    inverse(sk_c4) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_7537,c_70]) ).

tff(c_68,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c9 )
    | ( inverse(sk_c2) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_7590,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_7537,c_68]) ).

tff(c_8076,plain,
    multiply(sk_c4,sk_c5) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_7590]) ).

tff(c_9908,plain,
    multiply(sk_c4,sk_c5) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_9803,c_8076]) ).

tff(c_9912,plain,
    multiply(inverse(sk_c4),sk_c1) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_9908,c_7658]) ).

tff(c_9918,plain,
    sk_c5 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_9896,c_7549,c_9912]) ).

tff(c_9921,plain,
    multiply(sk_c1,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_9918,c_9896]) ).

tff(c_9924,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9823,c_9921]) ).

tff(c_9936,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9924,c_9803]) ).

tff(c_10091,plain,
    ! [X_203] : ( multiply(X_203,inverse(X_203)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_10070,c_4]) ).

tff(c_8149,plain,
    ! [X_167,Z_168] : ( multiply(inverse(X_167),multiply(X_167,Z_168)) = Z_168 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7646]) ).

tff(c_8363,plain,
    ! [X_171,Z_172] : ( multiply(inverse(inverse(X_171)),Z_172) = multiply(X_171,Z_172) ),
    inference(superposition,[status(thm),theory(equality)],[c_8149,c_7658]) ).

tff(c_8179,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_8149]) ).

tff(c_8370,plain,
    ! [X_171] : ( multiply(X_171,identity) = X_171 ),
    inference(superposition,[status(thm),theory(equality)],[c_8363,c_8179]) ).

tff(c_7688,plain,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_7575,c_7673]) ).

tff(c_8104,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8082,c_7688]) ).

tff(c_8078,plain,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_7575]) ).

tff(c_8125,plain,
    sk_c8 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7694,c_8104,c_8078]) ).

tff(c_8127,plain,
    multiply(sk_c1,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8125,c_8125,c_8082]) ).

tff(c_8186,plain,
    multiply(sk_c5,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_8125,c_8125,c_8077]) ).

tff(c_8224,plain,
    multiply(sk_c4,sk_c5) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_8125,c_8076]) ).

tff(c_8228,plain,
    multiply(inverse(sk_c4),sk_c1) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_8224,c_7658]) ).

tff(c_8234,plain,
    sk_c5 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_8186,c_7549,c_8228]) ).

tff(c_8237,plain,
    multiply(sk_c1,sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_8234,c_8186]) ).

tff(c_8240,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8127,c_8237]) ).

tff(c_8251,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8240,c_8125]) ).

tff(c_7716,plain,
    sk_c6 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7694,c_7691]) ).

tff(c_7725,plain,
    multiply(sk_c1,sk_c9) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_7716,c_7569]) ).

tff(c_7763,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_7725,c_7656]) ).

tff(c_7769,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7575,c_7763]) ).

tff(c_7777,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7769,c_7582]) ).

tff(c_7776,plain,
    multiply(sk_c4,sk_c5) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7769,c_7590]) ).

tff(c_7863,plain,
    ! [X_163,Z_164] : ( multiply(inverse(X_163),multiply(X_163,Z_164)) = Z_164 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7646]) ).

tff(c_7884,plain,
    multiply(inverse(sk_c4),sk_c8) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_7776,c_7863]) ).

tff(c_7921,plain,
    sk_c8 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7777,c_7549,c_7884]) ).

tff(c_7783,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_7769,c_97]) ).

tff(c_7935,plain,
    inverse(sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7921,c_7921,c_7783]) ).

tff(c_7706,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_97,c_80]) ).

tff(c_7707,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(splitLeft,[status(thm)],[c_7706]) ).

tff(c_7802,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c8 )
      | ( inverse(X4_12) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7769,c_7769,c_7707]) ).

tff(c_7861,plain,
    inverse(sk_c5) != sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_7777,c_7802]) ).

tff(c_7926,plain,
    inverse(sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7921,c_7861]) ).

tff(c_8017,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7935,c_7926]) ).

tff(c_8018,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_7706]) ).

tff(c_8095,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X7_9) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_9,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8070,c_8070,c_8070,c_8070,c_8070,c_8070,c_8070,c_8070,c_8018]) ).

tff(c_8096,plain,
    ! [X7_9] :
      ( ( inverse(X7_9) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_9,sk_c8)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_8095]) ).

tff(c_9737,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8370,c_8251,c_8251,c_2,c_8251,c_8251,c_8096]) ).

tff(c_8128,plain,
    inverse(sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_8125,c_8125,c_8083]) ).

tff(c_8249,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8240,c_8240,c_8128]) ).

tff(c_9739,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9737,c_8249]) ).

tff(c_9740,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_8095]) ).

tff(c_30398,plain,
    ! [X2_11,X6_7] :
      ( ( inverse(X2_11) != identity )
      | ( inverse(X6_7) != identity )
      | ( identity != X6_7 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10077,c_9936,c_9936,c_2,c_9936,c_9936,c_10091,c_9936,c_10077,c_9936,c_9936,c_9740]) ).

tff(c_30400,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_30398]) ).

tff(c_9810,plain,
    inverse(sk_c1) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_9803,c_9803,c_8083]) ).

tff(c_9933,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9924,c_9924,c_9810]) ).

tff(c_30402,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30400,c_9933]) ).

tff(c_30403,plain,
    ! [X2_11] : ( inverse(X2_11) != identity ),
    inference(splitRight,[status(thm)],[c_30398]) ).

tff(c_30405,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30403,c_9933]) ).

tff(c_30407,plain,
    inverse(sk_c1) != sk_c9,
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_26,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_30471,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_30407,c_26]) ).

tff(c_28,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_30461,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_30407,c_28]) ).

tff(c_30,plain,
    ( ( inverse(sk_c6) = sk_c9 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_30415,plain,
    inverse(sk_c1) = sk_c9,
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_30416,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30407,c_30415]) ).

tff(c_30417,plain,
    inverse(sk_c6) = sk_c9,
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_30422,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30417,c_4]) ).

tff(c_30523,plain,
    ! [Z_361] : ( multiply(sk_c9,multiply(sk_c6,Z_361)) = multiply(identity,Z_361) ),
    inference(superposition,[status(thm),theory(equality)],[c_30422,c_30493]) ).

tff(c_30882,plain,
    ! [Z_369] : ( multiply(sk_c9,multiply(sk_c6,Z_369)) = Z_369 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30523]) ).

tff(c_30894,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_30461,c_30882]) ).

tff(c_30898,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30471,c_30894]) ).

tff(c_20,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c9 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_30438,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_30407,c_20]) ).

tff(c_30406,plain,
    inverse(sk_c4) = sk_c5,
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_30411,plain,
    multiply(sk_c5,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30406,c_4]) ).

tff(c_30526,plain,
    ! [Z_361] : ( multiply(sk_c5,multiply(sk_c4,Z_361)) = multiply(identity,Z_361) ),
    inference(superposition,[status(thm),theory(equality)],[c_30411,c_30493]) ).

tff(c_30559,plain,
    ! [Z_363] : ( multiply(sk_c5,multiply(sk_c4,Z_363)) = Z_363 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30526]) ).

tff(c_30571,plain,
    multiply(sk_c5,sk_c9) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_30438,c_30559]) ).

tff(c_30930,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_30898,c_30571]) ).

tff(c_32546,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_30930,c_30544]) ).

tff(c_32552,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_32546]) ).

tff(c_32789,plain,
    ! [X_403] : ( multiply(X_403,inverse(X_403)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_32768,c_4]) ).

tff(c_31036,plain,
    ! [X_371,Z_372] : ( multiply(inverse(X_371),multiply(X_371,Z_372)) = Z_372 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30532]) ).

tff(c_31321,plain,
    ! [X_375,Z_376] : ( multiply(inverse(inverse(X_375)),Z_376) = multiply(X_375,Z_376) ),
    inference(superposition,[status(thm),theory(equality)],[c_30544,c_31036]) ).

tff(c_31069,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_31036]) ).

tff(c_31328,plain,
    ! [X_375] : ( multiply(X_375,identity) = X_375 ),
    inference(superposition,[status(thm),theory(equality)],[c_31321,c_31069]) ).

tff(c_24,plain,
    ( ( multiply(sk_c5,sk_c8) = sk_c9 )
    | ( inverse(sk_c1) = sk_c9 ) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_30444,plain,
    multiply(sk_c5,sk_c8) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_30407,c_24]) ).

tff(c_30936,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30898,c_30444]) ).

tff(c_31004,plain,
    sk_c8 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_30930,c_30936]) ).

tff(c_31012,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_31004,c_30930]) ).

tff(c_31144,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_31012,c_30544]) ).

tff(c_31150,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_31144]) ).

tff(c_31160,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_31150,c_31004]) ).

tff(c_30585,plain,
    ! [Z_364] : ( multiply(sk_c9,multiply(sk_c6,Z_364)) = Z_364 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30523]) ).

tff(c_30597,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_30461,c_30585]) ).

tff(c_30601,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30471,c_30597]) ).

tff(c_30603,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_30601,c_30571]) ).

tff(c_30609,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30601,c_30444]) ).

tff(c_30713,plain,
    sk_c8 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_30603,c_30609]) ).

tff(c_30615,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30601,c_97]) ).

tff(c_30614,plain,
    multiply(sk_c8,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30601,c_101]) ).

tff(c_30583,plain,
    ! [X7_9,X2_11,X6_7,X4_12] :
      ( ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_97,c_80]) ).

tff(c_30584,plain,
    ! [X4_12] :
      ( ( multiply(X4_12,sk_c8) != sk_c9 )
      | ( inverse(X4_12) != sk_c9 ) ),
    inference(splitLeft,[status(thm)],[c_30583]) ).

tff(c_30659,plain,
    ! [X4_365] :
      ( ( multiply(X4_365,sk_c8) != sk_c8 )
      | ( inverse(X4_365) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30601,c_30601,c_30584]) ).

tff(c_30662,plain,
    ( ( sk_c8 != identity )
    | ( inverse(sk_c8) != sk_c8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_30614,c_30659]) ).

tff(c_30676,plain,
    sk_c8 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30615,c_30662]) ).

tff(c_30719,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30713,c_30676]) ).

tff(c_30716,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_30713,c_30603]) ).

tff(c_30871,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_30716,c_30544]) ).

tff(c_30878,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30871]) ).

tff(c_30880,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30719,c_30878]) ).

tff(c_30881,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c9 )
      | ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c9 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c9 )
      | ( inverse(X7_9) != sk_c9 )
      | ( multiply(sk_c9,multiply(X7_9,sk_c9)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_30583]) ).

tff(c_30968,plain,
    ! [X6_7,X2_11,X7_9] :
      ( ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 )
      | ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X7_9) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_9,sk_c8)) != sk_c8 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30898,c_30898,c_30898,c_30898,c_30898,c_30898,c_30898,c_30898,c_30881]) ).

tff(c_30969,plain,
    ! [X7_9] :
      ( ( inverse(X7_9) != sk_c8 )
      | ( multiply(sk_c8,multiply(X7_9,sk_c8)) != sk_c8 ) ),
    inference(splitLeft,[status(thm)],[c_30968]) ).

tff(c_32480,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_31328,c_31160,c_31160,c_2,c_31160,c_31160,c_30969]) ).

tff(c_30942,plain,
    inverse(sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_30898,c_97]) ).

tff(c_31017,plain,
    inverse(sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_31004,c_31004,c_30942]) ).

tff(c_31158,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_31150,c_31150,c_31017]) ).

tff(c_32482,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32480,c_31158]) ).

tff(c_32483,plain,
    ! [X2_11,X6_7] :
      ( ( multiply(inverse(X2_11),sk_c8) != sk_c8 )
      | ( multiply(X2_11,inverse(X2_11)) != sk_c8 )
      | ( inverse(X6_7) != sk_c8 )
      | ( multiply(sk_c8,multiply(X6_7,sk_c8)) != sk_c8 ) ),
    inference(splitRight,[status(thm)],[c_30968]) ).

tff(c_39618,plain,
    ! [X2_11,X6_7] :
      ( ( inverse(X2_11) != identity )
      | ( inverse(X6_7) != identity )
      | ( identity != X6_7 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32775,c_32552,c_32552,c_2,c_32552,c_32552,c_32789,c_32552,c_32775,c_32552,c_32552,c_32483]) ).

tff(c_39620,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_39618]) ).

tff(c_32557,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_32552,c_32552,c_30942]) ).

tff(c_39622,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_39620,c_32557]) ).

tff(c_39623,plain,
    ! [X2_11] : ( inverse(X2_11) != identity ),
    inference(splitRight,[status(thm)],[c_39618]) ).

tff(c_39625,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_39623,c_32557]) ).

tff(c_39627,plain,
    inverse(sk_c9) != sk_c8,
    inference(splitRight,[status(thm)],[c_18]) ).

tff(c_14,plain,
    ( ( multiply(sk_c9,sk_c7) = sk_c8 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_40367,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_14]) ).

tff(c_16,plain,
    ( ( multiply(sk_c6,sk_c9) = sk_c7 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_40339,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_16]) ).

tff(c_39626,plain,
    inverse(sk_c6) = sk_c9,
    inference(splitRight,[status(thm)],[c_18]) ).

tff(c_39631,plain,
    multiply(sk_c9,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_39626,c_4]) ).

tff(c_40393,plain,
    ! [X_502,Y_503,Z_504] : ( multiply(multiply(X_502,Y_503),Z_504) = multiply(X_502,multiply(Y_503,Z_504)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_40426,plain,
    ! [Z_504] : ( multiply(sk_c9,multiply(sk_c6,Z_504)) = multiply(identity,Z_504) ),
    inference(superposition,[status(thm),theory(equality)],[c_39631,c_40393]) ).

tff(c_40465,plain,
    ! [Z_506] : ( multiply(sk_c9,multiply(sk_c6,Z_506)) = Z_506 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40426]) ).

tff(c_40477,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_40339,c_40465]) ).

tff(c_40481,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40367,c_40477]) ).

tff(c_39677,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_14]) ).

tff(c_39672,plain,
    multiply(sk_c6,sk_c9) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_16]) ).

tff(c_40048,plain,
    ! [X_494,Y_495,Z_496] : ( multiply(multiply(X_494,Y_495),Z_496) = multiply(X_494,multiply(Y_495,Z_496)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_40081,plain,
    ! [Z_496] : ( multiply(sk_c9,multiply(sk_c6,Z_496)) = multiply(identity,Z_496) ),
    inference(superposition,[status(thm),theory(equality)],[c_39631,c_40048]) ).

tff(c_40120,plain,
    ! [Z_498] : ( multiply(sk_c9,multiply(sk_c6,Z_498)) = Z_498 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40081]) ).

tff(c_40132,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_39672,c_40120]) ).

tff(c_40136,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_39677,c_40132]) ).

tff(c_39726,plain,
    ! [X_486,Y_487,Z_488] : ( multiply(multiply(X_486,Y_487),Z_488) = multiply(X_486,multiply(Y_487,Z_488)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_39762,plain,
    ! [Z_488] : ( multiply(sk_c9,multiply(sk_c6,Z_488)) = multiply(identity,Z_488) ),
    inference(superposition,[status(thm),theory(equality)],[c_39631,c_39726]) ).

tff(c_39802,plain,
    ! [Z_490] : ( multiply(sk_c9,multiply(sk_c6,Z_490)) = Z_490 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_39762]) ).

tff(c_39814,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_39672,c_39802]) ).

tff(c_39818,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_39677,c_39814]) ).

tff(c_8,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c9 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_39709,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_8]) ).

tff(c_10,plain,
    ( ( inverse(sk_c4) = sk_c5 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_39635,plain,
    inverse(sk_c9) = sk_c8,
    inference(splitLeft,[status(thm)],[c_10]) ).

tff(c_39636,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_39635]) ).

tff(c_39637,plain,
    inverse(sk_c4) = sk_c5,
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_39642,plain,
    multiply(sk_c5,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_39637,c_4]) ).

tff(c_39759,plain,
    ! [Z_488] : ( multiply(sk_c5,multiply(sk_c4,Z_488)) = multiply(identity,Z_488) ),
    inference(superposition,[status(thm),theory(equality)],[c_39642,c_39726]) ).

tff(c_39779,plain,
    ! [Z_489] : ( multiply(sk_c5,multiply(sk_c4,Z_489)) = Z_489 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_39759]) ).

tff(c_39791,plain,
    multiply(sk_c5,sk_c9) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_39709,c_39779]) ).

tff(c_39820,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_39818,c_39791]) ).

tff(c_39765,plain,
    ! [X_2,Z_488] : ( multiply(inverse(X_2),multiply(X_2,Z_488)) = multiply(identity,Z_488) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_39726]) ).

tff(c_39777,plain,
    ! [X_2,Z_488] : ( multiply(inverse(X_2),multiply(X_2,Z_488)) = Z_488 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_39765]) ).

tff(c_39918,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_39820,c_39777]) ).

tff(c_39924,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_39918]) ).

tff(c_12,plain,
    ( ( multiply(sk_c5,sk_c8) = sk_c9 )
    | ( inverse(sk_c9) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_39683,plain,
    multiply(sk_c5,sk_c8) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_12]) ).

tff(c_39824,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_39818,c_39683]) ).

tff(c_39914,plain,
    sk_c8 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_39820,c_39824]) ).

tff(c_39952,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_39924,c_39914]) ).

tff(c_39830,plain,
    inverse(sk_c8) != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_39818,c_39627]) ).

tff(c_39930,plain,
    inverse(sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_39914,c_39914,c_39830]) ).

tff(c_39970,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_39952,c_39952,c_39930]) ).

tff(c_39695,plain,
    inverse(sk_c2) = sk_c9,
    inference(splitLeft,[status(thm)],[c_68]) ).

tff(c_39823,plain,
    inverse(sk_c2) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_39818,c_39695]) ).

tff(c_39846,plain,
    multiply(sk_c8,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_39823,c_4]) ).

tff(c_40021,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_39924,c_39846]) ).

tff(c_39928,plain,
    inverse(sk_c2) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_39914,c_39823]) ).

tff(c_39999,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_39952,c_39928]) ).

tff(c_40022,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40021,c_39999]) ).

tff(c_40024,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_39970,c_40022]) ).

tff(c_40025,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(splitRight,[status(thm)],[c_68]) ).

tff(c_40078,plain,
    ! [Z_496] : ( multiply(sk_c5,multiply(sk_c4,Z_496)) = multiply(identity,Z_496) ),
    inference(superposition,[status(thm),theory(equality)],[c_39642,c_40048]) ).

tff(c_40097,plain,
    ! [Z_497] : ( multiply(sk_c5,multiply(sk_c4,Z_497)) = Z_497 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40078]) ).

tff(c_40109,plain,
    multiply(sk_c5,sk_c9) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_40025,c_40097]) ).

tff(c_40138,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40136,c_40109]) ).

tff(c_40084,plain,
    ! [X_2,Z_496] : ( multiply(inverse(X_2),multiply(X_2,Z_496)) = multiply(identity,Z_496) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_40048]) ).

tff(c_40095,plain,
    ! [X_2,Z_496] : ( multiply(inverse(X_2),multiply(X_2,Z_496)) = Z_496 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40084]) ).

tff(c_40253,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_40138,c_40095]) ).

tff(c_40259,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_40253]) ).

tff(c_40147,plain,
    inverse(sk_c8) != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40136,c_39627]) ).

tff(c_40265,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40259,c_40259,c_40147]) ).

tff(c_39659,plain,
    inverse(sk_c1) = sk_c9,
    inference(splitLeft,[status(thm)],[c_20]) ).

tff(c_40145,plain,
    inverse(sk_c1) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40136,c_39659]) ).

tff(c_40207,plain,
    multiply(sk_c8,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_40145,c_4]) ).

tff(c_40315,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40259,c_40207]) ).

tff(c_40263,plain,
    inverse(sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40259,c_40145]) ).

tff(c_40330,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40315,c_40263]) ).

tff(c_40331,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40265,c_40330]) ).

tff(c_40332,plain,
    multiply(sk_c4,sk_c5) = sk_c9,
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_40423,plain,
    ! [Z_504] : ( multiply(sk_c5,multiply(sk_c4,Z_504)) = multiply(identity,Z_504) ),
    inference(superposition,[status(thm),theory(equality)],[c_39642,c_40393]) ).

tff(c_40442,plain,
    ! [Z_505] : ( multiply(sk_c5,multiply(sk_c4,Z_505)) = Z_505 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40423]) ).

tff(c_40454,plain,
    multiply(sk_c5,sk_c9) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_40332,c_40442]) ).

tff(c_40483,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40481,c_40454]) ).

tff(c_40429,plain,
    ! [X_2,Z_504] : ( multiply(inverse(X_2),multiply(X_2,Z_504)) = multiply(identity,Z_504) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_40393]) ).

tff(c_40440,plain,
    ! [X_2,Z_504] : ( multiply(inverse(X_2),multiply(X_2,Z_504)) = Z_504 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40429]) ).

tff(c_40600,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_40483,c_40440]) ).

tff(c_40606,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_40600]) ).

tff(c_40492,plain,
    inverse(sk_c8) != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40481,c_39627]) ).

tff(c_40613,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40606,c_40606,c_40492]) ).

tff(c_40352,plain,
    inverse(sk_c2) = sk_c9,
    inference(splitLeft,[status(thm)],[c_74]) ).

tff(c_40486,plain,
    inverse(sk_c2) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40481,c_40352]) ).

tff(c_40508,plain,
    multiply(sk_c8,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_40486,c_4]) ).

tff(c_40662,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40606,c_40508]) ).

tff(c_40611,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40606,c_40486]) ).

tff(c_40663,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40662,c_40611]) ).

tff(c_40665,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40613,c_40663]) ).

tff(c_40666,plain,
    multiply(sk_c9,sk_c7) = sk_c8,
    inference(splitRight,[status(thm)],[c_74]) ).

tff(c_40700,plain,
    ! [X_510,Y_511,Z_512] : ( multiply(multiply(X_510,Y_511),Z_512) = multiply(X_510,multiply(Y_511,Z_512)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_40730,plain,
    ! [Z_512] : ( multiply(sk_c9,multiply(sk_c6,Z_512)) = multiply(identity,Z_512) ),
    inference(superposition,[status(thm),theory(equality)],[c_39631,c_40700]) ).

tff(c_40768,plain,
    ! [Z_514] : ( multiply(sk_c9,multiply(sk_c6,Z_514)) = Z_514 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40730]) ).

tff(c_40780,plain,
    multiply(sk_c9,sk_c7) = sk_c9,
    inference(superposition,[status(thm),theory(equality)],[c_40339,c_40768]) ).

tff(c_40784,plain,
    sk_c9 = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40666,c_40780]) ).

tff(c_40727,plain,
    ! [Z_512] : ( multiply(sk_c5,multiply(sk_c4,Z_512)) = multiply(identity,Z_512) ),
    inference(superposition,[status(thm),theory(equality)],[c_39642,c_40700]) ).

tff(c_40745,plain,
    ! [Z_513] : ( multiply(sk_c5,multiply(sk_c4,Z_513)) = Z_513 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40727]) ).

tff(c_40757,plain,
    multiply(sk_c5,sk_c9) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_40332,c_40745]) ).

tff(c_40800,plain,
    multiply(sk_c5,sk_c8) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40784,c_40757]) ).

tff(c_40733,plain,
    ! [X_2,Z_512] : ( multiply(inverse(X_2),multiply(X_2,Z_512)) = multiply(identity,Z_512) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_40700]) ).

tff(c_40743,plain,
    ! [X_2,Z_512] : ( multiply(inverse(X_2),multiply(X_2,Z_512)) = Z_512 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40733]) ).

tff(c_40930,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_40800,c_40743]) ).

tff(c_40936,plain,
    sk_c8 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_40930]) ).

tff(c_40347,plain,
    multiply(sk_c5,sk_c8) = sk_c9,
    inference(negUnitSimplification,[status(thm)],[c_39627,c_12]) ).

tff(c_40803,plain,
    multiply(sk_c5,sk_c8) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40784,c_40347]) ).

tff(c_40926,plain,
    sk_c8 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40800,c_40803]) ).

tff(c_40981,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40936,c_40926]) ).

tff(c_40808,plain,
    inverse(sk_c8) != sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40784,c_39627]) ).

tff(c_40943,plain,
    inverse(sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40926,c_40926,c_40808]) ).

tff(c_41047,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40981,c_40981,c_40943]) ).

tff(c_40807,plain,
    multiply(sk_c8,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40784,c_39631]) ).

tff(c_40939,plain,
    multiply(sk_c5,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40926,c_40807]) ).

tff(c_41072,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_40981,c_40939]) ).

tff(c_40809,plain,
    inverse(sk_c6) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_40784,c_39626]) ).

tff(c_40942,plain,
    inverse(sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_40926,c_40809]) ).

tff(c_41035,plain,
    inverse(sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_40981,c_40942]) ).

tff(c_41073,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_41072,c_41035]) ).

tff(c_41075,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_41047,c_41073]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP237-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n014.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 22:22:03 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 13.93/5.01  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.93/5.08  
% 13.93/5.08  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.93/5.16  
% 13.93/5.16  Inference rules
% 13.93/5.16  ----------------------
% 13.93/5.16  #Ref     : 0
% 13.93/5.16  #Sup     : 10151
% 13.93/5.16  #Fact    : 0
% 13.93/5.16  #Define  : 0
% 13.93/5.16  #Split   : 37
% 13.93/5.16  #Chain   : 0
% 13.93/5.16  #Close   : 0
% 13.93/5.16  
% 13.93/5.16  Ordering : KBO
% 13.93/5.16  
% 13.93/5.16  Simplification rules
% 13.93/5.16  ----------------------
% 13.93/5.16  #Subsume      : 22
% 13.93/5.16  #Demod        : 25399
% 13.93/5.16  #Tautology    : 8136
% 13.93/5.16  #SimpNegUnit  : 89
% 13.93/5.16  #BackRed      : 694
% 13.93/5.16  
% 13.93/5.16  #Partial instantiations: 0
% 13.93/5.16  #Strategies tried      : 1
% 13.93/5.16  
% 13.93/5.16  Timing (in seconds)
% 13.93/5.16  ----------------------
% 13.93/5.16  Preprocessing        : 0.51
% 13.93/5.16  Parsing              : 0.19
% 13.93/5.16  CNF conversion       : 0.03
% 13.93/5.16  Main loop            : 3.47
% 13.93/5.16  Inferencing          : 1.07
% 13.93/5.16  Reduction            : 1.77
% 13.93/5.16  Demodulation         : 1.57
% 13.93/5.16  BG Simplification    : 0.10
% 13.93/5.16  Subsumption          : 0.33
% 13.93/5.16  Abstraction          : 0.20
% 13.93/5.16  MUC search           : 0.00
% 13.93/5.16  Cooper               : 0.00
% 13.93/5.16  Total                : 4.15
% 13.93/5.16  Index Insertion      : 0.00
% 13.93/5.16  Index Deletion       : 0.00
% 13.93/5.16  Index Matching       : 0.00
% 13.93/5.16  BG Taut test         : 0.00
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