TSTP Solution File: GRP216-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP216-1 : 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 : n026.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 10:40:30 EDT 2023

% Result   : Unsatisfiable 9.09s 3.32s
% Output   : CNFRefutation 9.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  337 ( 260 unt;  10 typ;   0 def)
%            Number of atoms       :  463 ( 446 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  284 ( 148   ~; 136   |;   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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  165 (; 165   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_116,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c7 )
    | ( inverse(sk_c4) = sk_c7 ) ),
    file(unknown,unknown) ).

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

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

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

tff(f_164,axiom,
    ! [X5,X3,X1,X2,X4] :
      ( ( multiply(X3,sk_c7) != sk_c6 )
      | ( inverse(X3) != sk_c7 )
      | ( multiply(X4,sk_c6) != sk_c7 )
      | ( inverse(X4) != sk_c6 )
      | ( inverse(sk_c7) != sk_c6 )
      | ( inverse(X1) != sk_c7 )
      | ( multiply(X1,sk_c6) != sk_c7 )
      | ( multiply(sk_c7,X2) != sk_c6 )
      | ( multiply(X5,sk_c7) != X2 )
      | ( inverse(X5) != sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c7 )
    | ( inverse(sk_c7) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_107,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ( ( multiply(sk_c2,sk_c6) = sk_c7 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ( ( multiply(sk_c1,sk_c7) = sk_c6 )
    | ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

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

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

tff(f_128,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( inverse(sk_c4) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( inverse(sk_c3) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_125,axiom,
    ( ( inverse(sk_c2) = sk_c6 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

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

tff(f_83,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c7) = sk_c6 ) ),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( inverse(sk_c4) = sk_c7 ) ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ( ( inverse(sk_c1) = sk_c7 )
    | ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
    file(unknown,unknown) ).

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

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

tff(c_12345,plain,
    ! [X_191,Y_192,Z_193] : ( multiply(multiply(X_191,Y_192),Z_193) = multiply(X_191,multiply(Y_192,Z_193)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_12381,plain,
    ! [X_2,Z_193] : ( multiply(inverse(X_2),multiply(X_2,Z_193)) = multiply(identity,Z_193) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_12345]) ).

tff(c_12393,plain,
    ! [X_2,Z_193] : ( multiply(inverse(X_2),multiply(X_2,Z_193)) = Z_193 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12381]) ).

tff(c_14127,plain,
    ! [X_226,Z_227] : ( multiply(inverse(X_226),multiply(X_226,Z_227)) = Z_227 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12381]) ).

tff(c_14375,plain,
    ! [X_230,Z_231] : ( multiply(inverse(inverse(X_230)),Z_231) = multiply(X_230,Z_231) ),
    inference(superposition,[status(thm),theory(equality)],[c_12393,c_14127]) ).

tff(c_14178,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_14127]) ).

tff(c_14382,plain,
    ! [X_230] : ( multiply(X_230,identity) = X_230 ),
    inference(superposition,[status(thm),theory(equality)],[c_14375,c_14178]) ).

tff(c_127,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_154,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_127]) ).

tff(c_1775,plain,
    ! [X_49,Z_50] : ( multiply(inverse(X_49),multiply(X_49,Z_50)) = Z_50 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_154]) ).

tff(c_164,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_154]) ).

tff(c_1944,plain,
    ! [X_52,Z_53] : ( multiply(inverse(inverse(X_52)),Z_53) = multiply(X_52,Z_53) ),
    inference(superposition,[status(thm),theory(equality)],[c_1775,c_164]) ).

tff(c_1805,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_1775]) ).

tff(c_1951,plain,
    ! [X_52] : ( multiply(X_52,identity) = X_52 ),
    inference(superposition,[status(thm),theory(equality)],[c_1944,c_1805]) ).

tff(c_42,plain,
    ( ( inverse(sk_c4) = sk_c7 )
    | ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_111,plain,
    multiply(sk_c2,sk_c6) = sk_c7,
    inference(splitLeft,[status(thm)],[c_42]) ).

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

tff(c_86,plain,
    inverse(sk_c2) = sk_c6,
    inference(splitLeft,[status(thm)],[c_44]) ).

tff(c_90,plain,
    multiply(sk_c6,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_86,c_4]) ).

tff(c_148,plain,
    ! [Z_15] : ( multiply(sk_c6,multiply(sk_c2,Z_15)) = multiply(identity,Z_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_90,c_127]) ).

tff(c_166,plain,
    ! [Z_16] : ( multiply(sk_c6,multiply(sk_c2,Z_16)) = Z_16 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_148]) ).

tff(c_178,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_111,c_166]) ).

tff(c_254,plain,
    ! [X_19,Z_20] : ( multiply(inverse(X_19),multiply(X_19,Z_20)) = Z_20 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_154]) ).

tff(c_287,plain,
    multiply(inverse(sk_c6),sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_178,c_254]) ).

tff(c_324,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_287]) ).

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

tff(c_104,plain,
    multiply(sk_c1,sk_c7) = sk_c6,
    inference(splitLeft,[status(thm)],[c_10]) ).

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

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_151,plain,
    ! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_77,c_127]) ).

tff(c_190,plain,
    ! [Z_17] : ( multiply(sk_c7,multiply(sk_c1,Z_17)) = Z_17 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_151]) ).

tff(c_202,plain,
    multiply(sk_c7,sk_c6) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_104,c_190]) ).

tff(c_281,plain,
    multiply(inverse(sk_c7),sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_202,c_254]) ).

tff(c_323,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_281]) ).

tff(c_56,plain,
    ! [X5_6,X1_8,X4_10,X3_7] :
      ( ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(sk_c7) != sk_c6 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_164]) ).

tff(c_189,plain,
    inverse(sk_c7) != sk_c6,
    inference(splitLeft,[status(thm)],[c_56]) ).

tff(c_331,plain,
    inverse(sk_c7) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_323,c_189]) ).

tff(c_372,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_324,c_331]) ).

tff(c_337,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_323,c_86]) ).

tff(c_379,plain,
    multiply(identity,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_337,c_4]) ).

tff(c_386,plain,
    multiply(inverse(identity),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_379,c_164]) ).

tff(c_398,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_386]) ).

tff(c_402,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_337]) ).

tff(c_405,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_372,c_402]) ).

tff(c_407,plain,
    inverse(sk_c7) = sk_c6,
    inference(splitRight,[status(thm)],[c_56]) ).

tff(c_411,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_407,c_4]) ).

tff(c_415,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_178]) ).

tff(c_425,plain,
    inverse(sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_407]) ).

tff(c_438,plain,
    multiply(identity,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_425,c_4]) ).

tff(c_1843,plain,
    multiply(inverse(identity),identity) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_438,c_164]) ).

tff(c_1855,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_1843]) ).

tff(c_515,plain,
    ! [X_22,Z_23] : ( multiply(inverse(X_22),multiply(X_22,Z_23)) = Z_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_154]) ).

tff(c_619,plain,
    ! [X_25,Z_26] : ( multiply(inverse(inverse(X_25)),Z_26) = multiply(X_25,Z_26) ),
    inference(superposition,[status(thm),theory(equality)],[c_515,c_164]) ).

tff(c_539,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_515]) ).

tff(c_626,plain,
    ! [X_25] : ( multiply(X_25,identity) = X_25 ),
    inference(superposition,[status(thm),theory(equality)],[c_619,c_539]) ).

tff(c_424,plain,
    multiply(identity,sk_c7) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_411]) ).

tff(c_495,plain,
    sk_c7 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_424,c_2]) ).

tff(c_406,plain,
    ! [X3_7,X4_10,X1_8,X5_6] :
      ( ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_56]) ).

tff(c_442,plain,
    ! [X3_7,X4_10,X1_8,X5_6] :
      ( ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != identity )
      | ( inverse(X4_10) != identity )
      | ( multiply(X4_10,identity) != sk_c7 )
      | ( multiply(X1_8,identity) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_415,c_415,c_415,c_415,c_406]) ).

tff(c_443,plain,
    ! [X5_6] :
      ( ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != identity ) ),
    inference(splitLeft,[status(thm)],[c_442]) ).

tff(c_1771,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_626,c_495,c_2,c_495,c_495,c_443]) ).

tff(c_429,plain,
    multiply(identity,sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_90]) ).

tff(c_465,plain,
    sk_c2 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_429,c_2]) ).

tff(c_430,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_86]) ).

tff(c_474,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_465,c_430]) ).

tff(c_1773,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1771,c_474]) ).

tff(c_1774,plain,
    ! [X1_8,X4_10,X3_7] :
      ( ( multiply(X1_8,identity) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_10) != identity )
      | ( multiply(X4_10,identity) != sk_c7 )
      | ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != identity ) ),
    inference(splitRight,[status(thm)],[c_442]) ).

tff(c_10069,plain,
    ! [X1_8,X4_10,X3_7] :
      ( ( identity != X1_8 )
      | ( inverse(X1_8) != identity )
      | ( inverse(X4_10) != identity )
      | ( identity != X4_10 )
      | ( inverse(X3_7) != identity )
      | ( identity != X3_7 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1951,c_1855,c_1855,c_1951,c_1855,c_1855,c_1951,c_1855,c_1774]) ).

tff(c_10071,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_10069]) ).

tff(c_1799,plain,
    multiply(inverse(sk_c7),identity) = sk_c1,
    inference(superposition,[status(thm),theory(equality)],[c_77,c_1775]) ).

tff(c_1812,plain,
    sk_c1 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_425,c_1799]) ).

tff(c_1814,plain,
    inverse(identity) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_1812,c_73]) ).

tff(c_1859,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1855,c_1814]) ).

tff(c_10073,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10071,c_1859]) ).

tff(c_10074,plain,
    ! [X4_10,X1_8] :
      ( ( inverse(X4_10) != identity )
      | ( identity != X4_10 )
      | ( identity != X1_8 )
      | ( inverse(X1_8) != identity ) ),
    inference(splitRight,[status(thm)],[c_10069]) ).

tff(c_10076,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_10074]) ).

tff(c_10078,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10076,c_1859]) ).

tff(c_10081,plain,
    inverse(identity) != identity,
    inference(splitRight,[status(thm)],[c_10074]) ).

tff(c_10083,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10081,c_1859]) ).

tff(c_10085,plain,
    multiply(sk_c2,sk_c6) != sk_c7,
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_32,plain,
    ( ( inverse(sk_c7) = sk_c6 )
    | ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_10112,plain,
    inverse(sk_c7) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_10085,c_32]) ).

tff(c_10116,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_10112,c_4]) ).

tff(c_36,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_10137,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_10085,c_36]) ).

tff(c_34,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_10100,plain,
    inverse(sk_c3) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_10085,c_34]) ).

tff(c_10104,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_10100,c_4]) ).

tff(c_10142,plain,
    ! [X_144,Y_145,Z_146] : ( multiply(multiply(X_144,Y_145),Z_146) = multiply(X_144,multiply(Y_145,Z_146)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_10169,plain,
    ! [Z_146] : ( multiply(sk_c7,multiply(sk_c3,Z_146)) = multiply(identity,Z_146) ),
    inference(superposition,[status(thm),theory(equality)],[c_10104,c_10142]) ).

tff(c_10356,plain,
    ! [Z_153] : ( multiply(sk_c7,multiply(sk_c3,Z_153)) = Z_153 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10169]) ).

tff(c_10368,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_10137,c_10356]) ).

tff(c_10175,plain,
    ! [Z_146] : ( multiply(sk_c1,multiply(sk_c7,Z_146)) = multiply(sk_c6,Z_146) ),
    inference(superposition,[status(thm),theory(equality)],[c_104,c_10142]) ).

tff(c_10413,plain,
    multiply(sk_c6,sk_c7) = multiply(sk_c1,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_10368,c_10175]) ).

tff(c_10419,plain,
    multiply(sk_c1,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10116,c_10413]) ).

tff(c_10181,plain,
    ! [Z_146] : ( multiply(sk_c7,multiply(sk_c1,Z_146)) = multiply(identity,Z_146) ),
    inference(superposition,[status(thm),theory(equality)],[c_77,c_10142]) ).

tff(c_10196,plain,
    ! [Z_146] : ( multiply(sk_c7,multiply(sk_c1,Z_146)) = Z_146 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10181]) ).

tff(c_10431,plain,
    multiply(sk_c7,identity) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_10419,c_10196]) ).

tff(c_10442,plain,
    multiply(sk_c6,identity) = multiply(sk_c1,sk_c6),
    inference(superposition,[status(thm),theory(equality)],[c_10431,c_10175]) ).

tff(c_10448,plain,
    multiply(sk_c6,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10419,c_10442]) ).

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

tff(c_10454,plain,
    ! [Z_5] : ( multiply(sk_c6,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
    inference(superposition,[status(thm),theory(equality)],[c_10448,c_6]) ).

tff(c_10608,plain,
    ! [Z_158] : ( multiply(sk_c6,Z_158) = Z_158 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_10454]) ).

tff(c_10620,plain,
    sk_c7 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_10608,c_10116]) ).

tff(c_10640,plain,
    multiply(identity,identity) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_10620,c_10620,c_10368]) ).

tff(c_10658,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10640]) ).

tff(c_10623,plain,
    sk_c2 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_10608,c_90]) ).

tff(c_10652,plain,
    multiply(sk_c2,sk_c6) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10620,c_10085]) ).

tff(c_10784,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_10658,c_2,c_10623,c_10652]) ).

tff(c_10786,plain,
    multiply(sk_c1,sk_c7) != sk_c6,
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_14,plain,
    ( ( multiply(sk_c7,sk_c5) = sk_c6 )
    | ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_11434,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_10786,c_14]) ).

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

tff(c_11439,plain,
    multiply(sk_c4,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_10786,c_16]) ).

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

tff(c_10819,plain,
    inverse(sk_c7) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_10786,c_8]) ).

tff(c_10823,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_10819,c_4]) ).

tff(c_10799,plain,
    multiply(sk_c2,sk_c6) = sk_c7,
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_10850,plain,
    ! [X_162,Y_163,Z_164] : ( multiply(multiply(X_162,Y_163),Z_164) = multiply(X_162,multiply(Y_163,Z_164)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_10886,plain,
    ! [Z_164] : ( multiply(sk_c6,multiply(sk_c2,Z_164)) = multiply(identity,Z_164) ),
    inference(superposition,[status(thm),theory(equality)],[c_90,c_10850]) ).

tff(c_11042,plain,
    ! [Z_167] : ( multiply(sk_c6,multiply(sk_c2,Z_167)) = Z_167 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10886]) ).

tff(c_11054,plain,
    multiply(sk_c6,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_10799,c_11042]) ).

tff(c_11058,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10823,c_11054]) ).

tff(c_11159,plain,
    inverse(sk_c2) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11058,c_86]) ).

tff(c_11174,plain,
    multiply(identity,sk_c2) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_11159,c_4]) ).

tff(c_11184,plain,
    sk_c2 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_11174,c_2]) ).

tff(c_11156,plain,
    multiply(sk_c2,identity) = sk_c7,
    inference(demodulation,[status(thm),theory(equality)],[c_11058,c_10799]) ).

tff(c_11208,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_11184,c_11156]) ).

tff(c_11216,plain,
    multiply(identity,sk_c1) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11208,c_77]) ).

tff(c_11269,plain,
    sk_c1 = identity,
    inference(superposition,[status(thm),theory(equality)],[c_11216,c_2]) ).

tff(c_11157,plain,
    multiply(sk_c1,sk_c7) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11058,c_10786]) ).

tff(c_11209,plain,
    multiply(sk_c1,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11208,c_11157]) ).

tff(c_11400,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_11269,c_11209]) ).

tff(c_11402,plain,
    multiply(sk_c2,sk_c6) != sk_c7,
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_11414,plain,
    inverse(sk_c4) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_11402,c_42]) ).

tff(c_11418,plain,
    multiply(sk_c7,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_11414,c_4]) ).

tff(c_11455,plain,
    ! [X_171,Y_172,Z_173] : ( multiply(multiply(X_171,Y_172),Z_173) = multiply(X_171,multiply(Y_172,Z_173)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_11479,plain,
    ! [Z_173] : ( multiply(sk_c7,multiply(sk_c4,Z_173)) = multiply(identity,Z_173) ),
    inference(superposition,[status(thm),theory(equality)],[c_11418,c_11455]) ).

tff(c_11918,plain,
    ! [Z_186] : ( multiply(sk_c7,multiply(sk_c4,Z_186)) = Z_186 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_11479]) ).

tff(c_11930,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_11439,c_11918]) ).

tff(c_11934,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_11434,c_11930]) ).

tff(c_11401,plain,
    inverse(sk_c7) = sk_c6,
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_11406,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_11401,c_4]) ).

tff(c_11942,plain,
    multiply(sk_c6,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11934,c_11406]) ).

tff(c_10785,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_11947,plain,
    inverse(sk_c3) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_11934,c_10785]) ).

tff(c_11444,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_11402,c_36]) ).

tff(c_11937,plain,
    multiply(sk_c3,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_11934,c_11444]) ).

tff(c_11494,plain,
    ! [X_2,Z_173] : ( multiply(inverse(X_2),multiply(X_2,Z_173)) = multiply(identity,Z_173) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_11455]) ).

tff(c_12053,plain,
    ! [X_188,Z_189] : ( multiply(inverse(X_188),multiply(X_188,Z_189)) = Z_189 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_11494]) ).

tff(c_12086,plain,
    multiply(inverse(sk_c3),sk_c6) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_11937,c_12053]) ).

tff(c_12131,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_11942,c_11947,c_12086]) ).

tff(c_11944,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_11934,c_11401]) ).

tff(c_12113,plain,
    multiply(inverse(sk_c6),identity) = sk_c2,
    inference(superposition,[status(thm),theory(equality)],[c_90,c_12053]) ).

tff(c_12135,plain,
    multiply(sk_c6,identity) = sk_c2,
    inference(demodulation,[status(thm),theory(equality)],[c_11944,c_12113]) ).

tff(c_12235,plain,
    sk_c2 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12131,c_12135]) ).

tff(c_11943,plain,
    multiply(sk_c2,sk_c6) != sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_11934,c_11402]) ).

tff(c_12151,plain,
    multiply(sk_c2,identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12131,c_12131,c_11943]) ).

tff(c_12276,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12235,c_12151]) ).

tff(c_12278,plain,
    inverse(sk_c2) != sk_c6,
    inference(splitRight,[status(thm)],[c_44]) ).

tff(c_50,plain,
    ( ( multiply(sk_c7,sk_c5) = sk_c6 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_12316,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_12278,c_50]) ).

tff(c_52,plain,
    ( ( multiply(sk_c4,sk_c7) = sk_c5 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_12331,plain,
    multiply(sk_c4,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_12278,c_52]) ).

tff(c_54,plain,
    ( ( inverse(sk_c4) = sk_c7 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_12303,plain,
    inverse(sk_c4) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_12278,c_54]) ).

tff(c_12307,plain,
    multiply(sk_c7,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_12303,c_4]) ).

tff(c_12369,plain,
    ! [Z_193] : ( multiply(sk_c7,multiply(sk_c4,Z_193)) = multiply(identity,Z_193) ),
    inference(superposition,[status(thm),theory(equality)],[c_12307,c_12345]) ).

tff(c_12395,plain,
    ! [Z_194] : ( multiply(sk_c7,multiply(sk_c4,Z_194)) = Z_194 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12369]) ).

tff(c_12407,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_12331,c_12395]) ).

tff(c_12411,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12316,c_12407]) ).

tff(c_12277,plain,
    inverse(sk_c7) = sk_c6,
    inference(splitRight,[status(thm)],[c_44]) ).

tff(c_12282,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_12277,c_4]) ).

tff(c_12524,plain,
    multiply(sk_c6,sk_c6) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12282]) ).

tff(c_46,plain,
    ( ( inverse(sk_c3) = sk_c7 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_12286,plain,
    inverse(sk_c3) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_12278,c_46]) ).

tff(c_12525,plain,
    inverse(sk_c3) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12286]) ).

tff(c_48,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c2) = sk_c6 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_12323,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_12278,c_48]) ).

tff(c_12519,plain,
    multiply(sk_c3,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12323]) ).

tff(c_14154,plain,
    multiply(inverse(sk_c3),sk_c6) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_12519,c_14127]) ).

tff(c_14188,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12524,c_12525,c_14154]) ).

tff(c_12664,plain,
    ! [X_197,Z_198] : ( multiply(inverse(X_197),multiply(X_197,Z_198)) = Z_198 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12381]) ).

tff(c_12912,plain,
    ! [X_201,Z_202] : ( multiply(inverse(inverse(X_201)),Z_202) = multiply(X_201,Z_202) ),
    inference(superposition,[status(thm),theory(equality)],[c_12393,c_12664]) ).

tff(c_12715,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_12664]) ).

tff(c_12919,plain,
    ! [X_201] : ( multiply(X_201,identity) = X_201 ),
    inference(superposition,[status(thm),theory(equality)],[c_12912,c_12715]) ).

tff(c_12691,plain,
    multiply(inverse(sk_c3),sk_c6) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_12519,c_12664]) ).

tff(c_12725,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12524,c_12525,c_12691]) ).

tff(c_12423,plain,
    inverse(sk_c3) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12286]) ).

tff(c_12417,plain,
    multiply(sk_c3,sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12323]) ).

tff(c_12413,plain,
    ! [X5_6,X1_8,X4_10,X3_7] :
      ( ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12277,c_56]) ).

tff(c_12414,plain,
    ! [X3_7] :
      ( ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_12413]) ).

tff(c_12491,plain,
    ! [X3_195] :
      ( ( inverse(X3_195) != sk_c6 )
      | ( multiply(X3_195,sk_c6) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12411,c_12414]) ).

tff(c_12497,plain,
    inverse(sk_c3) != sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_12417,c_12491]) ).

tff(c_12515,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12423,c_12497]) ).

tff(c_12516,plain,
    ! [X4_10,X1_8,X5_6] :
      ( ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_12413]) ).

tff(c_12592,plain,
    ! [X4_10,X1_8,X5_6] :
      ( ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 )
      | ( inverse(X5_6) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12411,c_12411,c_12411,c_12411,c_12411,c_12516]) ).

tff(c_12593,plain,
    ! [X5_6] :
      ( ( inverse(X5_6) != sk_c6 )
      | ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_12592]) ).

tff(c_14053,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12919,c_12725,c_12725,c_2,c_12725,c_12725,c_12593]) ).

tff(c_12526,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_12411,c_12277]) ).

tff(c_12734,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12725,c_12725,c_12526]) ).

tff(c_14055,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14053,c_12734]) ).

tff(c_14056,plain,
    ! [X1_8,X4_10] :
      ( ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_12592]) ).

tff(c_16363,plain,
    ! [X1_8,X4_10] :
      ( ( identity != X1_8 )
      | ( inverse(X1_8) != identity )
      | ( inverse(X4_10) != identity )
      | ( identity != X4_10 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14382,c_14188,c_14188,c_14188,c_14188,c_14382,c_14188,c_14188,c_14056]) ).

tff(c_16365,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_16363]) ).

tff(c_14197,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_14188,c_14188,c_12526]) ).

tff(c_16367,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16365,c_14197]) ).

tff(c_16369,plain,
    inverse(identity) != identity,
    inference(splitRight,[status(thm)],[c_16363]) ).

tff(c_16371,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16369,c_14197]) ).

tff(c_16373,plain,
    inverse(sk_c1) != sk_c7,
    inference(splitRight,[status(thm)],[c_22]) ).

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

tff(c_16441,plain,
    multiply(sk_c7,sk_c5) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_16373,c_26]) ).

tff(c_20,plain,
    ( ( inverse(sk_c7) = sk_c6 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_16414,plain,
    inverse(sk_c7) = sk_c6,
    inference(negUnitSimplification,[status(thm)],[c_16373,c_20]) ).

tff(c_16418,plain,
    multiply(sk_c6,sk_c7) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_16414,c_4]) ).

tff(c_16456,plain,
    ! [X_266,Y_267,Z_268] : ( multiply(multiply(X_266,Y_267),Z_268) = multiply(X_266,multiply(Y_267,Z_268)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_16480,plain,
    ! [Z_268] : ( multiply(sk_c6,multiply(sk_c7,Z_268)) = multiply(identity,Z_268) ),
    inference(superposition,[status(thm),theory(equality)],[c_16418,c_16456]) ).

tff(c_16506,plain,
    ! [Z_269] : ( multiply(sk_c6,multiply(sk_c7,Z_269)) = Z_269 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16480]) ).

tff(c_16518,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_16441,c_16506]) ).

tff(c_16372,plain,
    inverse(sk_c3) = sk_c7,
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_16377,plain,
    multiply(sk_c7,sk_c3) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_16372,c_4]) ).

tff(c_16524,plain,
    multiply(sk_c6,identity) = sk_c3,
    inference(superposition,[status(thm),theory(equality)],[c_16377,c_16506]) ).

tff(c_30,plain,
    ( ( inverse(sk_c4) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_16381,plain,
    inverse(sk_c1) = sk_c7,
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_16382,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16373,c_16381]) ).

tff(c_16383,plain,
    inverse(sk_c4) = sk_c7,
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_16388,plain,
    multiply(sk_c7,sk_c4) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_16383,c_4]) ).

tff(c_16521,plain,
    multiply(sk_c6,identity) = sk_c4,
    inference(superposition,[status(thm),theory(equality)],[c_16388,c_16506]) ).

tff(c_16687,plain,
    sk_c4 = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_16524,c_16521]) ).

tff(c_28,plain,
    ( ( multiply(sk_c4,sk_c7) = sk_c5 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_16433,plain,
    multiply(sk_c4,sk_c7) = sk_c5,
    inference(negUnitSimplification,[status(thm)],[c_16373,c_28]) ).

tff(c_16696,plain,
    multiply(sk_c3,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16687,c_16433]) ).

tff(c_16489,plain,
    ! [Z_268] : ( multiply(sk_c7,multiply(sk_c3,Z_268)) = multiply(identity,Z_268) ),
    inference(superposition,[status(thm),theory(equality)],[c_16377,c_16456]) ).

tff(c_16832,plain,
    ! [Z_275] : ( multiply(sk_c7,multiply(sk_c3,Z_275)) = Z_275 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16489]) ).

tff(c_16847,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_16696,c_16832]) ).

tff(c_16854,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16441,c_16847]) ).

tff(c_24,plain,
    ( ( multiply(sk_c3,sk_c6) = sk_c7 )
    | ( inverse(sk_c1) = sk_c7 ) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_16428,plain,
    multiply(sk_c3,sk_c6) = sk_c7,
    inference(negUnitSimplification,[status(thm)],[c_16373,c_24]) ).

tff(c_16850,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_16428,c_16832]) ).

tff(c_17385,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16518,c_16854,c_16854,c_16850]) ).

tff(c_17391,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_17385,c_17385,c_16518]) ).

tff(c_16492,plain,
    ! [X_2,Z_268] : ( multiply(inverse(X_2),multiply(X_2,Z_268)) = multiply(identity,Z_268) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_16456]) ).

tff(c_16504,plain,
    ! [X_2,Z_268] : ( multiply(inverse(X_2),multiply(X_2,Z_268)) = Z_268 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16492]) ).

tff(c_17476,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_17391,c_16504]) ).

tff(c_17482,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_17476]) ).

tff(c_17491,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_17482,c_17385]) ).

tff(c_17398,plain,
    ! [X_286,Z_287] : ( multiply(inverse(X_286),multiply(X_286,Z_287)) = Z_287 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16492]) ).

tff(c_17616,plain,
    ! [X_290,Z_291] : ( multiply(inverse(inverse(X_290)),Z_291) = multiply(X_290,Z_291) ),
    inference(superposition,[status(thm),theory(equality)],[c_16504,c_17398]) ).

tff(c_17419,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_17398]) ).

tff(c_17623,plain,
    ! [X_290] : ( multiply(X_290,identity) = X_290 ),
    inference(superposition,[status(thm),theory(equality)],[c_17616,c_17419]) ).

tff(c_16948,plain,
    ! [X_276,Z_277] : ( multiply(inverse(X_276),multiply(X_276,Z_277)) = Z_277 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16492]) ).

tff(c_17119,plain,
    ! [X_279,Z_280] : ( multiply(inverse(inverse(X_279)),Z_280) = multiply(X_279,Z_280) ),
    inference(superposition,[status(thm),theory(equality)],[c_16948,c_16504]) ).

tff(c_16987,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_16948]) ).

tff(c_17126,plain,
    ! [X_279] : ( multiply(X_279,identity) = X_279 ),
    inference(superposition,[status(thm),theory(equality)],[c_17119,c_16987]) ).

tff(c_16885,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16518,c_16854,c_16854,c_16850]) ).

tff(c_16891,plain,
    multiply(sk_c5,sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16885,c_16885,c_16518]) ).

tff(c_16969,plain,
    multiply(inverse(sk_c5),sk_c5) = sk_c5,
    inference(superposition,[status(thm),theory(equality)],[c_16891,c_16948]) ).

tff(c_16995,plain,
    sk_c5 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_16969]) ).

tff(c_17005,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_16995,c_16885]) ).

tff(c_16713,plain,
    ! [Z_273] : ( multiply(sk_c7,multiply(sk_c3,Z_273)) = Z_273 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16489]) ).

tff(c_16728,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_16696,c_16713]) ).

tff(c_16735,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16441,c_16728]) ).

tff(c_16742,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16735,c_16414]) ).

tff(c_16753,plain,
    multiply(sk_c6,sk_c6) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_16742,c_4]) ).

tff(c_16731,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_16428,c_16713]) ).

tff(c_16777,plain,
    sk_c6 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_16753,c_16735,c_16735,c_16731]) ).

tff(c_16781,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_16777,c_16777,c_16742]) ).

tff(c_16782,plain,
    sk_c7 = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_16777,c_16735]) ).

tff(c_16546,plain,
    sk_c4 = sk_c3,
    inference(demodulation,[status(thm),theory(equality)],[c_16524,c_16521]) ).

tff(c_16555,plain,
    multiply(sk_c3,sk_c7) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16546,c_16433]) ).

tff(c_16599,plain,
    ! [Z_271] : ( multiply(sk_c7,multiply(sk_c3,Z_271)) = Z_271 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_16489]) ).

tff(c_16614,plain,
    multiply(sk_c7,sk_c5) = sk_c7,
    inference(superposition,[status(thm),theory(equality)],[c_16555,c_16599]) ).

tff(c_16624,plain,
    sk_c7 = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16441,c_16614]) ).

tff(c_16632,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16624,c_16414]) ).

tff(c_16536,plain,
    ! [X5_6,X1_8,X4_10,X3_7] :
      ( ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16414,c_56]) ).

tff(c_16537,plain,
    ! [X3_7] :
      ( ( inverse(X3_7) != sk_c7 )
      | ( multiply(X3_7,sk_c7) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_16536]) ).

tff(c_16648,plain,
    ! [X3_272] :
      ( ( inverse(X3_272) != sk_c6 )
      | ( multiply(X3_272,sk_c6) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16624,c_16624,c_16537]) ).

tff(c_16651,plain,
    ( ( inverse(sk_c6) != sk_c6 )
    | ( sk_c6 != sk_c5 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_16518,c_16648]) ).

tff(c_16665,plain,
    sk_c6 != sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16632,c_16651]) ).

tff(c_16620,plain,
    multiply(sk_c7,sk_c7) = sk_c6,
    inference(superposition,[status(thm),theory(equality)],[c_16428,c_16599]) ).

tff(c_16676,plain,
    sk_c6 = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16518,c_16624,c_16624,c_16620]) ).

tff(c_16677,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16665,c_16676]) ).

tff(c_16678,plain,
    ! [X4_10,X1_8,X5_6] :
      ( ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 )
      | ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_16536]) ).

tff(c_16712,plain,
    ! [X5_6] :
      ( ( inverse(X5_6) != sk_c7 )
      | ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_16678]) ).

tff(c_16797,plain,
    ! [X5_274] :
      ( ( inverse(X5_274) != identity )
      | ( multiply(X5_274,identity) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16782,c_2,c_16782,c_16777,c_16782,c_16712]) ).

tff(c_16811,plain,
    inverse(identity) != identity,
    inference(superposition,[status(thm),theory(equality)],[c_2,c_16797]) ).

tff(c_16830,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16781,c_16811]) ).

tff(c_16831,plain,
    ! [X1_8,X4_10] :
      ( ( multiply(X1_8,sk_c6) != sk_c7 )
      | ( inverse(X1_8) != sk_c7 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c7 ) ),
    inference(splitRight,[status(thm)],[c_16678]) ).

tff(c_16883,plain,
    ! [X1_8,X4_10] :
      ( ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 )
      | ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16854,c_16854,c_16854,c_16831]) ).

tff(c_16884,plain,
    ! [X4_10] :
      ( ( inverse(X4_10) != sk_c6 )
      | ( multiply(X4_10,sk_c6) != sk_c6 ) ),
    inference(splitLeft,[status(thm)],[c_16883]) ).

tff(c_17381,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_17126,c_17005,c_17005,c_17005,c_16884]) ).

tff(c_16861,plain,
    inverse(sk_c6) = sk_c6,
    inference(demodulation,[status(thm),theory(equality)],[c_16854,c_16414]) ).

tff(c_16888,plain,
    inverse(sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_16885,c_16885,c_16861]) ).

tff(c_17000,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_16995,c_16995,c_16888]) ).

tff(c_17383,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_17381,c_17000]) ).

tff(c_17384,plain,
    ! [X1_8] :
      ( ( multiply(X1_8,sk_c6) != sk_c6 )
      | ( inverse(X1_8) != sk_c6 ) ),
    inference(splitRight,[status(thm)],[c_16883]) ).

tff(c_18002,plain,
    inverse(identity) != identity,
    inference(demodulation,[status(thm),theory(equality)],[c_17491,c_17623,c_17491,c_17491,c_17384]) ).

tff(c_17388,plain,
    inverse(sk_c5) = sk_c5,
    inference(demodulation,[status(thm),theory(equality)],[c_17385,c_17385,c_16861]) ).

tff(c_17489,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_17482,c_17482,c_17388]) ).

tff(c_18004,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18002,c_17489]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP216-1 : 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
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 22:16:16 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 9.09/3.32  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.09/3.35  
% 9.09/3.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.54/3.41  
% 9.54/3.41  Inference rules
% 9.54/3.41  ----------------------
% 9.54/3.41  #Ref     : 0
% 9.54/3.41  #Sup     : 4478
% 9.54/3.41  #Fact    : 0
% 9.54/3.41  #Define  : 0
% 9.54/3.41  #Split   : 26
% 9.54/3.41  #Chain   : 0
% 9.54/3.41  #Close   : 0
% 9.54/3.41  
% 9.54/3.41  Ordering : KBO
% 9.54/3.41  
% 9.54/3.41  Simplification rules
% 9.54/3.41  ----------------------
% 9.54/3.41  #Subsume      : 2
% 9.54/3.41  #Demod        : 8381
% 9.54/3.41  #Tautology    : 3611
% 9.54/3.41  #SimpNegUnit  : 42
% 9.54/3.41  #BackRed      : 405
% 9.54/3.41  
% 9.54/3.41  #Partial instantiations: 0
% 9.54/3.41  #Strategies tried      : 1
% 9.54/3.41  
% 9.54/3.41  Timing (in seconds)
% 9.54/3.41  ----------------------
% 9.59/3.41  Preprocessing        : 0.51
% 9.59/3.41  Parsing              : 0.21
% 9.59/3.41  CNF conversion       : 0.02
% 9.59/3.41  Main loop            : 1.77
% 9.59/3.41  Inferencing          : 0.59
% 9.59/3.41  Reduction            : 0.75
% 9.59/3.41  Demodulation         : 0.62
% 9.59/3.41  BG Simplification    : 0.07
% 9.59/3.41  Subsumption          : 0.22
% 9.59/3.41  Abstraction          : 0.09
% 9.59/3.41  MUC search           : 0.00
% 9.59/3.41  Cooper               : 0.00
% 9.59/3.41  Total                : 2.39
% 9.59/3.41  Index Insertion      : 0.00
% 9.59/3.41  Index Deletion       : 0.00
% 9.59/3.41  Index Matching       : 0.00
% 9.59/3.41  BG Taut test         : 0.00
%------------------------------------------------------------------------------