TSTP Solution File: GRP315-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP315-1 : 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 : n021.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 10:40:53 EDT 2023

% Result   : Unsatisfiable 12.03s 4.37s
% Output   : CNFRefutation 12.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  483 ( 392 unt;  10 typ;   0 def)
%            Number of atoms       :  608 ( 572 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  345 ( 210   ~; 135   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  178 (; 178   !;   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_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_60,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_63,axiom,
    multiply(sk_c6,sk_c7) = sk_c5,
    file(unknown,unknown) ).

tff(f_138,axiom,
    ! [X3,X4,X1,X2] :
      ( ( multiply(sk_c6,sk_c7) != sk_c5 )
      | ( multiply(X3,sk_c7) != sk_c6 )
      | ( inverse(X3) != sk_c7 )
      | ( multiply(X4,sk_c6) != sk_c5 )
      | ( inverse(X4) != sk_c6 )
      | ( 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_72,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_84,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_96,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c5 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_99,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c5 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c5 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_93,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c5 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_81,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_87,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_111,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_108,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( inverse(sk_c4) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_105,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( multiply(sk_c3,sk_c6) = 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_28677,plain,
    ! [X_311,Y_312,Z_313] : ( multiply(multiply(X_311,Y_312),Z_313) = multiply(X_311,multiply(Y_312,Z_313)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_28707,plain,
    ! [X_2,Z_313] : ( multiply(inverse(X_2),multiply(X_2,Z_313)) = multiply(identity,Z_313) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_28677]) ).

tff(c_29316,plain,
    ! [X_327,Z_328] : ( multiply(inverse(X_327),multiply(X_327,Z_328)) = Z_328 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28707]) ).

tff(c_29379,plain,
    ! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_29316]) ).

tff(c_8,plain,
    multiply(sk_c6,sk_c7) = sk_c5,
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_42,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_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 )
      | ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_44,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_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_42]) ).

tff(c_26212,plain,
    ! [X3_263] :
      ( ( inverse(X3_263) != sk_c7 )
      | ( multiply(X3_263,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_44]) ).

tff(c_26226,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_26212]) ).

tff(c_26237,plain,
    sk_c6 != identity,
    inference(splitLeft,[status(thm)],[c_26226]) ).

tff(c_14,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_91,plain,
    multiply(sk_c1,sk_c7) = sk_c6,
    inference(splitLeft,[status(thm)],[c_14]) ).

tff(c_22,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_73,plain,
    inverse(sk_c1) = sk_c7,
    inference(splitLeft,[status(thm)],[c_22]) ).

tff(c_77,plain,
    multiply(sk_c7,sk_c1) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_73,c_4]) ).

tff(c_111,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_132,plain,
    ! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_77,c_111]) ).

tff(c_153,plain,
    ! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_132]) ).

tff(c_165,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_91,c_153]) ).

tff(c_138,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_111]) ).

tff(c_237,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_138]) ).

tff(c_270,plain,
    multiply(inverse(sk_c7),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_165,c_237]) ).

tff(c_309,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_270]) ).

tff(c_151,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_138]) ).

tff(c_950,plain,
    ! [X_32,Z_33] : ( multiply(inverse(inverse(X_32)),Z_33) = multiply(X_32,Z_33) ),
    inference(superposition,[status(thm),theory(equality)],[c_237,c_151]) ).

tff(c_297,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_237]) ).

tff(c_957,plain,
    ! [X_32] : ( multiply(X_32,identity) = X_32 ),
    inference(superposition,[status(thm),theory(equality)],[c_950,c_297]) ).

tff(c_30,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_96,plain,
    multiply(sk_c2,sk_c6) = sk_c5,
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_34,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_65,plain,
    inverse(sk_c2) = sk_c6,
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_69,plain,
    multiply(sk_c6,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).

tff(c_135,plain,
    ! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_69,c_111]) ).

tff(c_176,plain,
    ! [Z_16] : ( multiply(sk_c6,multiply(sk_c2,Z_16)) = Z_16 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_135]) ).

tff(c_188,plain,
    multiply(sk_c6,sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_96,c_176]) ).

tff(c_261,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_188,c_237]) ).

tff(c_308,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_261]) ).

tff(c_319,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_8]) ).

tff(c_807,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_309,c_319]) ).

tff(c_495,plain,
    ! [X_22,Z_23] : ( multiply(inverse(inverse(X_22)),Z_23) = multiply(X_22,Z_23) ),
    inference(superposition,[status(thm),theory(equality)],[c_151,c_237]) ).

tff(c_502,plain,
    ! [X_22] : ( multiply(X_22,identity) = X_22 ),
    inference(superposition,[status(thm),theory(equality)],[c_495,c_297]) ).

tff(c_348,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_309,c_319]) ).

tff(c_326,plain,
    ! [X2_9,X1_8,X4_7,X3_6] :
      ( ( multiply(X2_9,identity) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != identity )
      | ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_308,c_44]) ).

tff(c_327,plain,
    ! [X3_6] :
      ( ( inverse(X3_6) != sk_c7 )
      | ( multiply(X3_6,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_326]) ).

tff(c_765,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_502,c_348,c_309,c_348,c_327]) ).

tff(c_192,plain,
    ! [Z_17] : ( multiply(sk_c6,multiply(sk_c7,Z_17)) = multiply(sk_c5,Z_17) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_111]) ).

tff(c_210,plain,
    multiply(sk_c6,identity) = multiply(sk_c5,sk_c1),
    inference(superposition,[status(thm),theory(equality)],[c_77,c_192]) ).

tff(c_314,plain,
    multiply(sk_c6,identity) = multiply(identity,sk_c1),
    inference(demodulation,[status(thm),theory(equality)],[c_308,c_210]) ).

tff(c_320,plain,
    multiply(sk_c6,identity) = sk_c1,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_314]) ).

tff(c_413,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_309,c_320]) ).

tff(c_351,plain,
    inverse(sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_348,c_73]) ).

tff(c_415,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_351]) ).

tff(c_767,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_765,c_415]) ).

tff(c_768,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != identity )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( multiply(X2_9,identity) != sk_c6 )
      | ( inverse(X2_9) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_326]) ).

tff(c_22045,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != identity )
      | ( identity != X4_7 )
      | ( identity != X1_8 )
      | ( inverse(X1_8) != identity )
      | ( identity != X2_9 )
      | ( inverse(X2_9) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_957,c_309,c_807,c_957,c_807,c_309,c_957,c_309,c_309,c_768]) ).

tff(c_22047,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_22045]) ).

tff(c_773,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_65]) ).

tff(c_785,plain,
    multiply(identity,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_773,c_4]) ).

tff(c_829,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_785,c_151]) ).

tff(c_841,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_829]) ).

tff(c_846,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_841,c_773]) ).

tff(c_22049,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22047,c_846]) ).

tff(c_22050,plain,
    ! [X1_8,X4_7] :
      ( ( identity != X1_8 )
      | ( inverse(X1_8) != identity )
      | ( inverse(X4_7) != identity )
      | ( identity != X4_7 ) ),
    inference(splitRight,[status(thm)],[c_22045]) ).

tff(c_22052,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_22050]) ).

tff(c_22054,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22052,c_846]) ).

tff(c_22996,plain,
    inverse(identity) != identity,
    inference(splitRight,[status(thm)],[c_22050]) ).

tff(c_22998,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22996,c_846]) ).

tff(c_23000,plain,
    multiply(sk_c2,sk_c6) != sk_c5,
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_32,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_23036,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_23000,c_32]) ).

tff(c_22999,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_23004,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_22999,c_4]) ).

tff(c_23041,plain,
    ! [X_196,Y_197,Z_198] : ( multiply(multiply(X_196,Y_197),Z_198) = multiply(X_196,multiply(Y_197,Z_198)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_23065,plain,
    ! [Z_198] : ( multiply(sk_c6,multiply(sk_c4,Z_198)) = multiply(identity,Z_198) ),
    inference(superposition,[status(thm),theory(equality)],[c_23004,c_23041]) ).

tff(c_23901,plain,
    ! [Z_214] : ( multiply(sk_c6,multiply(sk_c4,Z_214)) = Z_214 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_23065]) ).

tff(c_23913,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_23036,c_23901]) ).

tff(c_23071,plain,
    ! [Z_198] : ( multiply(sk_c7,multiply(sk_c1,Z_198)) = multiply(identity,Z_198) ),
    inference(superposition,[status(thm),theory(equality)],[c_77,c_23041]) ).

tff(c_23094,plain,
    ! [Z_199] : ( multiply(sk_c7,multiply(sk_c1,Z_199)) = Z_199 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_23071]) ).

tff(c_23106,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_91,c_23094]) ).

tff(c_23924,plain,
    ! [Z_215] : ( multiply(sk_c1,multiply(sk_c7,Z_215)) = multiply(sk_c6,Z_215) ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_23041]) ).

tff(c_23945,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_23106,c_23924]) ).

tff(c_23959,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_23913,c_91,c_23945]) ).

tff(c_23130,plain,
    ! [Z_201] : ( multiply(sk_c6,multiply(sk_c7,Z_201)) = multiply(sk_c5,Z_201) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_23041]) ).

tff(c_23142,plain,
    multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_23106,c_23130]) ).

tff(c_23155,plain,
    multiply(sk_c5,sk_c6) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_23142]) ).

tff(c_23965,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_23959,c_23155]) ).

tff(c_23077,plain,
    ! [X_2,Z_198] : ( multiply(inverse(X_2),multiply(X_2,Z_198)) = multiply(identity,Z_198) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_23041]) ).

tff(c_24068,plain,
    ! [X_216,Z_217] : ( multiply(inverse(X_216),multiply(X_216,Z_217)) = Z_217 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_23077]) ).

tff(c_24104,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_23965,c_24068]) ).

tff(c_24151,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_24104]) ).

tff(c_23976,plain,
    inverse(sk_c2) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_23959,c_65]) ).

tff(c_23992,plain,
    multiply(sk_c5,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_23976,c_4]) ).

tff(c_24196,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24151,c_23992]) ).

tff(c_23972,plain,
    multiply(sk_c2,sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_23959,c_23000]) ).

tff(c_24186,plain,
    multiply(sk_c2,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_24151,c_24151,c_23972]) ).

tff(c_24309,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24196,c_24186]) ).

tff(c_24311,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_75]) ).

tff(c_26027,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_24311,c_16]) ).

tff(c_24310,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_24315,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_24310,c_4]) ).

tff(c_26036,plain,
    ! [X_255,Y_256,Z_257] : ( multiply(multiply(X_255,Y_256),Z_257) = multiply(X_255,multiply(Y_256,Z_257)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_26060,plain,
    ! [Z_257] : ( multiply(sk_c6,multiply(sk_c4,Z_257)) = multiply(identity,Z_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_24315,c_26036]) ).

tff(c_26112,plain,
    ! [Z_260] : ( multiply(sk_c6,multiply(sk_c4,Z_260)) = Z_260 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26060]) ).

tff(c_26124,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_26027,c_26112]) ).

tff(c_10,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_24332,plain,
    inverse(sk_c3) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_24311,c_10]) ).

tff(c_12,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_24351,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_24311,c_12]) ).

tff(c_26,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_24327,plain,
    multiply(sk_c2,sk_c6) = sk_c5,
    inference(splitLeft,[status(thm)],[c_26]) ).

tff(c_24345,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_24311,c_16]) ).

tff(c_24357,plain,
    ! [X_219,Y_220,Z_221] : ( multiply(multiply(X_219,Y_220),Z_221) = multiply(X_219,multiply(Y_220,Z_221)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_24384,plain,
    ! [Z_221] : ( multiply(sk_c6,multiply(sk_c4,Z_221)) = multiply(identity,Z_221) ),
    inference(superposition,[status(thm),theory(equality)],[c_24315,c_24357]) ).

tff(c_24486,plain,
    ! [Z_225] : ( multiply(sk_c6,multiply(sk_c4,Z_225)) = Z_225 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24384]) ).

tff(c_24498,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_24345,c_24486]) ).

tff(c_24528,plain,
    ! [X3_227] :
      ( ( inverse(X3_227) != sk_c7 )
      | ( multiply(X3_227,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_44]) ).

tff(c_24536,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_24528]) ).

tff(c_24571,plain,
    sk_c6 != identity,
    inference(splitLeft,[status(thm)],[c_24536]) ).

tff(c_24336,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_24332,c_4]) ).

tff(c_24378,plain,
    ! [Z_221] : ( multiply(sk_c7,multiply(sk_c3,Z_221)) = multiply(identity,Z_221) ),
    inference(superposition,[status(thm),theory(equality)],[c_24336,c_24357]) ).

tff(c_24509,plain,
    ! [Z_226] : ( multiply(sk_c7,multiply(sk_c3,Z_226)) = Z_226 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24378]) ).

tff(c_24524,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_24351,c_24509]) ).

tff(c_24399,plain,
    ! [Z_221] : ( multiply(sk_c6,multiply(sk_c7,Z_221)) = multiply(sk_c5,Z_221) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_24357]) ).

tff(c_24550,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_24524,c_24399]) ).

tff(c_24557,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_24498,c_24550]) ).

tff(c_24393,plain,
    ! [X_2,Z_221] : ( multiply(inverse(X_2),multiply(X_2,Z_221)) = multiply(identity,Z_221) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_24357]) ).

tff(c_24572,plain,
    ! [X_228,Z_229] : ( multiply(inverse(X_228),multiply(X_228,Z_229)) = Z_229 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24393]) ).

tff(c_24590,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_24557,c_24572]) ).

tff(c_24669,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_24590]) ).

tff(c_24723,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_24669,c_24669,c_24524]) ).

tff(c_24729,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24723]) ).

tff(c_24731,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24571,c_24729]) ).

tff(c_24733,plain,
    sk_c6 = identity,
    inference(splitRight,[status(thm)],[c_24536]) ).

tff(c_24543,plain,
    ( ( inverse(sk_c6) != sk_c7 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_24528]) ).

tff(c_24570,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_24543]) ).

tff(c_24734,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_24733,c_24570]) ).

tff(c_24738,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_24733,c_24733,c_24498]) ).

tff(c_24753,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24738]) ).

tff(c_24759,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24734,c_24753]) ).

tff(c_24761,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_24543]) ).

tff(c_24849,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24761,c_24536]) ).

tff(c_24850,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_24849]) ).

tff(c_24765,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_24761,c_24761,c_24498]) ).

tff(c_24862,plain,
    ! [X_230,Z_231] : ( multiply(inverse(X_230),multiply(X_230,Z_231)) = Z_231 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24393]) ).

tff(c_24880,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_24765,c_24862]) ).

tff(c_24941,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_24880]) ).

tff(c_24943,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24850,c_24941]) ).

tff(c_24945,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_24849]) ).

tff(c_24540,plain,
    ( ( inverse(identity) != sk_c7 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_24528]) ).

tff(c_24569,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_24540]) ).

tff(c_24762,plain,
    sk_c7 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_24761,c_24569]) ).

tff(c_24956,plain,
    sk_c7 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_24945,c_24762]) ).

tff(c_24958,plain,
    multiply(identity,sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_24945,c_24945,c_24557]) ).

tff(c_24408,plain,
    ! [X_2,Z_221] : ( multiply(inverse(X_2),multiply(X_2,Z_221)) = Z_221 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24393]) ).

tff(c_25215,plain,
    multiply(inverse(identity),identity) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_24958,c_24408]) ).

tff(c_25229,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_25215]) ).

tff(c_25231,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24956,c_25229]) ).

tff(c_25233,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_24540]) ).

tff(c_25236,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_25233,c_25233,c_24524]) ).

tff(c_25248,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_24498,c_25236]) ).

tff(c_25254,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_25248,c_25233]) ).

tff(c_25377,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25248,c_25254,c_25254,c_24536]) ).

tff(c_25378,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_25377]) ).

tff(c_25255,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_25248,c_25248,c_24498]) ).

tff(c_25442,plain,
    ! [X_239,Z_240] : ( multiply(inverse(X_239),multiply(X_239,Z_240)) = Z_240 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_24393]) ).

tff(c_25466,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_25255,c_25442]) ).

tff(c_25507,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_25466]) ).

tff(c_25509,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_25378,c_25507]) ).

tff(c_25511,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_25377]) ).

tff(c_25243,plain,
    inverse(sk_c3) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_25233,c_24332]) ).

tff(c_25274,plain,
    inverse(sk_c3) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_25248,c_25243]) ).

tff(c_25278,plain,
    multiply(sk_c5,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_25274,c_4]) ).

tff(c_25542,plain,
    sk_c3 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_25511,c_25278]) ).

tff(c_25526,plain,
    inverse(sk_c3) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_25511,c_25274]) ).

tff(c_25554,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_25542,c_25526]) ).

tff(c_25232,plain,
    inverse(identity) != sk_c7,
    inference(splitRight,[status(thm)],[c_24540]) ).

tff(c_25290,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_25254,c_25232]) ).

tff(c_25524,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_25511,c_25290]) ).

tff(c_25578,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_25554,c_25524]) ).

tff(c_25579,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 )
      | ( 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_44]) ).

tff(c_25698,plain,
    ! [X2_246] :
      ( ( multiply(X2_246,sk_c5) != sk_c6 )
      | ( inverse(X2_246) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_25579]) ).

tff(c_25708,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_24345,c_25698]) ).

tff(c_25721,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24310,c_25708]) ).

tff(c_25722,plain,
    ! [X1_8,X4_7] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 ) ),
    inference(splitRight,[status(thm)],[c_25579]) ).

tff(c_25859,plain,
    ! [X4_252] :
      ( ( inverse(X4_252) != sk_c6 )
      | ( multiply(X4_252,sk_c6) != sk_c5 ) ),
    inference(splitLeft,[status(thm)],[c_25722]) ).

tff(c_25872,plain,
    inverse(sk_c2) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_24327,c_25859]) ).

tff(c_25886,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_65,c_25872]) ).

tff(c_25980,plain,
    ! [X1_254] :
      ( ( multiply(X1_254,sk_c6) != sk_c7 )
      | ( inverse(X1_254) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_25722]) ).

tff(c_25990,plain,
    inverse(sk_c3) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_24351,c_25980]) ).

tff(c_26005,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24332,c_25990]) ).

tff(c_26007,plain,
    multiply(sk_c2,sk_c6) != sk_c5,
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_28,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_26022,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_26007,c_28]) ).

tff(c_26006,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_26011,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_26006,c_4]) ).

tff(c_26057,plain,
    ! [Z_257] : ( multiply(sk_c7,multiply(sk_c3,Z_257)) = multiply(identity,Z_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_26011,c_26036]) ).

tff(c_26174,plain,
    ! [Z_262] : ( multiply(sk_c7,multiply(sk_c3,Z_262)) = Z_262 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26057]) ).

tff(c_26189,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_26022,c_26174]) ).

tff(c_26075,plain,
    ! [Z_257] : ( multiply(sk_c6,multiply(sk_c7,Z_257)) = multiply(sk_c5,Z_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26036]) ).

tff(c_26196,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_26189,c_26075]) ).

tff(c_26202,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26124,c_26196]) ).

tff(c_26069,plain,
    ! [X_2,Z_257] : ( multiply(inverse(X_2),multiply(X_2,Z_257)) = multiply(identity,Z_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_26036]) ).

tff(c_26238,plain,
    ! [X_264,Z_265] : ( multiply(inverse(X_264),multiply(X_264,Z_265)) = Z_265 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26069]) ).

tff(c_26256,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_26202,c_26238]) ).

tff(c_26329,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_26256]) ).

tff(c_26353,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_26329,c_26329,c_26189]) ).

tff(c_26360,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26353]) ).

tff(c_26362,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26237,c_26360]) ).

tff(c_26364,plain,
    sk_c6 = identity,
    inference(splitRight,[status(thm)],[c_26226]) ).

tff(c_26233,plain,
    ( ( inverse(sk_c6) != sk_c7 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26212]) ).

tff(c_26235,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_26233]) ).

tff(c_26408,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_26364,c_26235]) ).

tff(c_26412,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26364,c_26364,c_26124]) ).

tff(c_26427,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26412]) ).

tff(c_26432,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26408,c_26427]) ).

tff(c_26434,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_26233]) ).

tff(c_26515,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26434,c_26226]) ).

tff(c_26516,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_26515]) ).

tff(c_26438,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26434,c_26434,c_26124]) ).

tff(c_26540,plain,
    ! [X_268,Z_269] : ( multiply(inverse(X_268),multiply(X_268,Z_269)) = Z_269 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26069]) ).

tff(c_26561,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_26438,c_26540]) ).

tff(c_26619,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_26561]) ).

tff(c_26621,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26516,c_26619]) ).

tff(c_26623,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_26515]) ).

tff(c_26448,plain,
    multiply(sk_c5,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_26434,c_69]) ).

tff(c_26629,plain,
    multiply(identity,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_26623,c_26448]) ).

tff(c_26703,plain,
    sk_c2 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_26629,c_2]) ).

tff(c_26444,plain,
    multiply(sk_c2,sk_c5) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26434,c_26007]) ).

tff(c_26627,plain,
    multiply(sk_c2,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_26623,c_26623,c_26444]) ).

tff(c_26731,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26703,c_26627]) ).

tff(c_26733,plain,
    inverse(sk_c1) != sk_c7,
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_18,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_26750,plain,
    inverse(sk_c3) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_26733,c_18]) ).

tff(c_20,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_26773,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_26733,c_20]) ).

tff(c_26732,plain,
    inverse(sk_c4) = sk_c6,
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_24,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_26768,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_26733,c_24]) ).

tff(c_26737,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_26732,c_4]) ).

tff(c_26782,plain,
    ! [X_271,Y_272,Z_273] : ( multiply(multiply(X_271,Y_272),Z_273) = multiply(X_271,multiply(Y_272,Z_273)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_26806,plain,
    ! [Z_273] : ( multiply(sk_c6,multiply(sk_c4,Z_273)) = multiply(identity,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_26737,c_26782]) ).

tff(c_26852,plain,
    ! [Z_275] : ( multiply(sk_c6,multiply(sk_c4,Z_275)) = Z_275 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26806]) ).

tff(c_26864,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_26768,c_26852]) ).

tff(c_26926,plain,
    ! [X3_278] :
      ( ( inverse(X3_278) != sk_c7 )
      | ( multiply(X3_278,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_44]) ).

tff(c_26940,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_26926]) ).

tff(c_26951,plain,
    sk_c6 != identity,
    inference(splitLeft,[status(thm)],[c_26940]) ).

tff(c_26754,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_26750,c_4]) ).

tff(c_26803,plain,
    ! [Z_273] : ( multiply(sk_c7,multiply(sk_c3,Z_273)) = multiply(identity,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_26754,c_26782]) ).

tff(c_26828,plain,
    ! [Z_274] : ( multiply(sk_c7,multiply(sk_c3,Z_274)) = Z_274 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26803]) ).

tff(c_26840,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_26773,c_26828]) ).

tff(c_26888,plain,
    ! [Z_277] : ( multiply(sk_c6,multiply(sk_c7,Z_277)) = multiply(sk_c5,Z_277) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26782]) ).

tff(c_26900,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_26840,c_26888]) ).

tff(c_26910,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26864,c_26900]) ).

tff(c_26812,plain,
    ! [X_2,Z_273] : ( multiply(inverse(X_2),multiply(X_2,Z_273)) = multiply(identity,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_26782]) ).

tff(c_26952,plain,
    ! [X_279,Z_280] : ( multiply(inverse(X_279),multiply(X_279,Z_280)) = Z_280 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26812]) ).

tff(c_26973,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_26910,c_26952]) ).

tff(c_27031,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_26973]) ).

tff(c_27042,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_27031,c_27031,c_26840]) ).

tff(c_27050,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_27042]) ).

tff(c_27052,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26951,c_27050]) ).

tff(c_27054,plain,
    sk_c6 = identity,
    inference(splitRight,[status(thm)],[c_26940]) ).

tff(c_26947,plain,
    ( ( inverse(sk_c6) != sk_c7 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26926]) ).

tff(c_26950,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_26947]) ).

tff(c_27055,plain,
    sk_c5 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_27054,c_26950]) ).

tff(c_27061,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27054,c_27054,c_26864]) ).

tff(c_27072,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_27061]) ).

tff(c_27077,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27055,c_27072]) ).

tff(c_27079,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_26947]) ).

tff(c_27100,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_27079,c_26940]) ).

tff(c_27101,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_27100]) ).

tff(c_27085,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27079,c_27079,c_26864]) ).

tff(c_27177,plain,
    ! [X_281,Z_282] : ( multiply(inverse(X_281),multiply(X_281,Z_282)) = Z_282 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26812]) ).

tff(c_27198,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_27085,c_27177]) ).

tff(c_27245,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_27198]) ).

tff(c_27247,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27101,c_27245]) ).

tff(c_27249,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_27100]) ).

tff(c_26944,plain,
    ( ( inverse(identity) != sk_c7 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_26926]) ).

tff(c_26949,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_26944]) ).

tff(c_27080,plain,
    sk_c7 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27079,c_26949]) ).

tff(c_27250,plain,
    sk_c7 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_27249,c_27080]) ).

tff(c_27252,plain,
    multiply(identity,sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_27249,c_27249,c_26910]) ).

tff(c_27348,plain,
    sk_c7 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_27252,c_2]) ).

tff(c_27356,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27250,c_27348]) ).

tff(c_27358,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_26944]) ).

tff(c_27363,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_27358,c_27358,c_26840]) ).

tff(c_27370,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_26864,c_27363]) ).

tff(c_27376,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27370,c_27358]) ).

tff(c_27357,plain,
    inverse(identity) != sk_c7,
    inference(splitRight,[status(thm)],[c_26944]) ).

tff(c_27411,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27376,c_27357]) ).

tff(c_26823,plain,
    ! [Z_273] : ( multiply(sk_c7,multiply(sk_c3,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26803]) ).

tff(c_27364,plain,
    ! [Z_273] : ( multiply(sk_c6,multiply(sk_c3,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_27358,c_26823]) ).

tff(c_27475,plain,
    ! [Z_273] : ( multiply(sk_c5,multiply(sk_c3,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_27370,c_27364]) ).

tff(c_26797,plain,
    ! [Z_273] : ( multiply(sk_c3,multiply(sk_c6,Z_273)) = multiply(sk_c7,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_26773,c_26782]) ).

tff(c_27494,plain,
    ! [Z_285] : ( multiply(sk_c3,multiply(sk_c5,Z_285)) = multiply(sk_c5,Z_285) ),
    inference(demodulation,[status(thm),theory(equality)],[c_27376,c_27370,c_26797]) ).

tff(c_27509,plain,
    ! [Z_273] : ( multiply(sk_c5,multiply(sk_c3,Z_273)) = multiply(sk_c3,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_27475,c_27494]) ).

tff(c_27525,plain,
    ! [Z_273] : ( multiply(sk_c3,Z_273) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_27475,c_27509]) ).

tff(c_27549,plain,
    ! [Z_287] : ( multiply(sk_c5,Z_287) = Z_287 ),
    inference(demodulation,[status(thm),theory(equality)],[c_27525,c_27475]) ).

tff(c_27382,plain,
    multiply(sk_c5,sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_27370,c_26737]) ).

tff(c_27555,plain,
    sk_c4 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_27549,c_27382]) ).

tff(c_27384,plain,
    inverse(sk_c4) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27370,c_26732]) ).

tff(c_27582,plain,
    inverse(identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27555,c_27384]) ).

tff(c_27586,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27411,c_27582]) ).

tff(c_27587,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 )
      | ( 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_44]) ).

tff(c_27663,plain,
    ! [X2_291] :
      ( ( multiply(X2_291,sk_c5) != sk_c6 )
      | ( inverse(X2_291) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_27587]) ).

tff(c_27670,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_26768,c_27663]) ).

tff(c_27682,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_26732,c_27670]) ).

tff(c_27683,plain,
    ! [X1_8,X4_7] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 ) ),
    inference(splitRight,[status(thm)],[c_27587]) ).

tff(c_27721,plain,
    ! [X4_294] :
      ( ( inverse(X4_294) != sk_c6 )
      | ( multiply(X4_294,sk_c6) != sk_c5 ) ),
    inference(splitLeft,[status(thm)],[c_27683]) ).

tff(c_27739,plain,
    ( ( inverse(identity) != sk_c6 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_27721]) ).

tff(c_27742,plain,
    sk_c6 != sk_c5,
    inference(splitLeft,[status(thm)],[c_27739]) ).

tff(c_27735,plain,
    ( ( inverse(inverse(sk_c6)) != sk_c6 )
    | ( sk_c5 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_27721]) ).

tff(c_27744,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_27735]) ).

tff(c_27684,plain,
    ! [Z_292] : ( multiply(sk_c6,multiply(sk_c4,Z_292)) = Z_292 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26806]) ).

tff(c_27696,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_26768,c_27684]) ).

tff(c_27957,plain,
    ! [Z_299] : ( multiply(sk_c6,multiply(sk_c7,Z_299)) = multiply(sk_c5,Z_299) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26782]) ).

tff(c_27972,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
    inference(superposition,[status(thm),theory(equality)],[c_26840,c_27957]) ).

tff(c_27982,plain,
    multiply(sk_c5,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27696,c_27972]) ).

tff(c_26826,plain,
    ! [X_2,Z_273] : ( multiply(inverse(X_2),multiply(X_2,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26812]) ).

tff(c_27986,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_27982,c_26826]) ).

tff(c_27992,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_27986]) ).

tff(c_27999,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_27992,c_27992,c_26840]) ).

tff(c_28008,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_27999]) ).

tff(c_28005,plain,
    multiply(sk_c6,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_27992,c_8]) ).

tff(c_28028,plain,
    multiply(identity,identity) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28008,c_28005]) ).

tff(c_28038,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28028]) ).

tff(c_28040,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27744,c_28038]) ).

tff(c_28042,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_27735]) ).

tff(c_27731,plain,
    ( ( inverse(sk_c3) != sk_c6 )
    | ( sk_c7 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_26773,c_27721]) ).

tff(c_27741,plain,
    ( ( sk_c7 != sk_c6 )
    | ( sk_c7 != sk_c5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26750,c_27731]) ).

tff(c_27743,plain,
    sk_c7 != sk_c5,
    inference(splitLeft,[status(thm)],[c_27741]) ).

tff(c_28043,plain,
    sk_c7 != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28042,c_27743]) ).

tff(c_28047,plain,
    multiply(sk_c4,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_28042,c_26768]) ).

tff(c_26824,plain,
    ! [Z_273] : ( multiply(sk_c6,multiply(sk_c4,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26806]) ).

tff(c_28056,plain,
    multiply(sk_c6,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_28047,c_26824]) ).

tff(c_26818,plain,
    ! [Z_273] : ( multiply(sk_c6,multiply(sk_c7,Z_273)) = multiply(sk_c5,Z_273) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_26782]) ).

tff(c_28082,plain,
    ! [Z_300] : ( multiply(sk_c6,multiply(sk_c7,Z_300)) = Z_300 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28042,c_26818]) ).

tff(c_28094,plain,
    multiply(sk_c6,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_26840,c_28082]) ).

tff(c_28104,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28056,c_28094]) ).

tff(c_28106,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28043,c_28104]) ).

tff(c_28108,plain,
    sk_c7 = sk_c5,
    inference(splitRight,[status(thm)],[c_27741]) ).

tff(c_28109,plain,
    multiply(sk_c5,sk_c5) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_28108,c_28108,c_26840]) ).

tff(c_28298,plain,
    ! [Z_305] : ( multiply(sk_c6,multiply(sk_c5,Z_305)) = multiply(sk_c5,Z_305) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28108,c_26818]) ).

tff(c_28316,plain,
    multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5),
    inference(superposition,[status(thm),theory(equality)],[c_28109,c_28298]) ).

tff(c_28324,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28109,c_27696,c_28316]) ).

tff(c_28326,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27742,c_28324]) ).

tff(c_28328,plain,
    sk_c6 = sk_c5,
    inference(splitRight,[status(thm)],[c_27739]) ).

tff(c_28420,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28328,c_28328,c_27735]) ).

tff(c_28421,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_28420]) ).

tff(c_28332,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28328,c_28328,c_27696]) ).

tff(c_28422,plain,
    ! [X_306,Z_307] : ( multiply(inverse(X_306),multiply(X_306,Z_307)) = Z_307 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_26812]) ).

tff(c_28440,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_28332,c_28422]) ).

tff(c_28486,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_28440]) ).

tff(c_28488,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28421,c_28486]) ).

tff(c_28490,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_28420]) ).

tff(c_28327,plain,
    inverse(identity) != sk_c6,
    inference(splitRight,[status(thm)],[c_27739]) ).

tff(c_28367,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28328,c_28327]) ).

tff(c_28499,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28490,c_28367]) ).

tff(c_28338,plain,
    multiply(sk_c5,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28328,c_69]) ).

tff(c_28497,plain,
    multiply(identity,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28490,c_28338]) ).

tff(c_28569,plain,
    sk_c2 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_28497,c_2]) ).

tff(c_28340,plain,
    inverse(sk_c2) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28328,c_65]) ).

tff(c_28501,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28490,c_28340]) ).

tff(c_28578,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_28569,c_28501]) ).

tff(c_28581,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28499,c_28578]) ).

tff(c_28596,plain,
    ! [X1_310] :
      ( ( multiply(X1_310,sk_c6) != sk_c7 )
      | ( inverse(X1_310) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_27683]) ).

tff(c_28606,plain,
    inverse(sk_c3) != sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_26773,c_28596]) ).

tff(c_28618,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_26750,c_28606]) ).

tff(c_28620,plain,
    inverse(sk_c2) != sk_c6,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_40,plain,
    ( ( multiply(sk_c4,sk_c5) = sk_c6 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_28659,plain,
    multiply(sk_c4,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_28620,c_40]) ).

tff(c_38,plain,
    ( ( inverse(sk_c4) = sk_c6 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_28644,plain,
    inverse(sk_c4) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_28620,c_38]) ).

tff(c_28648,plain,
    multiply(sk_c6,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_28644,c_4]) ).

tff(c_28698,plain,
    ! [Z_313] : ( multiply(sk_c6,multiply(sk_c4,Z_313)) = multiply(identity,Z_313) ),
    inference(superposition,[status(thm),theory(equality)],[c_28648,c_28677]) ).

tff(c_28723,plain,
    ! [Z_314] : ( multiply(sk_c6,multiply(sk_c4,Z_314)) = Z_314 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28698]) ).

tff(c_28735,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_28659,c_28723]) ).

tff(c_29343,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_28735,c_29316]) ).

tff(c_29382,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_8,c_29316]) ).

tff(c_29700,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29343,c_29382]) ).

tff(c_36,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_28665,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_28620,c_36]) ).

tff(c_28619,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_28625,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_28619,c_4]) ).

tff(c_28704,plain,
    ! [Z_313] : ( multiply(sk_c7,multiply(sk_c3,Z_313)) = multiply(identity,Z_313) ),
    inference(superposition,[status(thm),theory(equality)],[c_28625,c_28677]) ).

tff(c_28746,plain,
    ! [Z_315] : ( multiply(sk_c7,multiply(sk_c3,Z_315)) = Z_315 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28704]) ).

tff(c_28758,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_28665,c_28746]) ).

tff(c_29337,plain,
    multiply(inverse(sk_c7),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_28758,c_29316]) ).

tff(c_29816,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29700,c_29700,c_29337]) ).

tff(c_29824,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_29816]) ).

tff(c_29358,plain,
    multiply(inverse(sk_c6),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_28648,c_29316]) ).

tff(c_29833,plain,
    multiply(inverse(identity),identity) = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_29824,c_29358]) ).

tff(c_29840,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29379,c_29833]) ).

tff(c_29838,plain,
    inverse(sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29824,c_28644]) ).

tff(c_29879,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29840,c_29838]) ).

tff(c_29831,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29824,c_29700]) ).

tff(c_29712,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29700,c_29700,c_29337]) ).

tff(c_29720,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_29712]) ).

tff(c_29729,plain,
    multiply(inverse(identity),identity) = sk_c4,
    inference(demodulation,[status(thm),theory(equality)],[c_29720,c_29358]) ).

tff(c_29736,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_29729]) ).

tff(c_29734,plain,
    inverse(sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29720,c_28644]) ).

tff(c_29775,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29736,c_29734]) ).

tff(c_29716,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29700,c_29700,c_28758]) ).

tff(c_29721,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28735,c_29716]) ).

tff(c_29742,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29720,c_29721]) ).

tff(c_28783,plain,
    ! [X3_317] :
      ( ( inverse(X3_317) != sk_c7 )
      | ( multiply(X3_317,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_44]) ).

tff(c_28798,plain,
    ( ( inverse(identity) != sk_c7 )
    | ( sk_c7 != sk_c6 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_28783]) ).

tff(c_28803,plain,
    sk_c7 != sk_c6,
    inference(splitLeft,[status(thm)],[c_28798]) ).

tff(c_28806,plain,
    ! [X_318,Z_319] : ( multiply(inverse(X_318),multiply(X_318,Z_319)) = Z_319 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28707]) ).

tff(c_28833,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_28735,c_28806]) ).

tff(c_28872,plain,
    multiply(inverse(sk_c6),sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_8,c_28806]) ).

tff(c_29001,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_28833,c_28872]) ).

tff(c_29003,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28803,c_29001]) ).

tff(c_29005,plain,
    sk_c7 = sk_c6,
    inference(splitRight,[status(thm)],[c_28798]) ).

tff(c_29009,plain,
    multiply(sk_c6,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_29005,c_29005,c_28758]) ).

tff(c_29017,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_28735,c_29009]) ).

tff(c_29023,plain,
    sk_c7 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_29017,c_29005]) ).

tff(c_28794,plain,
    ( ( inverse(inverse(sk_c7)) != sk_c7 )
    | ( sk_c6 != identity ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_28783]) ).

tff(c_29115,plain,
    ( ( inverse(inverse(sk_c5)) != sk_c5 )
    | ( sk_c5 != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_29017,c_29023,c_29023,c_28794]) ).

tff(c_29116,plain,
    sk_c5 != identity,
    inference(splitLeft,[status(thm)],[c_29115]) ).

tff(c_29024,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_29017,c_29017,c_28735]) ).

tff(c_29117,plain,
    ! [X_321,Z_322] : ( multiply(inverse(X_321),multiply(X_321,Z_322)) = Z_322 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28707]) ).

tff(c_29135,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_29024,c_29117]) ).

tff(c_29172,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_29135]) ).

tff(c_29175,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_29116,c_29172]) ).

tff(c_29177,plain,
    sk_c5 = identity,
    inference(splitRight,[status(thm)],[c_29115]) ).

tff(c_29004,plain,
    inverse(identity) != sk_c7,
    inference(splitRight,[status(thm)],[c_28798]) ).

tff(c_29054,plain,
    inverse(identity) != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_29023,c_29004]) ).

tff(c_29187,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29177,c_29054]) ).

tff(c_29028,plain,
    inverse(sk_c4) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_29017,c_28644]) ).

tff(c_29184,plain,
    inverse(sk_c4) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29177,c_29028]) ).

tff(c_29224,plain,
    multiply(identity,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_29184,c_4]) ).

tff(c_28721,plain,
    ! [X_2,Z_313] : ( multiply(inverse(X_2),multiply(X_2,Z_313)) = Z_313 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_28707]) ).

tff(c_29282,plain,
    multiply(inverse(identity),identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_29224,c_28721]) ).

tff(c_29294,plain,
    sk_c4 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_29282]) ).

tff(c_29298,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_29294,c_29184]) ).

tff(c_29301,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_29187,c_29298]) ).

tff(c_29302,plain,
    ! [X4_7,X1_8,X2_9] :
      ( ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 )
      | ( 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_44]) ).

tff(c_29548,plain,
    ! [X2_331] :
      ( ( multiply(X2_331,sk_c5) != sk_c6 )
      | ( inverse(X2_331) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_29302]) ).

tff(c_29562,plain,
    inverse(sk_c4) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_28659,c_29548]) ).

tff(c_29575,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28644,c_29562]) ).

tff(c_29576,plain,
    ! [X1_8,X4_7] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 ) ),
    inference(splitRight,[status(thm)],[c_29302]) ).

tff(c_29711,plain,
    ! [X4_7] :
      ( ( inverse(X4_7) != sk_c6 )
      | ( multiply(X4_7,sk_c6) != sk_c5 ) ),
    inference(splitLeft,[status(thm)],[c_29576]) ).

tff(c_29795,plain,
    ! [X4_335] :
      ( ( inverse(X4_335) != identity )
      | ( multiply(X4_335,identity) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_29742,c_29720,c_29720,c_29711]) ).

tff(c_29806,plain,
    inverse(inverse(identity)) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_4,c_29795]) ).

tff(c_29814,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29775,c_29775,c_29806]) ).

tff(c_29815,plain,
    ! [X1_8] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_29576]) ).

tff(c_29899,plain,
    ! [X1_337] :
      ( ( multiply(X1_337,identity) != identity )
      | ( inverse(X1_337) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_29831,c_29831,c_29824,c_29815]) ).

tff(c_29910,plain,
    inverse(inverse(identity)) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_4,c_29899]) ).

tff(c_29918,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29879,c_29879,c_29910]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP315-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 22:00:36 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 12.03/4.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.37/4.43  
% 12.37/4.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.66/4.49  
% 12.66/4.49  Inference rules
% 12.66/4.49  ----------------------
% 12.66/4.49  #Ref     : 0
% 12.66/4.49  #Sup     : 7418
% 12.66/4.49  #Fact    : 0
% 12.66/4.49  #Define  : 0
% 12.66/4.49  #Split   : 47
% 12.66/4.49  #Chain   : 0
% 12.66/4.49  #Close   : 0
% 12.66/4.49  
% 12.66/4.49  Ordering : KBO
% 12.66/4.49  
% 12.66/4.49  Simplification rules
% 12.66/4.49  ----------------------
% 12.66/4.49  #Subsume      : 30
% 12.66/4.49  #Demod        : 20498
% 12.66/4.49  #Tautology    : 5749
% 12.66/4.49  #SimpNegUnit  : 43
% 12.66/4.49  #BackRed      : 588
% 12.66/4.49  
% 12.66/4.49  #Partial instantiations: 0
% 12.66/4.49  #Strategies tried      : 1
% 12.66/4.49  
% 12.66/4.49  Timing (in seconds)
% 12.66/4.49  ----------------------
% 12.66/4.50  Preprocessing        : 0.46
% 12.66/4.50  Parsing              : 0.20
% 12.66/4.50  CNF conversion       : 0.02
% 12.66/4.50  Main loop            : 2.88
% 12.66/4.50  Inferencing          : 0.87
% 12.66/4.50  Reduction            : 1.49
% 12.66/4.50  Demodulation         : 1.35
% 12.66/4.50  BG Simplification    : 0.08
% 12.66/4.50  Subsumption          : 0.29
% 12.66/4.50  Abstraction          : 0.17
% 12.66/4.50  MUC search           : 0.00
% 12.66/4.50  Cooper               : 0.00
% 12.66/4.50  Total                : 3.47
% 12.66/4.50  Index Insertion      : 0.00
% 12.66/4.50  Index Deletion       : 0.00
% 12.66/4.50  Index Matching       : 0.00
% 12.66/4.50  BG Taut test         : 0.00
%------------------------------------------------------------------------------