TSTP Solution File: GRP355-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP355-1 : 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 : n013.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 10:41:02 EDT 2023

% Result   : Unsatisfiable 15.26s 5.35s
% Output   : CNFRefutation 15.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  233 ( 163 unt;  11 typ;   0 def)
%            Number of atoms       :  339 ( 328 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  233 ( 116   ~; 117   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :  123 (; 123   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_104,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( inverse(sk_c4) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( inverse(sk_c3) = sk_c6 ) ),
    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_74,axiom,
    ( ( multiply(sk_c7,sk_c6) = sk_c8 )
    | ( inverse(sk_c3) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_155,axiom,
    ! [X5,X3,X1,X2,X4] :
      ( ( multiply(sk_c7,sk_c6) != sk_c8 )
      | ( multiply(X2,sk_c8) != sk_c7 )
      | ( inverse(X2) != sk_c8 )
      | ( multiply(X1,sk_c8) != sk_c7 )
      | ( inverse(X1) != sk_c8 )
      | ( multiply(X3,sk_c6) != sk_c7 )
      | ( inverse(X3) != sk_c6 )
      | ( multiply(sk_c8,X4) != sk_c6 )
      | ( multiply(X5,sk_c8) != X4 )
      | ( inverse(X5) != sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( inverse(sk_c3) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( multiply(sk_c8,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( inverse(sk_c2) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ( ( multiply(sk_c1,sk_c8) = sk_c7 )
    | ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ( ( multiply(sk_c7,sk_c6) = sk_c8 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ( ( multiply(sk_c7,sk_c6) = sk_c8 )
    | ( multiply(sk_c8,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ( ( multiply(sk_c7,sk_c6) = sk_c8 )
    | ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ( ( multiply(sk_c7,sk_c6) = sk_c8 )
    | ( inverse(sk_c4) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_119,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( multiply(sk_c8,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_125,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( inverse(sk_c4) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( inverse(sk_c2) = sk_c8 ) ),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_107,axiom,
    ( ( inverse(sk_c1) = sk_c8 )
    | ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
    file(unknown,unknown) ).

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

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

tff(c_34,plain,
    ( ( inverse(sk_c4) = sk_c8 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_83,plain,
    multiply(sk_c1,sk_c8) = sk_c7,
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_42,plain,
    ( ( inverse(sk_c3) = sk_c6 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_67,plain,
    inverse(sk_c1) = sk_c8,
    inference(splitLeft,[status(thm)],[c_42]) ).

tff(c_71,plain,
    multiply(sk_c8,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_67,c_4]) ).

tff(c_107,plain,
    ! [X_13,Y_14,Z_15] : ( multiply(multiply(X_13,Y_14),Z_15) = multiply(X_13,multiply(Y_14,Z_15)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_128,plain,
    ! [Z_15] : ( multiply(sk_c8,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_71,c_107]) ).

tff(c_142,plain,
    ! [Z_16] : ( multiply(sk_c8,multiply(sk_c1,Z_16)) = Z_16 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_128]) ).

tff(c_154,plain,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_83,c_142]) ).

tff(c_131,plain,
    ! [X_2,Z_15] : ( multiply(inverse(X_2),multiply(X_2,Z_15)) = multiply(identity,Z_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_107]) ).

tff(c_196,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_131]) ).

tff(c_214,plain,
    multiply(inverse(sk_c8),sk_c8) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_154,c_196]) ).

tff(c_242,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_214]) ).

tff(c_14,plain,
    ( ( inverse(sk_c3) = sk_c6 )
    | ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_82,plain,
    multiply(sk_c7,sk_c6) = sk_c8,
    inference(splitLeft,[status(thm)],[c_14]) ).

tff(c_247,plain,
    multiply(identity,sk_c6) = sk_c8,
    inference(demodulation,[status(thm),theory(equality)],[c_242,c_82]) ).

tff(c_248,plain,
    sk_c8 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_247]) ).

tff(c_5800,plain,
    inverse(sk_c1) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_67]) ).

tff(c_246,plain,
    multiply(sk_c1,sk_c8) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_242,c_83]) ).

tff(c_5815,plain,
    multiply(sk_c1,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_246]) ).

tff(c_257,plain,
    inverse(sk_c1) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_67]) ).

tff(c_140,plain,
    ! [X_2,Z_15] : ( multiply(inverse(X_2),multiply(X_2,Z_15)) = Z_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_131]) ).

tff(c_611,plain,
    ! [X_27,Z_28] : ( multiply(inverse(inverse(X_27)),Z_28) = multiply(X_27,Z_28) ),
    inference(superposition,[status(thm),theory(equality)],[c_140,c_196]) ).

tff(c_235,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_196]) ).

tff(c_625,plain,
    ! [X_27] : ( multiply(X_27,identity) = X_27 ),
    inference(superposition,[status(thm),theory(equality)],[c_611,c_235]) ).

tff(c_677,plain,
    ! [X_29] : ( multiply(X_29,identity) = X_29 ),
    inference(superposition,[status(thm),theory(equality)],[c_611,c_235]) ).

tff(c_139,plain,
    ! [Z_15] : ( multiply(sk_c8,multiply(sk_c1,Z_15)) = Z_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_128]) ).

tff(c_217,plain,
    ! [Z_15] : ( multiply(inverse(sk_c8),Z_15) = multiply(sk_c1,Z_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_139,c_196]) ).

tff(c_563,plain,
    ! [Z_15] : ( multiply(inverse(sk_c6),Z_15) = multiply(sk_c1,Z_15) ),
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_217]) ).

tff(c_688,plain,
    multiply(sk_c1,identity) = inverse(sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_677,c_563]) ).

tff(c_760,plain,
    inverse(sk_c6) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_625,c_688]) ).

tff(c_661,plain,
    ! [X_27,Z_15] : ( multiply(X_27,multiply(inverse(X_27),Z_15)) = Z_15 ),
    inference(superposition,[status(thm),theory(equality)],[c_140,c_611]) ).

tff(c_50,plain,
    ! [X5_6,X3_7,X1_8,X2_9] :
      ( ( inverse(X5_6) != sk_c8 )
      | ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c8 )
      | ( multiply(X1_8,sk_c8) != sk_c7 )
      | ( inverse(X2_9) != sk_c8 )
      | ( multiply(X2_9,sk_c8) != sk_c7 )
      | ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_159,plain,
    ! [X5_6,X3_7,X1_8,X2_9] :
      ( ( inverse(X5_6) != sk_c8 )
      | ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c8 )
      | ( multiply(X1_8,sk_c8) != sk_c7 )
      | ( inverse(X2_9) != sk_c8 )
      | ( multiply(X2_9,sk_c8) != sk_c7 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_50]) ).

tff(c_168,plain,
    ! [X2_17] :
      ( ( inverse(X2_17) != sk_c8 )
      | ( multiply(X2_17,sk_c8) != sk_c7 ) ),
    inference(splitLeft,[status(thm)],[c_159]) ).

tff(c_175,plain,
    inverse(sk_c1) != sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_83,c_168]) ).

tff(c_187,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_67,c_175]) ).

tff(c_188,plain,
    ! [X1_8,X3_7,X5_6] :
      ( ( inverse(X1_8) != sk_c8 )
      | ( multiply(X1_8,sk_c8) != sk_c7 )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != sk_c7 )
      | ( inverse(X5_6) != sk_c8 )
      | ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_159]) ).

tff(c_253,plain,
    ! [X1_8,X3_7,X5_6] :
      ( ( inverse(X1_8) != sk_c8 )
      | ( multiply(X1_8,sk_c8) != identity )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity )
      | ( inverse(X5_6) != sk_c8 )
      | ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_242,c_242,c_188]) ).

tff(c_254,plain,
    ! [X5_6] :
      ( ( inverse(X5_6) != sk_c8 )
      | ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_253]) ).

tff(c_5734,plain,
    ! [X5_81] :
      ( ( inverse(X5_81) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_81,sk_c6)) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_248,c_248,c_254]) ).

tff(c_5767,plain,
    inverse(inverse(sk_c6)) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_661,c_5734]) ).

tff(c_5796,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_257,c_760,c_5767]) ).

tff(c_5797,plain,
    ! [X3_7,X1_8] :
      ( ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity )
      | ( inverse(X1_8) != sk_c8 )
      | ( multiply(X1_8,sk_c8) != identity ) ),
    inference(splitRight,[status(thm)],[c_253]) ).

tff(c_29484,plain,
    ! [X3_7,X1_8] :
      ( ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity )
      | ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_248,c_248,c_5797]) ).

tff(c_29486,plain,
    ! [X1_226] :
      ( ( inverse(X1_226) != sk_c6 )
      | ( multiply(X1_226,sk_c6) != identity ) ),
    inference(splitLeft,[status(thm)],[c_29484]) ).

tff(c_29538,plain,
    inverse(sk_c1) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5815,c_29486]) ).

tff(c_29564,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5800,c_29538]) ).

tff(c_29566,plain,
    ! [X3_227] :
      ( ( inverse(X3_227) != sk_c6 )
      | ( multiply(X3_227,sk_c6) != identity ) ),
    inference(splitRight,[status(thm)],[c_29484]) ).

tff(c_29618,plain,
    inverse(sk_c1) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_5815,c_29566]) ).

tff(c_29644,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5800,c_29618]) ).

tff(c_29646,plain,
    multiply(sk_c1,sk_c8) != sk_c7,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_28,plain,
    ( ( inverse(sk_c3) = sk_c6 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_29665,plain,
    inverse(sk_c3) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_28]) ).

tff(c_26,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_29709,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_26]) ).

tff(c_29715,plain,
    ! [X_228,Y_229,Z_230] : ( multiply(multiply(X_228,Y_229),Z_230) = multiply(X_228,multiply(Y_229,Z_230)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_29757,plain,
    ! [X_2,Z_230] : ( multiply(inverse(X_2),multiply(X_2,Z_230)) = multiply(identity,Z_230) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_29715]) ).

tff(c_30041,plain,
    ! [X_237,Z_238] : ( multiply(inverse(X_237),multiply(X_237,Z_238)) = Z_238 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_29757]) ).

tff(c_30080,plain,
    multiply(inverse(sk_c3),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_29709,c_30041]) ).

tff(c_30098,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29665,c_30080]) ).

tff(c_29769,plain,
    ! [X_2,Z_230] : ( multiply(inverse(X_2),multiply(X_2,Z_230)) = Z_230 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_29757]) ).

tff(c_30108,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_30098,c_29769]) ).

tff(c_30117,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30108]) ).

tff(c_30,plain,
    ( ( multiply(sk_c8,sk_c5) = sk_c6 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_29691,plain,
    multiply(sk_c8,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_30]) ).

tff(c_32,plain,
    ( ( multiply(sk_c4,sk_c8) = sk_c5 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_29698,plain,
    multiply(sk_c4,sk_c8) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_32]) ).

tff(c_29645,plain,
    inverse(sk_c4) = sk_c8,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_29650,plain,
    multiply(sk_c8,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_29645,c_4]) ).

tff(c_29748,plain,
    ! [Z_230] : ( multiply(sk_c8,multiply(sk_c4,Z_230)) = multiply(identity,Z_230) ),
    inference(superposition,[status(thm),theory(equality)],[c_29650,c_29715]) ).

tff(c_29807,plain,
    ! [Z_233] : ( multiply(sk_c8,multiply(sk_c4,Z_233)) = Z_233 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_29748]) ).

tff(c_29819,plain,
    multiply(sk_c8,sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_29698,c_29807]) ).

tff(c_29823,plain,
    sk_c8 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29691,c_29819]) ).

tff(c_29834,plain,
    multiply(sk_c1,sk_c6) != sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_29823,c_29646]) ).

tff(c_30222,plain,
    multiply(sk_c1,sk_c6) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30117,c_29834]) ).

tff(c_29837,plain,
    multiply(sk_c6,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29823,c_71]) ).

tff(c_29830,plain,
    multiply(sk_c6,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29823,c_29691]) ).

tff(c_30059,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_29830,c_30041]) ).

tff(c_30096,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30059]) ).

tff(c_29736,plain,
    ! [Z_230] : ( multiply(sk_c4,multiply(sk_c8,Z_230)) = multiply(sk_c5,Z_230) ),
    inference(superposition,[status(thm),theory(equality)],[c_29698,c_29715]) ).

tff(c_30178,plain,
    ! [Z_230] : ( multiply(sk_c4,multiply(sk_c6,Z_230)) = Z_230 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30096,c_29823,c_29736]) ).

tff(c_30211,plain,
    multiply(sk_c4,identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_29837,c_30178]) ).

tff(c_24,plain,
    ( ( inverse(sk_c2) = sk_c8 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_29679,plain,
    inverse(sk_c2) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_24]) ).

tff(c_29683,plain,
    multiply(sk_c8,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_29679,c_4]) ).

tff(c_29831,plain,
    multiply(sk_c6,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29823,c_29683]) ).

tff(c_30179,plain,
    ! [Z_239] : ( multiply(sk_c4,multiply(sk_c6,Z_239)) = Z_239 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30096,c_29823,c_29736]) ).

tff(c_30194,plain,
    multiply(sk_c4,identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_29831,c_30179]) ).

tff(c_30306,plain,
    sk_c2 = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_30211,c_30194]) ).

tff(c_22,plain,
    ( ( multiply(sk_c2,sk_c8) = sk_c7 )
    | ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_29703,plain,
    multiply(sk_c2,sk_c8) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_29646,c_22]) ).

tff(c_29828,plain,
    multiply(sk_c2,sk_c6) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_29823,c_29703]) ).

tff(c_30139,plain,
    multiply(sk_c2,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30117,c_29828]) ).

tff(c_30308,plain,
    multiply(sk_c1,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30306,c_30139]) ).

tff(c_30312,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30222,c_30308]) ).

tff(c_30313,plain,
    inverse(sk_c3) = sk_c6,
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_30314,plain,
    multiply(sk_c7,sk_c6) != sk_c8,
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_12,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_30372,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_30314,c_12]) ).

tff(c_30384,plain,
    ! [X_241,Y_242,Z_243] : ( multiply(multiply(X_241,Y_242),Z_243) = multiply(X_241,multiply(Y_242,Z_243)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_30426,plain,
    ! [X_2,Z_243] : ( multiply(inverse(X_2),multiply(X_2,Z_243)) = multiply(identity,Z_243) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_30384]) ).

tff(c_30519,plain,
    ! [X_246,Z_247] : ( multiply(inverse(X_246),multiply(X_246,Z_247)) = Z_247 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30426]) ).

tff(c_30549,plain,
    multiply(inverse(sk_c3),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_30372,c_30519]) ).

tff(c_30565,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30313,c_30549]) ).

tff(c_30438,plain,
    ! [X_2,Z_243] : ( multiply(inverse(X_2),multiply(X_2,Z_243)) = Z_243 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30426]) ).

tff(c_30569,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_30565,c_30438]) ).

tff(c_30575,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30569]) ).

tff(c_16,plain,
    ( ( multiply(sk_c8,sk_c5) = sk_c6 )
    | ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_30360,plain,
    multiply(sk_c8,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_30314,c_16]) ).

tff(c_18,plain,
    ( ( multiply(sk_c4,sk_c8) = sk_c5 )
    | ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_30366,plain,
    multiply(sk_c4,sk_c8) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_30314,c_18]) ).

tff(c_20,plain,
    ( ( inverse(sk_c4) = sk_c8 )
    | ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_30331,plain,
    inverse(sk_c4) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_30314,c_20]) ).

tff(c_30335,plain,
    multiply(sk_c8,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30331,c_4]) ).

tff(c_30414,plain,
    ! [Z_243] : ( multiply(sk_c8,multiply(sk_c4,Z_243)) = multiply(identity,Z_243) ),
    inference(superposition,[status(thm),theory(equality)],[c_30335,c_30384]) ).

tff(c_30463,plain,
    ! [Z_245] : ( multiply(sk_c8,multiply(sk_c4,Z_245)) = Z_245 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30414]) ).

tff(c_30475,plain,
    multiply(sk_c8,sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_30366,c_30463]) ).

tff(c_30479,plain,
    sk_c8 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30360,c_30475]) ).

tff(c_30491,plain,
    multiply(sk_c7,sk_c6) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30479,c_30314]) ).

tff(c_30641,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30575,c_30491]) ).

tff(c_30643,plain,
    inverse(sk_c1) != sk_c8,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_44,plain,
    ( ( multiply(sk_c8,sk_c5) = sk_c6 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_30689,plain,
    multiply(sk_c8,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_44]) ).

tff(c_46,plain,
    ( ( multiply(sk_c4,sk_c8) = sk_c5 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_30683,plain,
    multiply(sk_c4,sk_c8) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_46]) ).

tff(c_48,plain,
    ( ( inverse(sk_c4) = sk_c8 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_30667,plain,
    inverse(sk_c4) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_48]) ).

tff(c_30671,plain,
    multiply(sk_c8,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30667,c_4]) ).

tff(c_30713,plain,
    ! [X_248,Y_249,Z_250] : ( multiply(multiply(X_248,Y_249),Z_250) = multiply(X_248,multiply(Y_249,Z_250)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_30740,plain,
    ! [Z_250] : ( multiply(sk_c8,multiply(sk_c4,Z_250)) = multiply(identity,Z_250) ),
    inference(superposition,[status(thm),theory(equality)],[c_30671,c_30713]) ).

tff(c_30762,plain,
    ! [Z_251] : ( multiply(sk_c8,multiply(sk_c4,Z_251)) = Z_251 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30740]) ).

tff(c_30774,plain,
    multiply(sk_c8,sk_c5) = sk_c8,
    inference(superposition,[status(thm),theory(equality)],[c_30683,c_30762]) ).

tff(c_30778,plain,
    sk_c8 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30689,c_30774]) ).

tff(c_38,plain,
    ( ( inverse(sk_c2) = sk_c8 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_30655,plain,
    inverse(sk_c2) = sk_c8,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_38]) ).

tff(c_30786,plain,
    inverse(sk_c2) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30778,c_30655]) ).

tff(c_30642,plain,
    inverse(sk_c3) = sk_c6,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_40,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_30694,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_40]) ).

tff(c_30749,plain,
    ! [X_2,Z_250] : ( multiply(inverse(X_2),multiply(X_2,Z_250)) = multiply(identity,Z_250) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_30713]) ).

tff(c_30993,plain,
    ! [X_255,Z_256] : ( multiply(inverse(X_255),multiply(X_255,Z_256)) = Z_256 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30749]) ).

tff(c_31035,plain,
    multiply(inverse(sk_c3),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_30694,c_30993]) ).

tff(c_31053,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30642,c_31035]) ).

tff(c_30760,plain,
    ! [X_2,Z_250] : ( multiply(inverse(X_2),multiply(X_2,Z_250)) = Z_250 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30749]) ).

tff(c_31062,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_31053,c_30760]) ).

tff(c_31068,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_31062]) ).

tff(c_36,plain,
    ( ( multiply(sk_c2,sk_c8) = sk_c7 )
    | ( inverse(sk_c1) = sk_c8 ) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_30700,plain,
    multiply(sk_c2,sk_c8) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_30643,c_36]) ).

tff(c_30780,plain,
    multiply(sk_c2,sk_c6) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_30778,c_30700]) ).

tff(c_31071,plain,
    multiply(sk_c2,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_31068,c_30780]) ).

tff(c_31429,plain,
    ! [X_263,Z_264] : ( multiply(inverse(inverse(X_263)),Z_264) = multiply(X_263,Z_264) ),
    inference(superposition,[status(thm),theory(equality)],[c_30993,c_30760]) ).

tff(c_31044,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_30993]) ).

tff(c_31477,plain,
    ! [X_265] : ( multiply(X_265,identity) = X_265 ),
    inference(superposition,[status(thm),theory(equality)],[c_31429,c_31044]) ).

tff(c_30802,plain,
    multiply(sk_c6,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30786,c_4]) ).

tff(c_30781,plain,
    multiply(sk_c6,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30778,c_30689]) ).

tff(c_31017,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_30781,c_30993]) ).

tff(c_31052,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_31017]) ).

tff(c_30737,plain,
    ! [Z_250] : ( multiply(sk_c4,multiply(sk_c8,Z_250)) = multiply(sk_c5,Z_250) ),
    inference(superposition,[status(thm),theory(equality)],[c_30683,c_30713]) ).

tff(c_31131,plain,
    ! [Z_257] : ( multiply(sk_c4,multiply(sk_c6,Z_257)) = Z_257 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_31052,c_30778,c_30737]) ).

tff(c_31152,plain,
    multiply(sk_c4,identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_30802,c_31131]) ).

tff(c_30783,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_30778,c_30671]) ).

tff(c_31149,plain,
    multiply(sk_c4,identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_30783,c_31131]) ).

tff(c_31211,plain,
    sk_c4 = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_31152,c_31149]) ).

tff(c_31224,plain,
    multiply(sk_c2,identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_31211,c_31152]) ).

tff(c_30647,plain,
    multiply(sk_c6,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_30642,c_4]) ).

tff(c_31155,plain,
    multiply(sk_c4,identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_30647,c_31131]) ).

tff(c_31249,plain,
    sk_c3 = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_31224,c_31211,c_31155]) ).

tff(c_31038,plain,
    multiply(inverse(sk_c6),identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_30647,c_30993]) ).

tff(c_31261,plain,
    multiply(inverse(sk_c6),identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_31249,c_31038]) ).

tff(c_31498,plain,
    inverse(sk_c6) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_31477,c_31261]) ).

tff(c_31463,plain,
    ! [X_263,Z_250] : ( multiply(X_263,multiply(inverse(X_263),Z_250)) = Z_250 ),
    inference(superposition,[status(thm),theory(equality)],[c_30760,c_31429]) ).

tff(c_30863,plain,
    ! [X_253,Z_254] : ( multiply(inverse(X_253),multiply(X_253,Z_254)) = Z_254 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30749]) ).

tff(c_30908,plain,
    multiply(inverse(sk_c3),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_30694,c_30863]) ).

tff(c_30927,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30642,c_30908]) ).

tff(c_30938,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_30927,c_30760]) ).

tff(c_30944,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30938]) ).

tff(c_30806,plain,
    ! [X5_6,X3_7,X1_8,X2_9] :
      ( ( inverse(X5_6) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X2_9,sk_c6) != sk_c7 )
      | ( multiply(sk_c7,sk_c6) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30778,c_30778,c_30778,c_30778,c_30778,c_30778,c_30778,c_30778,c_50]) ).

tff(c_30807,plain,
    multiply(sk_c7,sk_c6) != sk_c6,
    inference(splitLeft,[status(thm)],[c_30806]) ).

tff(c_30947,plain,
    multiply(identity,sk_c6) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_30944,c_30807]) ).

tff(c_30952,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_30947]) ).

tff(c_30953,plain,
    ! [X2_9,X1_8,X3_7,X5_6] :
      ( ( inverse(X2_9) != sk_c6 )
      | ( multiply(X2_9,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != sk_c7 )
      | ( inverse(X5_6) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_30806]) ).

tff(c_38036,plain,
    ! [X2_9,X1_8,X3_7,X5_6] :
      ( ( inverse(X2_9) != sk_c6 )
      | ( multiply(X2_9,sk_c6) != identity )
      | ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != identity )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity )
      | ( inverse(X5_6) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_31068,c_31068,c_31068,c_30953]) ).

tff(c_38038,plain,
    ! [X5_330] :
      ( ( inverse(X5_330) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_330,sk_c6)) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_38036]) ).

tff(c_38067,plain,
    inverse(inverse(sk_c6)) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_31463,c_38038]) ).

tff(c_38095,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30786,c_31498,c_38067]) ).

tff(c_38096,plain,
    ! [X3_7,X1_8,X2_9] :
      ( ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity )
      | ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != identity )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X2_9,sk_c6) != identity ) ),
    inference(splitRight,[status(thm)],[c_38036]) ).

tff(c_39213,plain,
    ! [X2_338] :
      ( ( inverse(X2_338) != sk_c6 )
      | ( multiply(X2_338,sk_c6) != identity ) ),
    inference(splitLeft,[status(thm)],[c_38096]) ).

tff(c_39241,plain,
    inverse(sk_c2) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_31071,c_39213]) ).

tff(c_39262,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30786,c_39241]) ).

tff(c_39263,plain,
    ! [X1_8,X3_7] :
      ( ( inverse(X1_8) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != identity )
      | ( inverse(X3_7) != sk_c6 )
      | ( multiply(X3_7,sk_c6) != identity ) ),
    inference(splitRight,[status(thm)],[c_38096]) ).

tff(c_41655,plain,
    ! [X3_352] :
      ( ( inverse(X3_352) != sk_c6 )
      | ( multiply(X3_352,sk_c6) != identity ) ),
    inference(splitLeft,[status(thm)],[c_39263]) ).

tff(c_41687,plain,
    inverse(sk_c2) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_31071,c_41655]) ).

tff(c_41709,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30786,c_41687]) ).

tff(c_41711,plain,
    ! [X1_353] :
      ( ( inverse(X1_353) != sk_c6 )
      | ( multiply(X1_353,sk_c6) != identity ) ),
    inference(splitRight,[status(thm)],[c_39263]) ).

tff(c_41743,plain,
    inverse(sk_c2) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_31071,c_41711]) ).

tff(c_41765,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_30786,c_41743]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : GRP355-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.14  % 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
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 21:50:32 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 15.26/5.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.26/5.37  
% 15.26/5.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.26/5.42  
% 15.26/5.42  Inference rules
% 15.26/5.42  ----------------------
% 15.26/5.42  #Ref     : 0
% 15.26/5.42  #Sup     : 10049
% 15.26/5.42  #Fact    : 0
% 15.26/5.42  #Define  : 0
% 15.26/5.42  #Split   : 12
% 15.26/5.42  #Chain   : 0
% 15.26/5.42  #Close   : 0
% 15.26/5.42  
% 15.26/5.42  Ordering : KBO
% 15.26/5.42  
% 15.26/5.42  Simplification rules
% 15.26/5.42  ----------------------
% 15.26/5.42  #Subsume      : 3
% 15.26/5.42  #Demod        : 23310
% 15.26/5.42  #Tautology    : 7732
% 15.26/5.42  #SimpNegUnit  : 19
% 15.26/5.42  #BackRed      : 119
% 15.26/5.42  
% 15.26/5.42  #Partial instantiations: 0
% 15.26/5.42  #Strategies tried      : 1
% 15.26/5.42  
% 15.26/5.42  Timing (in seconds)
% 15.26/5.42  ----------------------
% 15.26/5.42  Preprocessing        : 0.50
% 15.26/5.42  Parsing              : 0.21
% 15.26/5.42  CNF conversion       : 0.03
% 15.26/5.42  Main loop            : 3.82
% 15.26/5.42  Inferencing          : 0.94
% 15.26/5.42  Reduction            : 2.13
% 15.26/5.42  Demodulation         : 1.95
% 15.26/5.42  BG Simplification    : 0.09
% 15.26/5.42  Subsumption          : 0.45
% 15.26/5.42  Abstraction          : 0.17
% 15.26/5.42  MUC search           : 0.00
% 15.26/5.42  Cooper               : 0.00
% 15.26/5.42  Total                : 4.40
% 15.26/5.42  Index Insertion      : 0.00
% 15.26/5.42  Index Deletion       : 0.00
% 15.26/5.42  Index Matching       : 0.00
% 15.26/5.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------