%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP274-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:40:44 EDT 2023

% Result   : Unsatisfiable 13.87s 4.48s
% Output   : CNFRefutation 14.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  780 ( 655 unt;  10 typ;   0 def)
%            Number of atoms       : 1015 ( 972 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  585 ( 340   ~; 245   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   2 avg)
%            Maximal term depth    :    5 (   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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  330 (; 330   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > 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(multiply,type,
    multiply: ( $i * $i ) > $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_74,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    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_113,axiom,
    ( ( multiply(sk_c2,sk_c5) = sk_c7 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ( ( inverse(sk_c2) = sk_c5 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ( ( multiply(sk_c7,sk_c5) = sk_c6 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_167,axiom,
    ! [X3,X4,X1,X2] :
      ( ( multiply(X3,sk_c7) != sk_c6 )
      | ( inverse(X3) != sk_c7 )
      | ( multiply(sk_c7,sk_c5) != sk_c6 )
      | ( multiply(X4,sk_c5) != sk_c7 )
      | ( inverse(X4) != sk_c5 )
      | ( multiply(sk_c6,sk_c7) != sk_c5 )
      | ( inverse(X1) != sk_c7 )
      | ( multiply(X1,sk_c6) != sk_c7 )
      | ( inverse(X2) != sk_c6 )
      | ( multiply(X2,sk_c5) != sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    ( ( multiply(sk_c2,sk_c5) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ( ( multiply(sk_c2,sk_c5) = sk_c7 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_119,axiom,
    ( ( multiply(sk_c2,sk_c5) = sk_c7 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ( ( multiply(sk_c2,sk_c5) = sk_c7 )
    | ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_107,axiom,
    ( ( multiply(sk_c7,sk_c5) = sk_c6 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ( ( multiply(sk_c7,sk_c5) = sk_c6 )
    | ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_65,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_137,axiom,
    ( ( inverse(sk_c2) = sk_c5 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ( ( inverse(sk_c2) = sk_c5 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_125,axiom,
    ( ( inverse(sk_c2) = sk_c5 )
    | ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ( ( inverse(sk_c2) = sk_c5 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    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_14,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_102,plain,
    multiply(sk_c1,sk_c7) = sk_c6,
    inference(splitLeft,[status(thm)],[c_14]) ).

tff(c_20,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_87,plain,
    inverse(sk_c1) = sk_c7,
    inference(splitLeft,[status(thm)],[c_20]) ).

tff(c_91,plain,
    multiply(sk_c7,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_87,c_4]) ).

tff(c_3273,plain,
    ! [X_81,Y_82,Z_83] : ( multiply(multiply(X_81,Y_82),Z_83) = multiply(X_81,multiply(Y_82,Z_83)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_3306,plain,
    ! [Z_83] : ( multiply(sk_c7,multiply(sk_c1,Z_83)) = multiply(identity,Z_83) ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_3273]) ).

tff(c_3341,plain,
    ! [Z_85] : ( multiply(sk_c7,multiply(sk_c1,Z_85)) = Z_85 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3306]) ).

tff(c_3353,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_3341]) ).

tff(c_3312,plain,
    ! [X_2,Z_83] : ( multiply(inverse(X_2),multiply(X_2,Z_83)) = multiply(identity,Z_83) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_3273]) ).

tff(c_3387,plain,
    ! [X_87,Z_88] : ( multiply(inverse(X_87),multiply(X_87,Z_88)) = Z_88 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3312]) ).

tff(c_3411,plain,
    multiply(inverse(sk_c7),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_3353,c_3387]) ).

tff(c_3466,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_3411]) ).

tff(c_134,plain,
    ! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_164,plain,
    ! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_134]) ).

tff(c_174,plain,
    ! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).

tff(c_717,plain,
    ! [X_27,Z_28] : ( multiply(inverse(X_27),multiply(X_27,Z_28)) = Z_28 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).

tff(c_1368,plain,
    ! [X_38,Z_39] : ( multiply(inverse(inverse(X_38)),Z_39) = multiply(X_38,Z_39) ),
    inference(superposition,[status(thm),theory(equality)],[c_174,c_717]) ).

tff(c_774,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_717]) ).

tff(c_1379,plain,
    ! [X_38] : ( multiply(X_38,identity) = X_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_1368,c_774]) ).

tff(c_40,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_112,plain,
    multiply(sk_c2,sk_c5) = sk_c7,
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_50,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( inverse(sk_c2) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_75,plain,
    inverse(sk_c2) = sk_c5,
    inference(splitLeft,[status(thm)],[c_50]) ).

tff(c_79,plain,
    multiply(sk_c5,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).

tff(c_161,plain,
    ! [Z_14] : ( multiply(sk_c5,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_134]) ).

tff(c_694,plain,
    ! [Z_26] : ( multiply(sk_c5,multiply(sk_c2,Z_26)) = Z_26 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).

tff(c_706,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_112,c_694]) ).

tff(c_735,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_706,c_717]) ).

tff(c_781,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_735]) ).

tff(c_933,plain,
    multiply(identity,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_91]) ).

tff(c_1040,plain,
    multiply(inverse(identity),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_933,c_174]) ).

tff(c_1052,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_1040]) ).

tff(c_934,plain,
    inverse(sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_87]) ).

tff(c_1057,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1052,c_934]) ).

tff(c_1122,plain,
    ! [X_32] : ( multiply(inverse(inverse(X_32)),identity) = X_32 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_717]) ).

tff(c_1128,plain,
    ! [X_32] : ( multiply(inverse(inverse(inverse(X_32))),X_32) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_1122,c_174]) ).

tff(c_158,plain,
    ! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_134]) ).

tff(c_524,plain,
    ! [Z_22] : ( multiply(sk_c7,multiply(sk_c1,Z_22)) = Z_22 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).

tff(c_536,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_524]) ).

tff(c_741,plain,
    multiply(inverse(sk_c7),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_536,c_717]) ).

tff(c_782,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_741]) ).

tff(c_34,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_107,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_931,plain,
    multiply(identity,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_107]) ).

tff(c_935,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_931]) ).

tff(c_944,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_782,c_935]) ).

tff(c_796,plain,
    inverse(sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_87]) ).

tff(c_794,plain,
    multiply(sk_c1,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_102]) ).

tff(c_884,plain,
    multiply(sk_c1,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_782,c_794]) ).

tff(c_233,plain,
    ! [Z_17] : ( multiply(sk_c7,multiply(sk_c1,Z_17)) = Z_17 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).

tff(c_245,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_233]) ).

tff(c_264,plain,
    ! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).

tff(c_285,plain,
    multiply(inverse(sk_c7),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_245,c_264]) ).

tff(c_334,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_285]) ).

tff(c_179,plain,
    ! [Z_15] : ( multiply(sk_c5,multiply(sk_c2,Z_15)) = Z_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).

tff(c_191,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_112,c_179]) ).

tff(c_202,plain,
    ! [Z_16] : ( multiply(sk_c7,multiply(sk_c5,Z_16)) = multiply(sk_c6,Z_16) ),
    inference(superposition,[status(thm),theory(equality)],[c_107,c_134]) ).

tff(c_214,plain,
    multiply(sk_c7,sk_c5) = multiply(sk_c6,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_191,c_202]) ).

tff(c_224,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_214]) ).

tff(c_58,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(sk_c6,sk_c7) != sk_c5 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(sk_c7,sk_c5) != sk_c6 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_177,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(sk_c6,sk_c7) != sk_c5 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_58]) ).

tff(c_178,plain,
    multiply(sk_c6,sk_c7) != sk_c5,
    inference(splitLeft,[status(thm)],[c_177]) ).

tff(c_225,plain,
    sk_c6 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_178]) ).

tff(c_343,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_334,c_225]) ).

tff(c_297,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_191,c_264]) ).

tff(c_336,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_297]) ).

tff(c_346,plain,
    multiply(sk_c7,sk_c5) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_334,c_107]) ).

tff(c_513,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_336,c_346]) ).

tff(c_514,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_343,c_513]) ).

tff(c_516,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(splitRight,[status(thm)],[c_177]) ).

tff(c_548,plain,
    ! [Z_23] : ( multiply(sk_c5,multiply(sk_c2,Z_23)) = Z_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).

tff(c_560,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_112,c_548]) ).

tff(c_571,plain,
    ! [Z_24] : ( multiply(sk_c7,multiply(sk_c5,Z_24)) = multiply(sk_c6,Z_24) ),
    inference(superposition,[status(thm),theory(equality)],[c_107,c_134]) ).

tff(c_583,plain,
    multiply(sk_c7,sk_c5) = multiply(sk_c6,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_560,c_571]) ).

tff(c_593,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_516,c_107,c_583]) ).

tff(c_597,plain,
    multiply(sk_c7,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_593,c_107]) ).

tff(c_595,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_593,c_536]) ).

tff(c_611,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_597,c_595]) ).

tff(c_622,plain,
    multiply(sk_c2,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_611,c_112]) ).

tff(c_515,plain,
    ! [X3_6,X4_7,X1_8,X2_9] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_177]) ).

tff(c_540,plain,
    ! [X2_9] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_515]) ).

tff(c_636,plain,
    ! [X2_9] :
      ( ( multiply(X2_9,sk_c5) != sk_c5 )
      | ( inverse(X2_9) != sk_c5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_593,c_593,c_540]) ).

tff(c_673,plain,
    inverse(sk_c2) != sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_622,c_636]) ).

tff(c_685,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_75,c_673]) ).

tff(c_686,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_515]) ).

tff(c_787,plain,
    ! [X3_6] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_686]) ).

tff(c_898,plain,
    ! [X3_30] :
      ( ( inverse(X3_30) != identity )
      | ( multiply(X3_30,identity) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_782,c_781,c_781,c_787]) ).

tff(c_901,plain,
    inverse(sk_c1) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_884,c_898]) ).

tff(c_924,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_796,c_901]) ).

tff(c_925,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_686]) ).

tff(c_1035,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != identity )
      | ( multiply(X4_7,identity) != identity )
      | ( multiply(X1_8,identity) != identity )
      | ( inverse(X1_8) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_782,c_781,c_944,c_781,c_944,c_925]) ).

tff(c_1182,plain,
    ! [X1_34] :
      ( ( multiply(X1_34,identity) != identity )
      | ( inverse(X1_34) != identity ) ),
    inference(splitLeft,[status(thm)],[c_1035]) ).

tff(c_1186,plain,
    inverse(inverse(inverse(inverse(identity)))) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_1128,c_1182]) ).

tff(c_1205,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1057,c_1057,c_1057,c_1057,c_1186]) ).

tff(c_1206,plain,
    ! [X4_7] :
      ( ( inverse(X4_7) != identity )
      | ( multiply(X4_7,identity) != identity ) ),
    inference(splitRight,[status(thm)],[c_1035]) ).

tff(c_1648,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1379,c_1206]) ).

tff(c_777,plain,
    ! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_717]) ).

tff(c_1210,plain,
    multiply(inverse(identity),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_933,c_174]) ).

tff(c_1222,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_777,c_1210]) ).

tff(c_1227,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1222,c_934]) ).

tff(c_1650,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1648,c_1227]) ).

tff(c_1651,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_1652,plain,
    multiply(sk_c2,sk_c5) != sk_c7,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_42,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_1686,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_1652,c_42]) ).

tff(c_46,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_1699,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_1652,c_46]) ).

tff(c_44,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_1665,plain,
    inverse(sk_c4) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_1652,c_44]) ).

tff(c_1669,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_1665,c_4]) ).

tff(c_1704,plain,
    ! [X_45,Y_46,Z_47] : ( multiply(multiply(X_45,Y_46),Z_47) = multiply(X_45,multiply(Y_46,Z_47)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_1728,plain,
    ! [Z_47] : ( multiply(sk_c6,multiply(sk_c4,Z_47)) = multiply(identity,Z_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_1669,c_1704]) ).

tff(c_1937,plain,
    ! [Z_56] : ( multiply(sk_c6,multiply(sk_c4,Z_56)) = Z_56 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1728]) ).

tff(c_1949,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_1699,c_1937]) ).

tff(c_1740,plain,
    ! [Z_47] : ( multiply(sk_c7,multiply(sk_c1,Z_47)) = multiply(identity,Z_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_1704]) ).

tff(c_1760,plain,
    ! [Z_48] : ( multiply(sk_c7,multiply(sk_c1,Z_48)) = Z_48 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1740]) ).

tff(c_1772,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_1760]) ).

tff(c_1953,plain,
    ! [Z_57] : ( multiply(sk_c1,multiply(sk_c7,Z_57)) = multiply(sk_c6,Z_57) ),
    inference(superposition,[status(thm),theory(equality)],[c_102,c_1704]) ).

tff(c_1974,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_1772,c_1953]) ).

tff(c_1991,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_102,c_1974]) ).

tff(c_1999,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_1949,c_1991]) ).

tff(c_38,plain,
    ( ( multiply(sk_c6,sk_c7) = sk_c5 )
    | ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_1694,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_1652,c_38]) ).

tff(c_1656,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_1651,c_4]) ).

tff(c_1731,plain,
    ! [Z_47] : ( multiply(sk_c7,multiply(sk_c3,Z_47)) = multiply(identity,Z_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_1656,c_1704]) ).

tff(c_1914,plain,
    ! [Z_55] : ( multiply(sk_c7,multiply(sk_c3,Z_55)) = Z_55 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1731]) ).

tff(c_1926,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_1686,c_1914]) ).

tff(c_1968,plain,
    multiply(sk_c6,sk_c7) = multiply(sk_c1,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_1926,c_1953]) ).

tff(c_1990,plain,
    multiply(sk_c1,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_1694,c_1968]) ).

tff(c_2075,plain,
    multiply(sk_c1,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_1999,c_1990]) ).

tff(c_1784,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_1694,c_58]) ).

tff(c_1872,plain,
    ! [X3_53] :
      ( ( inverse(X3_53) != sk_c7 )
      | ( multiply(X3_53,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_1784]) ).

tff(c_1885,plain,
    inverse(sk_c1) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_1872]) ).

tff(c_1898,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_87,c_1885]) ).

tff(c_1899,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_1784]) ).

tff(c_1913,plain,
    ! [X2_9] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_1899]) ).

tff(c_2037,plain,
    ! [X2_9] :
      ( ( multiply(X2_9,sk_c5) != sk_c5 )
      | ( inverse(X2_9) != sk_c5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1999,c_1999,c_1913]) ).

tff(c_2079,plain,
    inverse(sk_c1) != sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_2075,c_2037]) ).

tff(c_2089,plain,
    sk_c7 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_87,c_2079]) ).

tff(c_2010,plain,
    multiply(sk_c7,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_1999,c_107]) ).

tff(c_2004,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_1999,c_1772]) ).

tff(c_2101,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2010,c_2004]) ).

tff(c_2103,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2089,c_2101]) ).

tff(c_2104,plain,
    ! [X1_8,X4_7] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_1899]) ).

tff(c_2179,plain,
    ! [X4_62] :
      ( ( inverse(X4_62) != sk_c5 )
      | ( multiply(X4_62,sk_c5) != sk_c7 ) ),
    inference(splitLeft,[status(thm)],[c_2104]) ).

tff(c_2193,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c7 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2179]) ).

tff(c_2201,plain,
    sk_c7 != identity,
    inference(splitLeft,[status(thm)],[c_2193]) ).

tff(c_2129,plain,
    ! [Z_60] : ( multiply(sk_c6,multiply(sk_c4,Z_60)) = Z_60 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1728]) ).

tff(c_2141,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_1699,c_2129]) ).

tff(c_2202,plain,
    ! [Z_63] : ( multiply(sk_c1,multiply(sk_c7,Z_63)) = multiply(sk_c6,Z_63) ),
    inference(superposition,[status(thm),theory(equality)],[c_102,c_1704]) ).

tff(c_2229,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_1772,c_2202]) ).

tff(c_2246,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2141,c_102,c_2229]) ).

tff(c_2145,plain,
    ! [Z_61] : ( multiply(sk_c7,multiply(sk_c5,Z_61)) = multiply(sk_c6,Z_61) ),
    inference(superposition,[status(thm),theory(equality)],[c_107,c_1704]) ).

tff(c_2160,plain,
    multiply(sk_c7,identity) = multiply(sk_c6,sk_c2),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_2145]) ).

tff(c_2249,plain,
    multiply(sk_c7,identity) = multiply(sk_c5,sk_c2),
    inference(demodulation,[status(thm),theory(equality)],[c_2246,c_2160]) ).

tff(c_2262,plain,
    multiply(sk_c7,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_79,c_2249]) ).

tff(c_2250,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2246,c_2246,c_2141]) ).

tff(c_1746,plain,
    ! [X_2,Z_47] : ( multiply(inverse(X_2),multiply(X_2,Z_47)) = multiply(identity,Z_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_1704]) ).

tff(c_1758,plain,
    ! [X_2,Z_47] : ( multiply(inverse(X_2),multiply(X_2,Z_47)) = Z_47 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1746]) ).

tff(c_2362,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_2250,c_1758]) ).

tff(c_2371,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2362]) ).

tff(c_2254,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_2246,c_1772]) ).

tff(c_2439,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2262,c_2371,c_2254]) ).

tff(c_2440,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2201,c_2439]) ).

tff(c_2442,plain,
    sk_c7 = identity,
    inference(splitRight,[status(thm)],[c_2193]) ).

tff(c_2197,plain,
    ( ( inverse(identity) != sk_c5 )
    | ( sk_c7 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_2179]) ).

tff(c_2200,plain,
    sk_c7 != sk_c5,
    inference(splitLeft,[status(thm)],[c_2197]) ).

tff(c_2443,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2442,c_2200]) ).

tff(c_2106,plain,
    ! [Z_59] : ( multiply(sk_c7,multiply(sk_c3,Z_59)) = Z_59 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1731]) ).

tff(c_2118,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_1686,c_2106]) ).

tff(c_2448,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_2442,c_2442,c_2118]) ).

tff(c_2463,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2448]) ).

tff(c_2457,plain,
    multiply(identity,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_2442,c_107]) ).

tff(c_2464,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2457]) ).

tff(c_2505,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2463,c_2464]) ).

tff(c_2507,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2443,c_2505]) ).

tff(c_2509,plain,
    sk_c7 = sk_c5,
    inference(splitRight,[status(thm)],[c_2197]) ).

tff(c_2186,plain,
    ( ( inverse(sk_c4) != sk_c5 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1699,c_2179]) ).

tff(c_2198,plain,
    ( ( sk_c6 != sk_c5 )
    | ( sk_c7 != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1665,c_2186]) ).

tff(c_2199,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_2198]) ).

tff(c_2510,plain,
    sk_c6 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2509,c_2199]) ).

tff(c_2524,plain,
    multiply(sk_c1,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_2509,c_102]) ).

tff(c_2516,plain,
    multiply(sk_c5,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2509,c_2509,c_1772]) ).

tff(c_1737,plain,
    ! [Z_47] : ( multiply(sk_c1,multiply(sk_c7,Z_47)) = multiply(sk_c6,Z_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_102,c_1704]) ).

tff(c_2603,plain,
    ! [Z_67] : ( multiply(sk_c1,multiply(sk_c5,Z_67)) = multiply(sk_c6,Z_67) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2509,c_1737]) ).

tff(c_2615,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_2516,c_2603]) ).

tff(c_2634,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2524,c_2141,c_2615]) ).

tff(c_2636,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2510,c_2634]) ).

tff(c_2637,plain,
    sk_c6 != sk_c5,
    inference(splitRight,[status(thm)],[c_2198]) ).

tff(c_2638,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_2198]) ).

tff(c_2642,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_2638,c_2638,c_2118]) ).

tff(c_2655,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2141,c_2642]) ).

tff(c_2662,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2637,c_2655]) ).

tff(c_2687,plain,
    ! [X1_69] :
      ( ( multiply(X1_69,sk_c6) != sk_c7 )
      | ( inverse(X1_69) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_2104]) ).

tff(c_2697,plain,
    inverse(sk_c3) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_1686,c_2687]) ).

tff(c_2710,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1651,c_2697]) ).

tff(c_2711,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_2712,plain,
    multiply(sk_c7,sk_c5) != sk_c6,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_36,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_3264,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_2712,c_36]) ).

tff(c_3423,plain,
    multiply(inverse(sk_c4),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_3264,c_3387]) ).

tff(c_3467,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2711,c_3423]) ).

tff(c_3496,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_3466,c_2,c_3466,c_3467]) ).

tff(c_28,plain,
    ( ( multiply(sk_c6,sk_c7) = sk_c5 )
    | ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_3249,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_2712,c_28]) ).

tff(c_3294,plain,
    ! [Z_83] : ( multiply(sk_c6,multiply(sk_c7,Z_83)) = multiply(sk_c5,Z_83) ),
    inference(superposition,[status(thm),theory(equality)],[c_3249,c_3273]) ).

tff(c_3664,plain,
    ! [Z_83] : ( multiply(sk_c7,Z_83) = Z_83 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3496,c_2,c_3466,c_3294]) ).

tff(c_3474,plain,
    multiply(sk_c7,identity) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_3466,c_3353]) ).

tff(c_3665,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_3664,c_3474]) ).

tff(c_3500,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_3496,c_75]) ).

tff(c_3538,plain,
    multiply(identity,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3500,c_4]) ).

tff(c_3324,plain,
    ! [X_2,Z_83] : ( multiply(inverse(X_2),multiply(X_2,Z_83)) = Z_83 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3312]) ).

tff(c_3624,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_3538,c_3324]) ).

tff(c_3636,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_3624]) ).

tff(c_2724,plain,
    multiply(sk_c2,sk_c5) = sk_c7,
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_2769,plain,
    ! [X_70,Y_71,Z_72] : ( multiply(multiply(X_70,Y_71),Z_72) = multiply(X_70,multiply(Y_71,Z_72)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_2808,plain,
    ! [Z_72] : ( multiply(sk_c5,multiply(sk_c2,Z_72)) = multiply(identity,Z_72) ),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_2769]) ).

tff(c_2848,plain,
    ! [Z_74] : ( multiply(sk_c5,multiply(sk_c2,Z_74)) = Z_74 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2808]) ).

tff(c_2860,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_2724,c_2848]) ).

tff(c_2811,plain,
    ! [X_2,Z_72] : ( multiply(inverse(X_2),multiply(X_2,Z_72)) = multiply(identity,Z_72) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2769]) ).

tff(c_3000,plain,
    ! [X_78,Z_79] : ( multiply(inverse(X_78),multiply(X_78,Z_79)) = Z_79 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2811]) ).

tff(c_3033,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_2860,c_3000]) ).

tff(c_3075,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_3033]) ).

tff(c_2763,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_2712,c_36]) ).

tff(c_2716,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_2711,c_4]) ).

tff(c_2799,plain,
    ! [Z_72] : ( multiply(sk_c6,multiply(sk_c4,Z_72)) = multiply(identity,Z_72) ),
    inference(superposition,[status(thm),theory(equality)],[c_2716,c_2769]) ).

tff(c_2896,plain,
    ! [Z_76] : ( multiply(sk_c6,multiply(sk_c4,Z_76)) = Z_76 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2799]) ).

tff(c_2908,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_2763,c_2896]) ).

tff(c_2805,plain,
    ! [Z_72] : ( multiply(sk_c7,multiply(sk_c1,Z_72)) = multiply(identity,Z_72) ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_2769]) ).

tff(c_2825,plain,
    ! [Z_73] : ( multiply(sk_c7,multiply(sk_c1,Z_73)) = Z_73 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2805]) ).

tff(c_2837,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_102,c_2825]) ).

tff(c_2919,plain,
    ! [Z_77] : ( multiply(sk_c1,multiply(sk_c7,Z_77)) = multiply(sk_c6,Z_77) ),
    inference(superposition,[status(thm),theory(equality)],[c_102,c_2769]) ).

tff(c_2940,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_2837,c_2919]) ).

tff(c_2954,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2908,c_102,c_2940]) ).

tff(c_2964,plain,
    multiply(sk_c7,sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2954,c_2712]) ).

tff(c_3225,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3075,c_2964]) ).

tff(c_3227,plain,
    multiply(sk_c2,sk_c5) != sk_c7,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_3498,plain,
    multiply(sk_c2,identity) != sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_3496,c_3227]) ).

tff(c_3768,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3665,c_2,c_3636,c_3498]) ).

tff(c_3770,plain,
    multiply(sk_c1,sk_c7) != sk_c6,
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_16,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_7025,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_3770,c_16]) ).

tff(c_3769,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_3774,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3769,c_4]) ).

tff(c_7036,plain,
    ! [X_150,Y_151,Z_152] : ( multiply(multiply(X_150,Y_151),Z_152) = multiply(X_150,multiply(Y_151,Z_152)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_7063,plain,
    ! [Z_152] : ( multiply(sk_c6,multiply(sk_c4,Z_152)) = multiply(identity,Z_152) ),
    inference(superposition,[status(thm),theory(equality)],[c_3774,c_7036]) ).

tff(c_7137,plain,
    ! [Z_156] : ( multiply(sk_c6,multiply(sk_c4,Z_156)) = Z_156 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7063]) ).

tff(c_7149,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_7025,c_7137]) ).

tff(c_12,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_3818,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_3770,c_12]) ).

tff(c_10,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_3793,plain,
    inverse(sk_c3) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_3770,c_10]) ).

tff(c_3797,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_3793,c_4]) ).

tff(c_3832,plain,
    ! [X_92,Y_93,Z_94] : ( multiply(multiply(X_92,Y_93),Z_94) = multiply(X_92,multiply(Y_93,Z_94)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_3859,plain,
    ! [Z_94] : ( multiply(sk_c7,multiply(sk_c3,Z_94)) = multiply(identity,Z_94) ),
    inference(superposition,[status(thm),theory(equality)],[c_3797,c_3832]) ).

tff(c_4509,plain,
    ! [Z_107] : ( multiply(sk_c7,multiply(sk_c3,Z_107)) = Z_107 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3859]) ).

tff(c_4521,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_3818,c_4509]) ).

tff(c_3784,plain,
    multiply(sk_c2,sk_c5) = sk_c7,
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_3871,plain,
    ! [Z_94] : ( multiply(sk_c5,multiply(sk_c2,Z_94)) = multiply(identity,Z_94) ),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_3832]) ).

tff(c_4486,plain,
    ! [Z_106] : ( multiply(sk_c5,multiply(sk_c2,Z_106)) = Z_106 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3871]) ).

tff(c_4498,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_3784,c_4486]) ).

tff(c_4668,plain,
    ! [Z_111] : ( multiply(sk_c2,multiply(sk_c5,Z_111)) = multiply(sk_c7,Z_111) ),
    inference(superposition,[status(thm),theory(equality)],[c_3784,c_3832]) ).

tff(c_4683,plain,
    multiply(sk_c7,sk_c7) = multiply(sk_c2,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_4498,c_4668]) ).

tff(c_4693,plain,
    multiply(sk_c7,sk_c7) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_3784,c_4683]) ).

tff(c_4701,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4521,c_4693]) ).

tff(c_8,plain,
    ( ( multiply(sk_c6,sk_c7) = sk_c5 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_3813,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_3770,c_8]) ).

tff(c_4708,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4701,c_3813]) ).

tff(c_4702,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4701,c_4701,c_4521]) ).

tff(c_4776,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4708,c_4702]) ).

tff(c_4784,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4776,c_4776,c_4708]) ).

tff(c_3874,plain,
    ! [X_2,Z_94] : ( multiply(inverse(X_2),multiply(X_2,Z_94)) = multiply(identity,Z_94) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_3832]) ).

tff(c_3886,plain,
    ! [X_2,Z_94] : ( multiply(inverse(X_2),multiply(X_2,Z_94)) = Z_94 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3874]) ).

tff(c_4921,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_4784,c_3886]) ).

tff(c_4927,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4921]) ).

tff(c_4938,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4927,c_4776]) ).

tff(c_4715,plain,
    inverse(sk_c1) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4701,c_87]) ).

tff(c_4730,plain,
    multiply(sk_c6,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_4715,c_4]) ).

tff(c_5040,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4938,c_4730]) ).

tff(c_4713,plain,
    multiply(sk_c1,sk_c6) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_4701,c_3770]) ).

tff(c_4787,plain,
    multiply(sk_c1,sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_4776,c_4776,c_4713]) ).

tff(c_5023,plain,
    multiply(sk_c1,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4927,c_4927,c_4787]) ).

tff(c_5041,plain,
    multiply(identity,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5040,c_5023]) ).

tff(c_5045,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5041]) ).

tff(c_5047,plain,
    multiply(sk_c2,sk_c5) != sk_c7,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_7014,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_5047,c_42]) ).

tff(c_5046,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_5051,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5046,c_4]) ).

tff(c_7060,plain,
    ! [Z_152] : ( multiply(sk_c7,multiply(sk_c3,Z_152)) = multiply(identity,Z_152) ),
    inference(superposition,[status(thm),theory(equality)],[c_5051,c_7036]) ).

tff(c_7114,plain,
    ! [Z_155] : ( multiply(sk_c7,multiply(sk_c3,Z_155)) = Z_155 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7060]) ).

tff(c_7126,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_7014,c_7114]) ).

tff(c_5095,plain,
    ! [X_115,Y_116,Z_117] : ( multiply(multiply(X_115,Y_116),Z_117) = multiply(X_115,multiply(Y_116,Z_117)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_5134,plain,
    ! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = multiply(identity,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5095]) ).

tff(c_6294,plain,
    ! [X_138,Z_139] : ( multiply(inverse(X_138),multiply(X_138,Z_139)) = Z_139 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5134]) ).

tff(c_6363,plain,
    multiply(inverse(sk_c7),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_91,c_6294]) ).

tff(c_6899,plain,
    ! [X_148] : ( multiply(inverse(inverse(X_148)),identity) = X_148 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_6294]) ).

tff(c_6914,plain,
    multiply(inverse(sk_c7),identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_5046,c_6899]) ).

tff(c_6927,plain,
    sk_c3 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_6363,c_6914]) ).

tff(c_5072,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_5047,c_42]) ).

tff(c_6931,plain,
    multiply(sk_c1,sk_c6) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_6927,c_5072]) ).

tff(c_6378,plain,
    ! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_6294]) ).

tff(c_5067,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(splitLeft,[status(thm)],[c_28]) ).

tff(c_6348,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_5067,c_6294]) ).

tff(c_5122,plain,
    ! [Z_117] : ( multiply(sk_c7,multiply(sk_c3,Z_117)) = multiply(identity,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_5051,c_5095]) ).

tff(c_5174,plain,
    ! [Z_120] : ( multiply(sk_c7,multiply(sk_c3,Z_120)) = Z_120 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5122]) ).

tff(c_5186,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5072,c_5174]) ).

tff(c_6324,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_5186,c_6294]) ).

tff(c_6533,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_6348,c_6324]) ).

tff(c_5084,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_3770,c_16]) ).

tff(c_5125,plain,
    ! [Z_117] : ( multiply(sk_c6,multiply(sk_c4,Z_117)) = multiply(identity,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_3774,c_5095]) ).

tff(c_5200,plain,
    ! [Z_121] : ( multiply(sk_c6,multiply(sk_c4,Z_121)) = Z_121 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5125]) ).

tff(c_5212,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_5084,c_5200]) ).

tff(c_5077,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_5047,c_38]) ).

tff(c_5198,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5067,c_5077,c_58]) ).

tff(c_5223,plain,
    ! [X3_122] :
      ( ( inverse(X3_122) != sk_c7 )
      | ( multiply(X3_122,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_5198]) ).

tff(c_5237,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5223]) ).

tff(c_5245,plain,
    sk_c6 != identity,
    inference(splitLeft,[status(thm)],[c_5237]) ).

tff(c_5507,plain,
    ! [Z_128] : ( multiply(sk_c6,multiply(sk_c7,Z_128)) = multiply(sk_c5,Z_128) ),
    inference(superposition,[status(thm),theory(equality)],[c_5077,c_5095]) ).

tff(c_5531,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_5067,c_5507]) ).

tff(c_5539,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5212,c_5531]) ).

tff(c_5146,plain,
    ! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = Z_117 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5134]) ).

tff(c_5546,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_5539,c_5146]) ).

tff(c_5553,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_5546]) ).

tff(c_5246,plain,
    ! [X_123,Z_124] : ( multiply(inverse(X_123),multiply(X_123,Z_124)) = Z_124 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5134]) ).

tff(c_5315,plain,
    multiply(inverse(sk_c5),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_79,c_5246]) ).

tff(c_5560,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_5553,c_5315]) ).

tff(c_5574,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_5560]) ).

tff(c_5569,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5553,c_75]) ).

tff(c_5636,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5574,c_5569]) ).

tff(c_5303,plain,
    multiply(inverse(sk_c6),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_3774,c_5246]) ).

tff(c_5288,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_5077,c_5246]) ).

tff(c_5558,plain,
    multiply(inverse(sk_c6),identity) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_5553,c_5288]) ).

tff(c_5573,plain,
    sk_c7 = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_5303,c_5558]) ).

tff(c_5525,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_5186,c_5507]) ).

tff(c_5538,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5212,c_5525]) ).

tff(c_5670,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5573,c_5553,c_2,c_5553,c_5538]) ).

tff(c_5679,plain,
    inverse(identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_5670,c_3769]) ).

tff(c_5682,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5636,c_5679]) ).

tff(c_5684,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5245,c_5682]) ).

tff(c_5686,plain,
    sk_c6 = identity,
    inference(splitRight,[status(thm)],[c_5237]) ).

tff(c_5233,plain,
    ( ( inverse(sk_c6) != sk_c7 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5077,c_5223]) ).

tff(c_5244,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_5233]) ).

tff(c_5687,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5686,c_5244]) ).

tff(c_5690,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5686,c_5686,c_5212]) ).

tff(c_5700,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5690]) ).

tff(c_5705,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5687,c_5700]) ).

tff(c_5707,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_5233]) ).

tff(c_5787,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5707,c_5237]) ).

tff(c_5788,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_5787]) ).

tff(c_5710,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5707,c_5707,c_5212]) ).

tff(c_5807,plain,
    ! [X_131,Z_132] : ( multiply(inverse(X_131),multiply(X_131,Z_132)) = Z_132 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5134]) ).

tff(c_5831,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_5710,c_5807]) ).

tff(c_5889,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_5831]) ).

tff(c_5891,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5788,c_5889]) ).

tff(c_5893,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_5787]) ).

tff(c_5241,plain,
    ( ( inverse(identity) != sk_c7 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_5223]) ).

tff(c_5243,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_5241]) ).

tff(c_5708,plain,
    sk_c7 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5707,c_5243]) ).

tff(c_5904,plain,
    sk_c7 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5893,c_5708]) ).

tff(c_5714,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5707,c_5077]) ).

tff(c_5897,plain,
    multiply(identity,sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5893,c_5893,c_5714]) ).

tff(c_5971,plain,
    sk_c7 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_5897,c_2]) ).

tff(c_5979,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5904,c_5971]) ).

tff(c_5981,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_5241]) ).

tff(c_5983,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_5981,c_5981,c_5186]) ).

tff(c_5995,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5212,c_5983]) ).

tff(c_6001,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5995,c_5981]) ).

tff(c_5980,plain,
    inverse(identity) != sk_c7,
    inference(splitRight,[status(thm)],[c_5241]) ).

tff(c_6033,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_6001,c_5980]) ).

tff(c_5131,plain,
    ! [Z_117] : ( multiply(sk_c5,multiply(sk_c2,Z_117)) = multiply(identity,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_5095]) ).

tff(c_5145,plain,
    ! [Z_117] : ( multiply(sk_c5,multiply(sk_c2,Z_117)) = Z_117 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5131]) ).

tff(c_5119,plain,
    ! [Z_117] : ( multiply(sk_c7,multiply(sk_c5,Z_117)) = multiply(sk_c6,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_5067,c_5095]) ).

tff(c_6100,plain,
    ! [Z_133] : ( multiply(sk_c5,multiply(sk_c5,Z_133)) = multiply(sk_c5,Z_133) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6001,c_5995,c_5119]) ).

tff(c_6130,plain,
    ! [Z_117] : ( multiply(sk_c5,multiply(sk_c2,Z_117)) = multiply(sk_c5,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_5145,c_6100]) ).

tff(c_6161,plain,
    ! [Z_134] : ( multiply(sk_c5,Z_134) = Z_134 ),
    inference(demodulation,[status(thm),theory(equality)],[c_5145,c_6130]) ).

tff(c_5989,plain,
    multiply(sk_c6,sk_c3) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5981,c_5051]) ).

tff(c_6068,plain,
    multiply(sk_c5,sk_c3) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5995,c_5989]) ).

tff(c_6167,plain,
    sk_c3 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_6161,c_6068]) ).

tff(c_5991,plain,
    inverse(sk_c3) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_5981,c_5046]) ).

tff(c_6017,plain,
    inverse(sk_c3) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_5995,c_5991]) ).

tff(c_6206,plain,
    inverse(identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_6167,c_6017]) ).

tff(c_6210,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6033,c_6206]) ).

tff(c_6211,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_5198]) ).

tff(c_6236,plain,
    ! [X2_136] :
      ( ( multiply(X2_136,sk_c5) != sk_c6 )
      | ( inverse(X2_136) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_6211]) ).

tff(c_6243,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5084,c_6236]) ).

tff(c_6258,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3769,c_6243]) ).

tff(c_6259,plain,
    ! [X1_8,X4_7] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_6211]) ).

tff(c_6445,plain,
    ! [X4_7] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 ) ),
    inference(splitLeft,[status(thm)],[c_6259]) ).

tff(c_6577,plain,
    ! [X4_142] :
      ( ( inverse(X4_142) != sk_c5 )
      | ( multiply(X4_142,sk_c5) != sk_c5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6533,c_6445]) ).

tff(c_6592,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c5 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_6577]) ).

tff(c_6695,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_6592]) ).

tff(c_6543,plain,
    multiply(sk_c5,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_6533,c_5067]) ).

tff(c_6212,plain,
    ! [Z_135] : ( multiply(sk_c6,multiply(sk_c4,Z_135)) = Z_135 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5125]) ).

tff(c_6224,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_5084,c_6212]) ).

tff(c_5113,plain,
    ! [Z_117] : ( multiply(sk_c6,multiply(sk_c7,Z_117)) = multiply(sk_c5,Z_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_5077,c_5095]) ).

tff(c_6641,plain,
    ! [Z_143] : ( multiply(sk_c6,multiply(sk_c5,Z_143)) = multiply(sk_c5,Z_143) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6533,c_5113]) ).

tff(c_6656,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_6543,c_6641]) ).

tff(c_6669,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_6543,c_6224,c_6656]) ).

tff(c_6680,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_6669,c_6669,c_6224]) ).

tff(c_6703,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_6680,c_5146]) ).

tff(c_6710,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_6703]) ).

tff(c_6712,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6695,c_6710]) ).

tff(c_6714,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_6592]) ).

tff(c_6369,plain,
    multiply(inverse(sk_c5),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_79,c_6294]) ).

tff(c_6753,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_6714,c_6369]) ).

tff(c_6758,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6378,c_6753]) ).

tff(c_6756,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6714,c_75]) ).

tff(c_6862,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6758,c_6756]) ).

tff(c_6599,plain,
    inverse(identity) != sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_2,c_6577]) ).

tff(c_6749,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6714,c_6599]) ).

tff(c_6886,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6862,c_6749]) ).

tff(c_6978,plain,
    ! [X1_149] :
      ( ( multiply(X1_149,sk_c6) != sk_c7 )
      | ( inverse(X1_149) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_6259]) ).

tff(c_6981,plain,
    inverse(sk_c1) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_6931,c_6978]) ).

tff(c_7007,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_87,c_6981]) ).

tff(c_7008,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_7400,plain,
    ! [Z_161] : ( multiply(sk_c6,multiply(sk_c7,Z_161)) = multiply(sk_c5,Z_161) ),
    inference(superposition,[status(thm),theory(equality)],[c_7008,c_7036]) ).

tff(c_7418,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_7126,c_7400]) ).

tff(c_7428,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7149,c_7418]) ).

tff(c_7072,plain,
    ! [X_2,Z_152] : ( multiply(inverse(X_2),multiply(X_2,Z_152)) = multiply(identity,Z_152) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7036]) ).

tff(c_7084,plain,
    ! [X_2,Z_152] : ( multiply(inverse(X_2),multiply(X_2,Z_152)) = Z_152 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7072]) ).

tff(c_7447,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_7428,c_7084]) ).

tff(c_7453,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_7447]) ).

tff(c_7009,plain,
    multiply(sk_c7,sk_c5) != sk_c6,
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_7463,plain,
    multiply(identity,sk_c5) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7453,c_7009]) ).

tff(c_7472,plain,
    sk_c6 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7463]) ).

tff(c_7160,plain,
    ! [X_157,Z_158] : ( multiply(inverse(X_157),multiply(X_157,Z_158)) = Z_158 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7072]) ).

tff(c_7220,plain,
    multiply(inverse(sk_c7),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_91,c_7160]) ).

tff(c_7459,plain,
    multiply(inverse(identity),identity) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7453,c_7220]) ).

tff(c_7470,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_7459]) ).

tff(c_7208,plain,
    multiply(inverse(sk_c7),identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_5051,c_7160]) ).

tff(c_7371,plain,
    sk_c3 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_7220,c_7208]) ).

tff(c_7245,plain,
    ! [Z_159] : ( multiply(sk_c3,multiply(sk_c6,Z_159)) = multiply(sk_c7,Z_159) ),
    inference(superposition,[status(thm),theory(equality)],[c_7014,c_7036]) ).

tff(c_7269,plain,
    multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_7008,c_7245]) ).

tff(c_7277,plain,
    multiply(sk_c3,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7126,c_7269]) ).

tff(c_7372,plain,
    multiply(sk_c1,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7371,c_7277]) ).

tff(c_7500,plain,
    multiply(identity,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7470,c_7372]) ).

tff(c_7502,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7500]) ).

tff(c_7504,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7472,c_7502]) ).

tff(c_7506,plain,
    inverse(sk_c1) != sk_c7,
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_26,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_7533,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_7506,c_26]) ).

tff(c_24,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_7519,plain,
    inverse(sk_c4) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_7506,c_24]) ).

tff(c_7523,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_7519,c_4]) ).

tff(c_7564,plain,
    ! [X_163,Y_164,Z_165] : ( multiply(multiply(X_163,Y_164),Z_165) = multiply(X_163,multiply(Y_164,Z_165)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_7588,plain,
    ! [Z_165] : ( multiply(sk_c6,multiply(sk_c4,Z_165)) = multiply(identity,Z_165) ),
    inference(superposition,[status(thm),theory(equality)],[c_7523,c_7564]) ).

tff(c_7610,plain,
    ! [Z_166] : ( multiply(sk_c6,multiply(sk_c4,Z_166)) = Z_166 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7588]) ).

tff(c_7622,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_7533,c_7610]) ).

tff(c_22,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_7541,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_7506,c_22]) ).

tff(c_7505,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_7510,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_7505,c_4]) ).

tff(c_7591,plain,
    ! [Z_165] : ( multiply(sk_c7,multiply(sk_c3,Z_165)) = multiply(identity,Z_165) ),
    inference(superposition,[status(thm),theory(equality)],[c_7510,c_7564]) ).

tff(c_7633,plain,
    ! [Z_167] : ( multiply(sk_c7,multiply(sk_c3,Z_167)) = Z_167 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7591]) ).

tff(c_7645,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_7541,c_7633]) ).

tff(c_18,plain,
    ( ( multiply(sk_c6,sk_c7) = sk_c5 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_7546,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_7506,c_18]) ).

tff(c_7852,plain,
    ! [Z_173] : ( multiply(sk_c6,multiply(sk_c7,Z_173)) = multiply(sk_c5,Z_173) ),
    inference(superposition,[status(thm),theory(equality)],[c_7546,c_7564]) ).

tff(c_7867,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_7645,c_7852]) ).

tff(c_7877,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7622,c_7867]) ).

tff(c_7597,plain,
    ! [X_2,Z_165] : ( multiply(inverse(X_2),multiply(X_2,Z_165)) = multiply(identity,Z_165) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7564]) ).

tff(c_7608,plain,
    ! [X_2,Z_165] : ( multiply(inverse(X_2),multiply(X_2,Z_165)) = Z_165 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7597]) ).

tff(c_7881,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_7877,c_7608]) ).

tff(c_7887,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_7881]) ).

tff(c_7894,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7887,c_7887,c_7645]) ).

tff(c_7904,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7894]) ).

tff(c_7950,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_7904,c_7904,c_7622]) ).

tff(c_7957,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7950]) ).

tff(c_7670,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(sk_c7,sk_c5) != sk_c6 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7546,c_58]) ).

tff(c_7671,plain,
    multiply(sk_c7,sk_c5) != sk_c6,
    inference(splitLeft,[status(thm)],[c_7670]) ).

tff(c_7893,plain,
    multiply(identity,sk_c5) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_7887,c_7671]) ).

tff(c_7903,plain,
    sk_c6 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7893]) ).

tff(c_7980,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7957,c_7904,c_7903]) ).

tff(c_7982,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(splitRight,[status(thm)],[c_7670]) ).

tff(c_7990,plain,
    ! [X_175,Z_176] : ( multiply(inverse(X_175),multiply(X_175,Z_176)) = Z_176 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_7597]) ).

tff(c_8008,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_7982,c_7990]) ).

tff(c_8014,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_7645,c_7990]) ).

tff(c_8275,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8008,c_8014]) ).

tff(c_8282,plain,
    multiply(sk_c6,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8275,c_7546]) ).

tff(c_8279,plain,
    multiply(sk_c5,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_8275,c_7982]) ).

tff(c_7585,plain,
    ! [Z_165] : ( multiply(sk_c4,multiply(sk_c5,Z_165)) = multiply(sk_c6,Z_165) ),
    inference(superposition,[status(thm),theory(equality)],[c_7533,c_7564]) ).

tff(c_8989,plain,
    multiply(sk_c6,sk_c5) = multiply(sk_c4,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_8279,c_7585]) ).

tff(c_8998,plain,
    multiply(sk_c4,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_8989]) ).

tff(c_9056,plain,
    multiply(inverse(sk_c4),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_8998,c_7608]) ).

tff(c_9065,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_7519,c_9056]) ).

tff(c_6,plain,
    ! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_7986,plain,
    ! [Z_5] : ( multiply(sk_c7,multiply(sk_c5,Z_5)) = multiply(sk_c6,Z_5) ),
    inference(superposition,[status(thm),theory(equality)],[c_7982,c_6]) ).

tff(c_9018,plain,
    ! [Z_195] : ( multiply(sk_c5,multiply(sk_c5,Z_195)) = multiply(sk_c6,Z_195) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8275,c_7986]) ).

tff(c_9042,plain,
    multiply(sk_c6,sk_c5) = multiply(sk_c5,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_8279,c_9018]) ).

tff(c_9052,plain,
    multiply(sk_c5,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_9042]) ).

tff(c_9120,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_9065,c_9052]) ).

tff(c_9127,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_9120,c_7608]) ).

tff(c_9134,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_9127]) ).

tff(c_9225,plain,
    ! [X_198,Z_199] : ( multiply(inverse(inverse(X_198)),Z_199) = multiply(X_198,Z_199) ),
    inference(superposition,[status(thm),theory(equality)],[c_7990,c_7608]) ).

tff(c_8056,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_7990]) ).

tff(c_9232,plain,
    ! [X_198] : ( multiply(X_198,identity) = X_198 ),
    inference(superposition,[status(thm),theory(equality)],[c_9225,c_8056]) ).

tff(c_9138,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9134,c_9065]) ).

tff(c_8577,plain,
    ! [X_185,Z_186] : ( multiply(inverse(inverse(X_185)),Z_186) = multiply(X_185,Z_186) ),
    inference(superposition,[status(thm),theory(equality)],[c_7990,c_7608]) ).

tff(c_8584,plain,
    ! [X_185] : ( multiply(X_185,identity) = X_185 ),
    inference(superposition,[status(thm),theory(equality)],[c_8577,c_8056]) ).

tff(c_8339,plain,
    multiply(sk_c6,sk_c5) = multiply(sk_c4,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_8279,c_7585]) ).

tff(c_8348,plain,
    multiply(sk_c4,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_8339]) ).

tff(c_8406,plain,
    multiply(inverse(sk_c4),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_8348,c_7608]) ).

tff(c_8415,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_7519,c_8406]) ).

tff(c_8368,plain,
    ! [Z_182] : ( multiply(sk_c5,multiply(sk_c5,Z_182)) = multiply(sk_c6,Z_182) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8275,c_7986]) ).

tff(c_8392,plain,
    multiply(sk_c6,sk_c5) = multiply(sk_c5,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_8279,c_8368]) ).

tff(c_8402,plain,
    multiply(sk_c5,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8282,c_8392]) ).

tff(c_8475,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8415,c_8402]) ).

tff(c_8482,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_8475,c_7608]) ).

tff(c_8489,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_8482]) ).

tff(c_8494,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8489,c_8415]) ).

tff(c_7981,plain,
    ! [X3_6,X4_7,X1_8,X2_9] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_7670]) ).

tff(c_8245,plain,
    ! [X2_180] :
      ( ( multiply(X2_180,sk_c5) != sk_c6 )
      | ( inverse(X2_180) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_7981]) ).

tff(c_8259,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_7533,c_8245]) ).

tff(c_8271,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7519,c_8259]) ).

tff(c_8272,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_7981]) ).

tff(c_8334,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c5 )
      | ( inverse(X1_8) != sk_c5 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c5 )
      | ( inverse(X3_6) != sk_c5 )
      | ( multiply(X3_6,sk_c5) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8275,c_8275,c_8275,c_8275,c_8275,c_8272]) ).

tff(c_8335,plain,
    ! [X3_6] :
      ( ( inverse(X3_6) != sk_c5 )
      | ( multiply(X3_6,sk_c5) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_8334]) ).

tff(c_8982,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8584,c_8494,c_8489,c_8489,c_8335]) ).

tff(c_8059,plain,
    ! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_7990]) ).

tff(c_8050,plain,
    multiply(inverse(sk_c5),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_79,c_7990]) ).

tff(c_8497,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_8489,c_8050]) ).

tff(c_8503,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8059,c_8497]) ).

tff(c_8500,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8489,c_75]) ).

tff(c_8549,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8503,c_8500]) ).

tff(c_8984,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8982,c_8549]) ).

tff(c_8985,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c5 )
      | ( multiply(X1_8,sk_c6) != sk_c5 )
      | ( inverse(X1_8) != sk_c5 ) ),
    inference(splitRight,[status(thm)],[c_8334]) ).

tff(c_19407,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != identity )
      | ( identity != X4_7 )
      | ( identity != X1_8 )
      | ( inverse(X1_8) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9134,c_9232,c_9138,c_9134,c_9232,c_9134,c_9134,c_9134,c_8985]) ).

tff(c_19409,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_19407]) ).

tff(c_9141,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_9134,c_8050]) ).

tff(c_9147,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_8059,c_9141]) ).

tff(c_9144,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9134,c_75]) ).

tff(c_9194,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_9147,c_9144]) ).

tff(c_19411,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_19409,c_9194]) ).

tff(c_19413,plain,
    inverse(identity) != identity,
    inference(splitRight,[status(thm)],[c_19407]) ).

tff(c_19415,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_19413,c_9194]) ).

tff(c_19417,plain,
    inverse(sk_c2) != sk_c5,
    inference(splitRight,[status(thm)],[c_50]) ).

tff(c_56,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( inverse(sk_c2) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_19466,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_19417,c_56]) ).

tff(c_54,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( inverse(sk_c2) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_19442,plain,
    inverse(sk_c4) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_19417,c_54]) ).

tff(c_19446,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_19442,c_4]) ).

tff(c_19487,plain,
    ! [X_303,Y_304,Z_305] : ( multiply(multiply(X_303,Y_304),Z_305) = multiply(X_303,multiply(Y_304,Z_305)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_19511,plain,
    ! [Z_305] : ( multiply(sk_c6,multiply(sk_c4,Z_305)) = multiply(identity,Z_305) ),
    inference(superposition,[status(thm),theory(equality)],[c_19446,c_19487]) ).

tff(c_19995,plain,
    ! [Z_315] : ( multiply(sk_c6,multiply(sk_c4,Z_315)) = Z_315 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19511]) ).

tff(c_20007,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_19466,c_19995]) ).

tff(c_19520,plain,
    ! [X_2,Z_305] : ( multiply(inverse(X_2),multiply(X_2,Z_305)) = multiply(identity,Z_305) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_19487]) ).

tff(c_20999,plain,
    ! [X_336,Z_337] : ( multiply(inverse(X_336),multiply(X_336,Z_337)) = Z_337 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19520]) ).

tff(c_21026,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_20007,c_20999]) ).

tff(c_48,plain,
    ( ( multiply(sk_c6,sk_c7) = sk_c5 )
    | ( inverse(sk_c2) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_19472,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_19417,c_48]) ).

tff(c_21038,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_19472,c_20999]) ).

tff(c_21388,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21026,c_21038]) ).

tff(c_19536,plain,
    ! [Z_306] : ( multiply(sk_c6,multiply(sk_c4,Z_306)) = Z_306 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19511]) ).

tff(c_19548,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_19466,c_19536]) ).

tff(c_19582,plain,
    ! [X_308,Z_309] : ( multiply(inverse(X_308),multiply(X_308,Z_309)) = Z_309 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19520]) ).

tff(c_19606,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_19548,c_19582]) ).

tff(c_19615,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_19472,c_19582]) ).

tff(c_19802,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_19606,c_19615]) ).

tff(c_52,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c2) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_19460,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_19417,c_52]) ).

tff(c_19416,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_50]) ).

tff(c_19421,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_19416,c_4]) ).

tff(c_19517,plain,
    ! [Z_305] : ( multiply(sk_c7,multiply(sk_c3,Z_305)) = multiply(identity,Z_305) ),
    inference(superposition,[status(thm),theory(equality)],[c_19421,c_19487]) ).

tff(c_19559,plain,
    ! [Z_307] : ( multiply(sk_c7,multiply(sk_c3,Z_307)) = Z_307 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19517]) ).

tff(c_19571,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_19460,c_19559]) ).

tff(c_19815,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_19802,c_19802,c_19571]) ).

tff(c_19820,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_19548,c_19815]) ).

tff(c_19860,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_19820,c_19820,c_19606]) ).

tff(c_19868,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_19860]) ).

tff(c_19878,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_19868,c_19820]) ).

tff(c_19534,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(sk_c7,sk_c5) != sk_c6 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_19472,c_58]) ).

tff(c_19535,plain,
    multiply(sk_c7,sk_c5) != sk_c6,
    inference(splitLeft,[status(thm)],[c_19534]) ).

tff(c_19816,plain,
    multiply(sk_c6,sk_c5) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_19802,c_19535]) ).

tff(c_19985,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_19878,c_2,c_19878,c_19868,c_19816]) ).

tff(c_19987,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(splitRight,[status(thm)],[c_19534]) ).

tff(c_21032,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_19987,c_20999]) ).

tff(c_21429,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_21388,c_21032]) ).

tff(c_21436,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_21429]) ).

tff(c_20100,plain,
    ! [Z_320] : ( multiply(sk_c7,multiply(sk_c3,Z_320)) = Z_320 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19517]) ).

tff(c_20112,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_19460,c_20100]) ).

tff(c_21431,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21388,c_21388,c_20112]) ).

tff(c_21437,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20007,c_21431]) ).

tff(c_21452,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_21436,c_21437]) ).

tff(c_21453,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_21452,c_21388]) ).

tff(c_19430,plain,
    inverse(sk_c1) = sk_c7,
    inference(splitLeft,[status(thm)],[c_24]) ).

tff(c_19434,plain,
    multiply(sk_c7,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_19430,c_4]) ).

tff(c_21053,plain,
    multiply(inverse(sk_c7),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_19434,c_20999]) ).

tff(c_21059,plain,
    multiply(inverse(sk_c7),identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_19421,c_20999]) ).

tff(c_21183,plain,
    sk_c3 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_21053,c_21059]) ).

tff(c_21196,plain,
    multiply(sk_c1,sk_c6) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_21183,c_19460]) ).

tff(c_19986,plain,
    ! [X3_6,X4_7,X1_8,X2_9] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_19534]) ).

tff(c_20068,plain,
    ! [X2_319] :
      ( ( multiply(X2_319,sk_c5) != sk_c6 )
      | ( inverse(X2_319) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_19986]) ).

tff(c_20078,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_19466,c_20068]) ).

tff(c_20091,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_19442,c_20078]) ).

tff(c_20092,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_19986]) ).

tff(c_20137,plain,
    ! [X3_322] :
      ( ( inverse(X3_322) != sk_c7 )
      | ( multiply(X3_322,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_20092]) ).

tff(c_20147,plain,
    ( ( inverse(sk_c6) != sk_c7 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_19472,c_20137]) ).

tff(c_20158,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_20147]) ).

tff(c_20160,plain,
    ! [X_323,Z_324] : ( multiply(inverse(X_323),multiply(X_323,Z_324)) = Z_324 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19520]) ).

tff(c_20193,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_19987,c_20160]) ).

tff(c_20181,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_20112,c_20160]) ).

tff(c_20358,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20193,c_20181]) ).

tff(c_20368,plain,
    multiply(sk_c5,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_20358,c_19987]) ).

tff(c_20369,plain,
    multiply(sk_c6,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20358,c_19472]) ).

tff(c_19991,plain,
    ! [Z_5] : ( multiply(sk_c7,multiply(sk_c5,Z_5)) = multiply(sk_c6,Z_5) ),
    inference(superposition,[status(thm),theory(equality)],[c_19987,c_6]) ).

tff(c_20471,plain,
    ! [Z_327] : ( multiply(sk_c5,multiply(sk_c5,Z_327)) = multiply(sk_c6,Z_327) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20358,c_19991]) ).

tff(c_20492,plain,
    multiply(sk_c6,sk_c5) = multiply(sk_c5,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_20368,c_20471]) ).

tff(c_20499,plain,
    multiply(sk_c5,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20369,c_20492]) ).

tff(c_20470,plain,
    ! [Z_5] : ( multiply(sk_c5,multiply(sk_c5,Z_5)) = multiply(sk_c6,Z_5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20358,c_19991]) ).

tff(c_20503,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_20499,c_20470]) ).

tff(c_20512,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20368,c_20007,c_20503]) ).

tff(c_20514,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20158,c_20512]) ).

tff(c_20516,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_20147]) ).

tff(c_20155,plain,
    ( ( inverse(identity) != sk_c7 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_20137]) ).

tff(c_20157,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_20155]) ).

tff(c_20517,plain,
    sk_c7 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20516,c_20157]) ).

tff(c_20526,plain,
    multiply(sk_c5,sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_20516,c_19446]) ).

tff(c_20583,plain,
    ! [Z_328] : ( multiply(sk_c7,multiply(sk_c5,Z_328)) = multiply(sk_c5,Z_328) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20516,c_19991]) ).

tff(c_20595,plain,
    multiply(sk_c7,identity) = multiply(sk_c5,sk_c4),
    inference(superposition,[status(thm),theory(equality)],[c_20526,c_20583]) ).

tff(c_20602,plain,
    multiply(sk_c7,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_20526,c_20595]) ).

tff(c_20607,plain,
    ! [Z_5] : ( multiply(sk_c7,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
    inference(superposition,[status(thm),theory(equality)],[c_20602,c_6]) ).

tff(c_20633,plain,
    ! [Z_329] : ( multiply(sk_c7,Z_329) = Z_329 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_20607]) ).

tff(c_20519,plain,
    multiply(sk_c7,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20516,c_20112]) ).

tff(c_20639,plain,
    sk_c7 = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_20633,c_20519]) ).

tff(c_20675,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20517,c_20639]) ).

tff(c_20677,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_20155]) ).

tff(c_20681,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_20677,c_20677,c_20112]) ).

tff(c_20690,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20007,c_20681]) ).

tff(c_20704,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20690,c_20677]) ).

tff(c_20151,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_20137]) ).

tff(c_20798,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20690,c_20704,c_20704,c_20151]) ).

tff(c_20799,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_20798]) ).

tff(c_20683,plain,
    multiply(sk_c6,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_20677,c_19987]) ).

tff(c_20752,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20690,c_20690,c_20683]) ).

tff(c_20800,plain,
    ! [X_330,Z_331] : ( multiply(inverse(X_330),multiply(X_330,Z_331)) = Z_331 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19520]) ).

tff(c_20830,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_20752,c_20800]) ).

tff(c_20857,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_20830]) ).

tff(c_20858,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20799,c_20857]) ).

tff(c_20860,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_20798]) ).

tff(c_20676,plain,
    inverse(identity) != sk_c7,
    inference(splitRight,[status(thm)],[c_20155]) ).

tff(c_20718,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20704,c_20676]) ).

tff(c_20871,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_20860,c_20718]) ).

tff(c_20709,plain,
    inverse(sk_c4) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_20690,c_19442]) ).

tff(c_20868,plain,
    inverse(sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_20860,c_20709]) ).

tff(c_20907,plain,
    multiply(identity,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_20868,c_4]) ).

tff(c_19531,plain,
    ! [X_2,Z_305] : ( multiply(inverse(X_2),multiply(X_2,Z_305)) = Z_305 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_19520]) ).

tff(c_20965,plain,
    multiply(inverse(identity),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_20907,c_19531]) ).

tff(c_20977,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_20965]) ).

tff(c_20981,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_20977,c_20868]) ).

tff(c_20984,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20871,c_20981]) ).

tff(c_20985,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_20092]) ).

tff(c_21233,plain,
    ! [X1_340] :
      ( ( multiply(X1_340,sk_c6) != sk_c7 )
      | ( inverse(X1_340) != sk_c7 ) ),
    inference(splitLeft,[status(thm)],[c_20985]) ).

tff(c_21236,plain,
    inverse(sk_c1) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_21196,c_21233]) ).

tff(c_21262,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_19430,c_21236]) ).

tff(c_21399,plain,
    ! [X4_343] :
      ( ( inverse(X4_343) != sk_c5 )
      | ( multiply(X4_343,sk_c5) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_20985]) ).

tff(c_21416,plain,
    ( ( inverse(sk_c4) != sk_c5 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_19466,c_21399]) ).

tff(c_21425,plain,
    ( ( sk_c6 != sk_c5 )
    | ( sk_c7 != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_19442,c_21416]) ).

tff(c_21483,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_21453,c_21452,c_21436,c_21452,c_21425]) ).

tff(c_21484,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_24]) ).

tff(c_21489,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_21484,c_4]) ).

tff(c_21535,plain,
    ! [X_344,Y_345,Z_346] : ( multiply(multiply(X_344,Y_345),Z_346) = multiply(X_344,multiply(Y_345,Z_346)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_21565,plain,
    ! [X_2,Z_346] : ( multiply(inverse(X_2),multiply(X_2,Z_346)) = multiply(identity,Z_346) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_21535]) ).

tff(c_21959,plain,
    ! [X_355,Z_356] : ( multiply(inverse(X_355),multiply(X_355,Z_356)) = Z_356 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21565]) ).

tff(c_22007,plain,
    multiply(inverse(sk_c6),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_21489,c_21959]) ).

tff(c_21485,plain,
    inverse(sk_c1) != sk_c7,
    inference(splitRight,[status(thm)],[c_24]) ).

tff(c_21499,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_21485,c_26]) ).

tff(c_21559,plain,
    ! [Z_346] : ( multiply(sk_c6,multiply(sk_c4,Z_346)) = multiply(identity,Z_346) ),
    inference(superposition,[status(thm),theory(equality)],[c_21489,c_21535]) ).

tff(c_21577,plain,
    ! [Z_347] : ( multiply(sk_c6,multiply(sk_c4,Z_347)) = Z_347 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21559]) ).

tff(c_21589,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_21499,c_21577]) ).

tff(c_21989,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_21589,c_21959]) ).

tff(c_21506,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_21485,c_18]) ).

tff(c_22001,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_21506,c_21959]) ).

tff(c_22268,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21989,c_22001]) ).

tff(c_21626,plain,
    ! [X_349,Z_350] : ( multiply(inverse(X_349),multiply(X_349,Z_350)) = Z_350 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21565]) ).

tff(c_21650,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_21589,c_21626]) ).

tff(c_21662,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_21506,c_21626]) ).

tff(c_21769,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21650,c_21662]) ).

tff(c_21511,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_21485,c_22]) ).

tff(c_21562,plain,
    ! [Z_346] : ( multiply(sk_c7,multiply(sk_c3,Z_346)) = multiply(identity,Z_346) ),
    inference(superposition,[status(thm),theory(equality)],[c_19421,c_21535]) ).

tff(c_21600,plain,
    ! [Z_348] : ( multiply(sk_c7,multiply(sk_c3,Z_348)) = Z_348 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21562]) ).

tff(c_21612,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_21511,c_21600]) ).

tff(c_21644,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_21612,c_21626]) ).

tff(c_21814,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21769,c_21644]) ).

tff(c_21824,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_21814]) ).

tff(c_21816,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21769,c_21612]) ).

tff(c_21825,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_21589,c_21816]) ).

tff(c_21845,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_21824,c_21825]) ).

tff(c_21617,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(sk_c7,sk_c5) != sk_c6 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_21506,c_58]) ).

tff(c_21618,plain,
    multiply(sk_c7,sk_c5) != sk_c6,
    inference(splitLeft,[status(thm)],[c_21617]) ).

tff(c_21817,plain,
    multiply(sk_c6,sk_c5) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21618]) ).

tff(c_21926,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_21845,c_21824,c_2,c_21824,c_21817]) ).

tff(c_21928,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(splitRight,[status(thm)],[c_21617]) ).

tff(c_21983,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_21928,c_21959]) ).

tff(c_22280,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_22268,c_21983]) ).

tff(c_22289,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_22280]) ).

tff(c_22296,plain,
    multiply(inverse(sk_c6),identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_22289,c_21989]) ).

tff(c_22301,plain,
    sk_c6 = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_22007,c_22296]) ).

tff(c_22281,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_22268,c_22268,c_21612]) ).

tff(c_22290,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_21589,c_22281]) ).

tff(c_22740,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22301,c_22289,c_22290]) ).

tff(c_22741,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22740,c_22301]) ).

tff(c_22019,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_21959]) ).

tff(c_21575,plain,
    ! [X_2,Z_346] : ( multiply(inverse(X_2),multiply(X_2,Z_346)) = Z_346 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21565]) ).

tff(c_22889,plain,
    ! [X_373,Z_374] : ( multiply(inverse(inverse(X_373)),Z_374) = multiply(X_373,Z_374) ),
    inference(superposition,[status(thm),theory(equality)],[c_21959,c_21575]) ).

tff(c_22923,plain,
    ! [X_2] : ( multiply(X_2,identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_22019,c_22889]) ).

tff(c_22446,plain,
    ! [X_363,Z_364] : ( multiply(inverse(inverse(X_363)),Z_364) = multiply(X_363,Z_364) ),
    inference(superposition,[status(thm),theory(equality)],[c_21575,c_21959]) ).

tff(c_22457,plain,
    ! [X_363] : ( multiply(X_363,identity) = X_363 ),
    inference(superposition,[status(thm),theory(equality)],[c_22446,c_22019]) ).

tff(c_22318,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22301,c_22289,c_22290]) ).

tff(c_22319,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22318,c_22301]) ).

tff(c_22110,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_21989,c_22001]) ).

tff(c_22122,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_22110,c_21983]) ).

tff(c_22131,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_22122]) ).

tff(c_22123,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_22110,c_22110,c_21612]) ).

tff(c_22132,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_21589,c_22123]) ).

tff(c_22172,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22131,c_22132]) ).

tff(c_21927,plain,
    ! [X3_6,X4_7,X1_8,X2_9] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_21617]) ).

tff(c_22073,plain,
    ! [X2_9] :
      ( ( multiply(X2_9,sk_c5) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_21927]) ).

tff(c_22189,plain,
    ! [X2_359] :
      ( ( multiply(X2_359,identity) != identity )
      | ( inverse(X2_359) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22172,c_22172,c_22131,c_22073]) ).

tff(c_22211,plain,
    inverse(identity) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_2,c_22189]) ).

tff(c_22166,plain,
    inverse(sk_c4) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_22132,c_21484]) ).

tff(c_22213,plain,
    inverse(sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22131,c_22166]) ).

tff(c_22217,plain,
    multiply(inverse(identity),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_22213,c_22019]) ).

tff(c_22226,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_22217]) ).

tff(c_22228,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22226,c_22213]) ).

tff(c_22230,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22211,c_22228]) ).

tff(c_22231,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c5 )
      | ( multiply(X4_7,sk_c5) != sk_c7 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_21927]) ).

tff(c_22307,plain,
    ! [X1_8,X4_7,X3_6] :
      ( ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 )
      | ( inverse(X4_7) != identity )
      | ( multiply(X4_7,identity) != sk_c6 )
      | ( inverse(X3_6) != sk_c6 )
      | ( multiply(X3_6,sk_c6) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22268,c_22268,c_22289,c_22268,c_22289,c_22268,c_22268,c_22231]) ).

tff(c_22308,plain,
    ! [X3_6] :
      ( ( inverse(X3_6) != sk_c6 )
      | ( multiply(X3_6,sk_c6) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_22307]) ).

tff(c_22727,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22457,c_22319,c_22319,c_22319,c_22308]) ).

tff(c_22313,plain,
    inverse(sk_c4) = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_22301,c_21484]) ).

tff(c_22349,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22318,c_22318,c_22313]) ).

tff(c_22729,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22727,c_22349]) ).

tff(c_22730,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != identity )
      | ( multiply(X4_7,identity) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_22307]) ).

tff(c_34069,plain,
    ! [X4_7,X1_8] :
      ( ( inverse(X4_7) != identity )
      | ( identity != X4_7 )
      | ( identity != X1_8 )
      | ( inverse(X1_8) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22741,c_22923,c_22741,c_22741,c_22923,c_22741,c_22730]) ).

tff(c_34071,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_34069]) ).

tff(c_22735,plain,
    inverse(sk_c4) = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_22301,c_21484]) ).

tff(c_22774,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_22740,c_22740,c_22735]) ).

tff(c_34073,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34071,c_22774]) ).

tff(c_34075,plain,
    inverse(identity) != identity,
    inference(splitRight,[status(thm)],[c_34069]) ).

tff(c_34077,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34075,c_22774]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP274-1 : TPTP v8.1.2. Released v2.5.0.
% 0.08/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:52:45 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 13.87/4.48  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.99/4.54  
% 13.99/4.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.30/4.62  
% 14.30/4.62  Inference rules
% 14.30/4.62  ----------------------
% 14.30/4.62  #Ref     : 0
% 14.30/4.62  #Sup     : 8515
% 14.30/4.62  #Fact    : 0
% 14.30/4.62  #Define  : 0
% 14.30/4.62  #Split   : 55
% 14.30/4.62  #Chain   : 0
% 14.30/4.62  #Close   : 0
% 14.30/4.62  
% 14.30/4.62  Ordering : KBO
% 14.30/4.62  
% 14.30/4.62  Simplification rules
% 14.30/4.62  ----------------------
% 14.30/4.62  #Subsume      : 27
% 14.30/4.62  #Demod        : 18679
% 14.30/4.62  #Tautology    : 6702
% 14.30/4.62  #SimpNegUnit  : 78
% 14.30/4.62  #BackRed      : 851
% 14.30/4.62  
% 14.30/4.62  #Partial instantiations: 0
% 14.30/4.62  #Strategies tried      : 1
% 14.30/4.62  
% 14.30/4.62  Timing (in seconds)
% 14.30/4.62  ----------------------
% 14.43/4.63  Preprocessing        : 0.48
% 14.43/4.63  Parsing              : 0.20
% 14.43/4.63  CNF conversion       : 0.02
% 14.43/4.63  Main loop            : 2.96
% 14.43/4.63  Inferencing          : 0.95
% 14.43/4.63  Reduction            : 1.36
% 14.43/4.63  Demodulation         : 1.15
% 14.43/4.63  BG Simplification    : 0.11
% 14.43/4.63  Subsumption          : 0.33
% 14.43/4.63  Abstraction          : 0.18
% 14.43/4.63  MUC search           : 0.00
% 14.43/4.63  Cooper               : 0.00
% 14.43/4.63  Total                : 3.60
% 14.43/4.63  Index Insertion      : 0.00
% 14.43/4.63  Index Deletion       : 0.00
% 14.43/4.63  Index Matching       : 0.00
% 14.43/4.63  BG Taut test         : 0.00
%------------------------------------------------------------------------------