%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP323-1 : TPTP v9.0.0. 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 : Wed Apr 9 06:25:56 PM UTC 2025
% Result : Unsatisfiable 14.73s 5.07s
% Output : CNFRefutation 15.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 568 ( 486 unt; 0 typ; 0 def)
% Number of atoms : 765 ( 732 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 436 ( 239 ~; 197 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 270 ( 270 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c8 > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(sk_c8,type,
sk_c8: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X5,X3,X1,X2,X4] :
( ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( inverse(X3) != sk_c7 )
| ( multiply(sk_c8,X4) != sk_c7 )
| ( multiply(X5,sk_c8) != X4 )
| ( inverse(X5) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( multiply(X2,sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
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_33228,plain,
! [X_406,Y_407,Z_408] : ( multiply(multiply(X_406,Y_407),Z_408) = multiply(X_406,multiply(Y_407,Z_408)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_33261,plain,
! [X_2,Z_408] : ( multiply(inverse(X_2),multiply(X_2,Z_408)) = multiply(identity,Z_408) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_33228]) ).
tff(c_33272,plain,
! [X_2,Z_408] : ( multiply(inverse(X_2),multiply(X_2,Z_408)) = Z_408 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33261]) ).
tff(c_33519,plain,
! [X_413,Z_414] : ( multiply(inverse(X_413),multiply(X_413,Z_414)) = Z_414 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33261]) ).
tff(c_33763,plain,
! [X_417,Z_418] : ( multiply(inverse(inverse(X_417)),Z_418) = multiply(X_417,Z_418) ),
inference(superposition,[status(thm),theory(equality)],[c_33272,c_33519]) ).
tff(c_33549,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_33519]) ).
tff(c_33770,plain,
! [X_417] : ( multiply(X_417,identity) = X_417 ),
inference(superposition,[status(thm),theory(equality)],[c_33763,c_33549]) ).
tff(c_16,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_117,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_24,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_14300,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_32,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_98,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_102,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_14324,plain,
! [X_156,Y_157,Z_158] : ( multiply(multiply(X_156,Y_157),Z_158) = multiply(X_156,multiply(Y_157,Z_158)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14363,plain,
! [Z_158] : ( multiply(sk_c7,multiply(sk_c1,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_14324]) ).
tff(c_14484,plain,
! [Z_161] : ( multiply(sk_c7,multiply(sk_c1,Z_161)) = Z_161 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14363]) ).
tff(c_14496,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14300,c_14484]) ).
tff(c_14500,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_117,c_14496]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_111,plain,
multiply(sk_c8,sk_c3) = sk_c7,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_52,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_122,plain,
multiply(sk_c2,sk_c8) = sk_c3,
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_66,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_85,plain,
inverse(sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_89,plain,
multiply(sk_c8,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_13607,plain,
! [X_146,Y_147,Z_148] : ( multiply(multiply(X_146,Y_147),Z_148) = multiply(X_146,multiply(Y_147,Z_148)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_13649,plain,
! [Z_148] : ( multiply(sk_c8,multiply(sk_c2,Z_148)) = multiply(identity,Z_148) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_13607]) ).
tff(c_13825,plain,
! [Z_152] : ( multiply(sk_c8,multiply(sk_c2,Z_152)) = Z_152 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13649]) ).
tff(c_13837,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_122,c_13825]) ).
tff(c_13841,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_13837]) ).
tff(c_13852,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13841,c_117]) ).
tff(c_153,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_186,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_153]) ).
tff(c_196,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_186]) ).
tff(c_495,plain,
! [X_21,Z_22] : ( multiply(inverse(X_21),multiply(X_21,Z_22)) = Z_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_186]) ).
tff(c_771,plain,
! [X_26,Z_27] : ( multiply(inverse(inverse(X_26)),Z_27) = multiply(X_26,Z_27) ),
inference(superposition,[status(thm),theory(equality)],[c_196,c_495]) ).
tff(c_546,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_495]) ).
tff(c_778,plain,
! [X_26] : ( multiply(X_26,identity) = X_26 ),
inference(superposition,[status(thm),theory(equality)],[c_771,c_546]) ).
tff(c_22,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_130,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_180,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_153]) ).
tff(c_198,plain,
! [Z_16] : ( multiply(sk_c7,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_180]) ).
tff(c_210,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_130,c_198]) ).
tff(c_214,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_117,c_210]) ).
tff(c_217,plain,
multiply(sk_c6,sk_c8) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_117]) ).
tff(c_528,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_217,c_495]) ).
tff(c_554,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_528]) ).
tff(c_218,plain,
multiply(sk_c8,sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_111]) ).
tff(c_183,plain,
! [Z_15] : ( multiply(sk_c8,multiply(sk_c2,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_153]) ).
tff(c_478,plain,
! [Z_20] : ( multiply(sk_c8,multiply(sk_c2,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_183]) ).
tff(c_490,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_122,c_478]) ).
tff(c_494,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_218,c_490]) ).
tff(c_570,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_554,c_494]) ).
tff(c_265,plain,
! [Z_17] : ( multiply(sk_c8,multiply(sk_c2,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_183]) ).
tff(c_277,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_122,c_265]) ).
tff(c_281,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_218,c_277]) ).
tff(c_286,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_281,c_217]) ).
tff(c_393,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_286,c_196]) ).
tff(c_399,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_393]) ).
tff(c_68,plain,
! [X2_9,X1_8,X5_6,X3_7] :
( ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_240,plain,
! [X2_9,X1_8,X5_6,X3_7] :
( ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c6 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_217,c_214,c_214,c_214,c_214,c_214,c_214,c_68]) ).
tff(c_241,plain,
multiply(sk_c8,sk_c6) != sk_c6,
inference(splitLeft,[status(thm)],[c_240]) ).
tff(c_285,plain,
multiply(sk_c6,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_281,c_241]) ).
tff(c_445,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_399,c_285]) ).
tff(c_446,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c8 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c6 )
| ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_240]) ).
tff(c_8636,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_778,c_570,c_554,c_554,c_778,c_570,c_554,c_554,c_778,c_570,c_554,c_2,c_554,c_554,c_778,c_570,c_554,c_570,c_446]) ).
tff(c_8638,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8636]) ).
tff(c_220,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_98]) ).
tff(c_612,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_570,c_220]) ).
tff(c_639,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_612,c_4]) ).
tff(c_685,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_639,c_196]) ).
tff(c_697,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_685]) ).
tff(c_702,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_697,c_612]) ).
tff(c_8640,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8638,c_702]) ).
tff(c_8641,plain,
! [X1_8,X5_6,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(splitRight,[status(thm)],[c_8636]) ).
tff(c_13540,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8641]) ).
tff(c_13542,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13540,c_702]) ).
tff(c_13543,plain,
! [X5_6,X1_8] :
( ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_8641]) ).
tff(c_13545,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_13543]) ).
tff(c_13547,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13545,c_702]) ).
tff(c_13550,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_13543]) ).
tff(c_13552,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13550,c_702]) ).
tff(c_13553,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_13850,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13841,c_13553]) ).
tff(c_13554,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_20,plain,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_13598,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_13554,c_20]) ).
tff(c_13843,plain,
multiply(sk_c4,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13841,c_13598]) ).
tff(c_13652,plain,
! [X_2,Z_148] : ( multiply(inverse(X_2),multiply(X_2,Z_148)) = multiply(identity,Z_148) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_13607]) ).
tff(c_13664,plain,
! [X_2,Z_148] : ( multiply(inverse(X_2),multiply(X_2,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13652]) ).
tff(c_14005,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_13843,c_13664]) ).
tff(c_14011,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13852,c_13850,c_14005]) ).
tff(c_18,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_13593,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_13554,c_18]) ).
tff(c_13844,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13841,c_13593]) ).
tff(c_14100,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14011,c_14011,c_13844]) ).
tff(c_14104,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14100,c_13664]) ).
tff(c_14110,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14104]) ).
tff(c_14024,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14011,c_102]) ).
tff(c_14215,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14110,c_14024]) ).
tff(c_13849,plain,
multiply(sk_c1,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13841,c_13554]) ).
tff(c_14087,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14011,c_14011,c_13849]) ).
tff(c_14114,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_14110,c_14110,c_14087]) ).
tff(c_14261,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14215,c_14114]) ).
tff(c_14263,plain,
multiply(sk_c2,sk_c8) != sk_c3,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_48,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_14307,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14263,c_48]) ).
tff(c_14503,plain,
multiply(sk_c8,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14500,c_14307]) ).
tff(c_54,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_14313,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14263,c_54]) ).
tff(c_56,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_14278,plain,
inverse(sk_c5) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_14263,c_56]) ).
tff(c_14282,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14278,c_4]) ).
tff(c_14351,plain,
! [Z_158] : ( multiply(sk_c8,multiply(sk_c5,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_14282,c_14324]) ).
tff(c_14579,plain,
! [Z_163] : ( multiply(sk_c8,multiply(sk_c5,Z_163)) = Z_163 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14351]) ).
tff(c_14591,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_14313,c_14579]) ).
tff(c_14595,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14503,c_14591]) ).
tff(c_14614,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14595,c_14503]) ).
tff(c_14369,plain,
! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14324]) ).
tff(c_14658,plain,
! [X_165,Z_166] : ( multiply(inverse(X_165),multiply(X_165,Z_166)) = Z_166 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14369]) ).
tff(c_14676,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14614,c_14658]) ).
tff(c_14704,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14676]) ).
tff(c_14624,plain,
multiply(sk_c6,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14595,c_89]) ).
tff(c_14800,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14704,c_14624]) ).
tff(c_14506,plain,
multiply(sk_c8,sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14500,c_111]) ).
tff(c_14615,plain,
multiply(sk_c6,sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14595,c_14506]) ).
tff(c_14793,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14704,c_2,c_14704,c_14615]) ).
tff(c_14622,plain,
multiply(sk_c2,sk_c6) != sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_14595,c_14263]) ).
tff(c_14774,plain,
multiply(sk_c2,identity) != sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_14704,c_14622]) ).
tff(c_14794,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_14793,c_14774]) ).
tff(c_14851,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14800,c_14794]) ).
tff(c_14853,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_14863,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14853,c_18]) ).
tff(c_14858,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_14853,c_20]) ).
tff(c_14262,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_14267,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14262,c_4]) ).
tff(c_14876,plain,
! [X_168,Y_169,Z_170] : ( multiply(multiply(X_168,Y_169),Z_170) = multiply(X_168,multiply(Y_169,Z_170)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14903,plain,
! [Z_170] : ( multiply(sk_c8,multiply(sk_c4,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_14267,c_14876]) ).
tff(c_15308,plain,
! [Z_178] : ( multiply(sk_c8,multiply(sk_c4,Z_178)) = Z_178 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14903]) ).
tff(c_15320,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_14858,c_15308]) ).
tff(c_15324,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14863,c_15320]) ).
tff(c_15329,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15324,c_14863]) ).
tff(c_14918,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14876]) ).
tff(c_15422,plain,
! [X_179,Z_180] : ( multiply(inverse(X_179),multiply(X_179,Z_180)) = Z_180 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14918]) ).
tff(c_15446,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_15329,c_15422]) ).
tff(c_15489,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15446]) ).
tff(c_15498,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15489,c_102]) ).
tff(c_14930,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = Z_170 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14918]) ).
tff(c_15692,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_15498,c_14930]) ).
tff(c_15704,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15692]) ).
tff(c_14852,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_14900,plain,
! [Z_170] : ( multiply(sk_c8,multiply(sk_c5,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_14282,c_14876]) ).
tff(c_14958,plain,
! [Z_173] : ( multiply(sk_c8,multiply(sk_c5,Z_173)) = Z_173 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14900]) ).
tff(c_14970,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_14852,c_14958]) ).
tff(c_15326,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15324,c_15324,c_14970]) ).
tff(c_15519,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15326,c_14930]) ).
tff(c_15525,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15519]) ).
tff(c_15331,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15324,c_14853]) ).
tff(c_15494,plain,
multiply(sk_c1,identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15489,c_15331]) ).
tff(c_15688,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15525,c_15494]) ).
tff(c_15708,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15704,c_15688]) ).
tff(c_15713,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15708]) ).
tff(c_15715,plain,
multiply(sk_c7,sk_c8) != sk_c6,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_14,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_16055,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_15715,c_14]) ).
tff(c_15714,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_16009,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15714,c_4]) ).
tff(c_16071,plain,
! [X_188,Y_189,Z_190] : ( multiply(multiply(X_188,Y_189),Z_190) = multiply(X_188,multiply(Y_189,Z_190)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16101,plain,
! [Z_190] : ( multiply(sk_c8,multiply(sk_c5,Z_190)) = multiply(identity,Z_190) ),
inference(superposition,[status(thm),theory(equality)],[c_16009,c_16071]) ).
tff(c_16207,plain,
! [Z_194] : ( multiply(sk_c8,multiply(sk_c5,Z_194)) = Z_194 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16101]) ).
tff(c_16219,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_16055,c_16207]) ).
tff(c_16113,plain,
! [X_2,Z_190] : ( multiply(inverse(X_2),multiply(X_2,Z_190)) = multiply(identity,Z_190) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_16071]) ).
tff(c_16230,plain,
! [X_195,Z_196] : ( multiply(inverse(X_195),multiply(X_195,Z_196)) = Z_196 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16113]) ).
tff(c_16248,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_16219,c_16230]) ).
tff(c_16321,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16248]) ).
tff(c_16040,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_16107,plain,
! [Z_190] : ( multiply(sk_c7,multiply(sk_c1,Z_190)) = multiply(identity,Z_190) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_16071]) ).
tff(c_16142,plain,
! [Z_192] : ( multiply(sk_c7,multiply(sk_c1,Z_192)) = Z_192 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16107]) ).
tff(c_16154,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16040,c_16142]) ).
tff(c_16158,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16154,c_15715]) ).
tff(c_16359,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_16321,c_16158]) ).
tff(c_15716,plain,
multiply(sk_c2,sk_c8) = sk_c3,
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_15781,plain,
! [X_182,Y_183,Z_184] : ( multiply(multiply(X_182,Y_183),Z_184) = multiply(X_182,multiply(Y_183,Z_184)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_15823,plain,
! [Z_184] : ( multiply(sk_c8,multiply(sk_c2,Z_184)) = multiply(identity,Z_184) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_15781]) ).
tff(c_15842,plain,
! [Z_185] : ( multiply(sk_c8,multiply(sk_c2,Z_185)) = Z_185 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15823]) ).
tff(c_15854,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_15716,c_15842]) ).
tff(c_15858,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_15854]) ).
tff(c_15867,plain,
multiply(sk_c7,sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15858,c_15715]) ).
tff(c_8,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_15758,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_15715,c_8]) ).
tff(c_15862,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_15858,c_15758]) ).
tff(c_16003,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15867,c_15862]) ).
tff(c_16005,plain,
multiply(sk_c2,sk_c8) != sk_c3,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_16047,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16005,c_48]) ).
tff(c_16004,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_10,plain,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_16061,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_15715,c_10]) ).
tff(c_16275,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_16061,c_16230]) ).
tff(c_16325,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16047,c_16004,c_16275]) ).
tff(c_16340,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16325,c_16047]) ).
tff(c_16513,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16321,c_2,c_16321,c_16340]) ).
tff(c_16514,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16359,c_16513]) ).
tff(c_16516,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_16526,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16516,c_18]) ).
tff(c_16515,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_16016,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16004,c_4]) ).
tff(c_16546,plain,
! [X_199,Y_200,Z_201] : ( multiply(multiply(X_199,Y_200),Z_201) = multiply(X_199,multiply(Y_200,Z_201)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16570,plain,
! [Z_201] : ( multiply(sk_c8,multiply(sk_c4,Z_201)) = multiply(identity,Z_201) ),
inference(superposition,[status(thm),theory(equality)],[c_16016,c_16546]) ).
tff(c_16627,plain,
! [Z_204] : ( multiply(sk_c8,multiply(sk_c4,Z_204)) = Z_204 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16570]) ).
tff(c_16639,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_16515,c_16627]) ).
tff(c_16643,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16526,c_16639]) ).
tff(c_16646,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16643,c_16526]) ).
tff(c_16585,plain,
! [X_2,Z_201] : ( multiply(inverse(X_2),multiply(X_2,Z_201)) = multiply(identity,Z_201) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_16546]) ).
tff(c_16597,plain,
! [X_2,Z_201] : ( multiply(inverse(X_2),multiply(X_2,Z_201)) = Z_201 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16585]) ).
tff(c_16806,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16646,c_16597]) ).
tff(c_16812,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16806]) ).
tff(c_16652,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16643,c_15715]) ).
tff(c_16819,plain,
multiply(identity,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16812,c_16652]) ).
tff(c_16827,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16819]) ).
tff(c_16829,plain,
multiply(sk_c8,sk_c3) != sk_c7,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_38,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_17215,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16829,c_38]) ).
tff(c_16847,plain,
multiply(sk_c2,sk_c8) = sk_c3,
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_16901,plain,
! [X_208,Y_209,Z_210] : ( multiply(multiply(X_208,Y_209),Z_210) = multiply(X_208,multiply(Y_209,Z_210)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16943,plain,
! [Z_210] : ( multiply(sk_c8,multiply(sk_c2,Z_210)) = multiply(identity,Z_210) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_16901]) ).
tff(c_17119,plain,
! [Z_213] : ( multiply(sk_c8,multiply(sk_c2,Z_213)) = Z_213 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16943]) ).
tff(c_17131,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_16847,c_17119]) ).
tff(c_16842,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_16873,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_16940,plain,
! [Z_210] : ( multiply(sk_c7,multiply(sk_c1,Z_210)) = multiply(identity,Z_210) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_16901]) ).
tff(c_16960,plain,
! [Z_211] : ( multiply(sk_c7,multiply(sk_c1,Z_211)) = Z_211 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16940]) ).
tff(c_16972,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16873,c_16960]) ).
tff(c_16976,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16842,c_16972]) ).
tff(c_17066,plain,
multiply(sk_c8,sk_c3) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16976,c_16829]) ).
tff(c_17135,plain,
sk_c8 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17131,c_17066]) ).
tff(c_16882,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16829,c_38]) ).
tff(c_17063,plain,
multiply(sk_c8,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16976,c_16882]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_16896,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_16829,c_40]) ).
tff(c_17062,plain,
multiply(sk_c4,sk_c8) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16976,c_16896]) ).
tff(c_16828,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_16833,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16828,c_4]) ).
tff(c_16937,plain,
! [Z_210] : ( multiply(sk_c8,multiply(sk_c4,Z_210)) = multiply(identity,Z_210) ),
inference(superposition,[status(thm),theory(equality)],[c_16833,c_16901]) ).
tff(c_17185,plain,
! [Z_215] : ( multiply(sk_c8,multiply(sk_c4,Z_215)) = Z_215 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16937]) ).
tff(c_17200,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_17062,c_17185]) ).
tff(c_17204,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17063,c_17200]) ).
tff(c_17206,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17135,c_17204]) ).
tff(c_17208,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_17222,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17208,c_20]) ).
tff(c_17235,plain,
! [X_216,Y_217,Z_218] : ( multiply(multiply(X_216,Y_217),Z_218) = multiply(X_216,multiply(Y_217,Z_218)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17268,plain,
! [Z_218] : ( multiply(sk_c8,multiply(sk_c4,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_16833,c_17235]) ).
tff(c_17354,plain,
! [Z_222] : ( multiply(sk_c8,multiply(sk_c4,Z_222)) = Z_222 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17268]) ).
tff(c_17366,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_17222,c_17354]) ).
tff(c_17370,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17215,c_17366]) ).
tff(c_17207,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_46,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_16852,plain,
inverse(sk_c5) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_16829,c_46]) ).
tff(c_16856,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16852,c_4]) ).
tff(c_17259,plain,
! [Z_218] : ( multiply(sk_c8,multiply(sk_c5,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_16856,c_17235]) ).
tff(c_17331,plain,
! [Z_221] : ( multiply(sk_c8,multiply(sk_c5,Z_221)) = Z_221 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17259]) ).
tff(c_17343,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_17207,c_17331]) ).
tff(c_17372,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17370,c_17370,c_17343]) ).
tff(c_17277,plain,
! [X_2,Z_218] : ( multiply(inverse(X_2),multiply(X_2,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17235]) ).
tff(c_17458,plain,
! [X_224,Z_225] : ( multiply(inverse(X_224),multiply(X_224,Z_225)) = Z_225 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17277]) ).
tff(c_17482,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17372,c_17458]) ).
tff(c_17518,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17482]) ).
tff(c_17274,plain,
! [Z_218] : ( multiply(sk_c8,multiply(sk_c2,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_17235]) ).
tff(c_17304,plain,
! [Z_220] : ( multiply(sk_c8,multiply(sk_c2,Z_220)) = Z_220 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17274]) ).
tff(c_17316,plain,
multiply(sk_c8,sk_c3) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_16847,c_17304]) ).
tff(c_17320,plain,
sk_c8 != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17316,c_16829]) ).
tff(c_17374,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17370,c_17320]) ).
tff(c_17531,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17518,c_17374]) ).
tff(c_17386,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17370,c_16828]) ).
tff(c_17529,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17518,c_17386]) ).
tff(c_17377,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17370,c_17222]) ).
tff(c_17581,plain,
multiply(sk_c4,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17518,c_17377]) ).
tff(c_17289,plain,
! [X_2,Z_218] : ( multiply(inverse(X_2),multiply(X_2,Z_218)) = Z_218 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17277]) ).
tff(c_17585,plain,
multiply(inverse(sk_c4),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17581,c_17289]) ).
tff(c_17591,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17529,c_17585]) ).
tff(c_17593,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17531,c_17591]) ).
tff(c_17595,plain,
multiply(sk_c2,sk_c8) != sk_c3,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_17620,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_17595,c_48]) ).
tff(c_17650,plain,
! [X_226,Y_227,Z_228] : ( multiply(multiply(X_226,Y_227),Z_228) = multiply(X_226,multiply(Y_227,Z_228)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17692,plain,
! [X_2,Z_228] : ( multiply(inverse(X_2),multiply(X_2,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17650]) ).
tff(c_17778,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_17692]) ).
tff(c_17704,plain,
! [X_2,Z_228] : ( multiply(inverse(X_2),multiply(X_2,Z_228)) = Z_228 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17692]) ).
tff(c_18089,plain,
! [X_235,Z_236] : ( multiply(inverse(inverse(X_235)),Z_236) = multiply(X_235,Z_236) ),
inference(superposition,[status(thm),theory(equality)],[c_17778,c_17704]) ).
tff(c_17835,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17778]) ).
tff(c_18096,plain,
! [X_235] : ( multiply(X_235,identity) = X_235 ),
inference(superposition,[status(thm),theory(equality)],[c_18089,c_17835]) ).
tff(c_17631,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_17686,plain,
! [Z_228] : ( multiply(sk_c7,multiply(sk_c1,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_17650]) ).
tff(c_17706,plain,
! [Z_229] : ( multiply(sk_c7,multiply(sk_c1,Z_229)) = Z_229 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17686]) ).
tff(c_17718,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17631,c_17706]) ).
tff(c_17722,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16842,c_17718]) ).
tff(c_17727,plain,
multiply(sk_c6,sk_c8) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17722,c_16842]) ).
tff(c_17805,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_17727,c_17778]) ).
tff(c_17843,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17805]) ).
tff(c_17726,plain,
multiply(sk_c8,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17722,c_17620]) ).
tff(c_17594,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_17626,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_17595,c_54]) ).
tff(c_17814,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_17626,c_17778]) ).
tff(c_17844,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17726,c_17594,c_17814]) ).
tff(c_17861,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17843,c_17844]) ).
tff(c_17742,plain,
! [X2_9,X1_8,X5_6,X3_7] :
( ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c6) != sk_c6 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c8 )
| ( multiply(sk_c6,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17722,c_17722,c_17722,c_17722,c_17722,c_17722,c_68]) ).
tff(c_17743,plain,
multiply(sk_c6,sk_c8) != sk_c6,
inference(splitLeft,[status(thm)],[c_17742]) ).
tff(c_17744,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17743,c_17727]) ).
tff(c_17745,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( multiply(sk_c8,sk_c6) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c8 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c6 )
| ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_17742]) ).
tff(c_25565,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_17861,c_17843,c_17843,c_18096,c_17861,c_17843,c_17843,c_18096,c_17861,c_17843,c_2,c_17843,c_17843,c_18096,c_17861,c_17843,c_17861,c_2,c_17843,c_17745]) ).
tff(c_25567,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_25565]) ).
tff(c_17599,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17594,c_4]) ).
tff(c_17850,plain,
multiply(sk_c6,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17844,c_17599]) ).
tff(c_17974,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17861,c_17850]) ).
tff(c_17852,plain,
inverse(sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17844,c_17594]) ).
tff(c_17935,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17861,c_17852]) ).
tff(c_17975,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17974,c_17935]) ).
tff(c_25569,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25567,c_17975]) ).
tff(c_25570,plain,
! [X1_8,X5_6,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(splitRight,[status(thm)],[c_25565]) ).
tff(c_29790,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_25570]) ).
tff(c_29792,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29790,c_17975]) ).
tff(c_29793,plain,
! [X5_6,X1_8] :
( ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_25570]) ).
tff(c_29795,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_29793]) ).
tff(c_29797,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29795,c_17975]) ).
tff(c_30546,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_29793]) ).
tff(c_30548,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30546,c_17975]) ).
tff(c_30549,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_30568,plain,
! [X_353,Y_354,Z_355] : ( multiply(multiply(X_353,Y_354),Z_355) = multiply(X_353,multiply(Y_354,Z_355)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_30598,plain,
! [Z_355] : ( multiply(sk_c8,multiply(sk_c4,Z_355)) = multiply(identity,Z_355) ),
inference(superposition,[status(thm),theory(equality)],[c_16833,c_30568]) ).
tff(c_30647,plain,
! [Z_358] : ( multiply(sk_c8,multiply(sk_c4,Z_358)) = Z_358 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30598]) ).
tff(c_30659,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_30549,c_30647]) ).
tff(c_30663,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17620,c_30659]) ).
tff(c_30669,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30663,c_17620]) ).
tff(c_30607,plain,
! [X_2,Z_355] : ( multiply(inverse(X_2),multiply(X_2,Z_355)) = multiply(identity,Z_355) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_30568]) ).
tff(c_30619,plain,
! [X_2,Z_355] : ( multiply(inverse(X_2),multiply(X_2,Z_355)) = Z_355 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30607]) ).
tff(c_30843,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_30669,c_30619]) ).
tff(c_30849,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30843]) ).
tff(c_30855,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_30849,c_98]) ).
tff(c_30868,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_30855,c_4]) ).
tff(c_30939,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_30868,c_30619]) ).
tff(c_30951,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30939]) ).
tff(c_30672,plain,
inverse(sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30663,c_17594]) ).
tff(c_30668,plain,
multiply(sk_c5,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30663,c_17626]) ).
tff(c_30902,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_30668,c_30619]) ).
tff(c_30908,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30672,c_30902]) ).
tff(c_30928,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_30908,c_30619]) ).
tff(c_30934,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30928]) ).
tff(c_30550,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_30666,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30663,c_30550]) ).
tff(c_30910,plain,
multiply(sk_c1,identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30849,c_30666]) ).
tff(c_30957,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_30934,c_30910]) ).
tff(c_31108,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30951,c_30957]) ).
tff(c_31110,plain,
multiply(sk_c7,sk_c8) != sk_c6,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_31135,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_31110,c_8]) ).
tff(c_31140,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_31110,c_10]) ).
tff(c_31166,plain,
! [X_362,Y_363,Z_364] : ( multiply(multiply(X_362,Y_363),Z_364) = multiply(X_362,multiply(Y_363,Z_364)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_31196,plain,
! [Z_364] : ( multiply(sk_c8,multiply(sk_c4,Z_364)) = multiply(identity,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_16833,c_31166]) ).
tff(c_31258,plain,
! [Z_367] : ( multiply(sk_c8,multiply(sk_c4,Z_367)) = Z_367 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31196]) ).
tff(c_31270,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31140,c_31258]) ).
tff(c_31274,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31135,c_31270]) ).
tff(c_31281,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31274,c_31135]) ).
tff(c_31205,plain,
! [X_2,Z_364] : ( multiply(inverse(X_2),multiply(X_2,Z_364)) = multiply(identity,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31166]) ).
tff(c_31217,plain,
! [X_2,Z_364] : ( multiply(inverse(X_2),multiply(X_2,Z_364)) = Z_364 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31205]) ).
tff(c_31447,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_31281,c_31217]) ).
tff(c_31453,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_31447]) ).
tff(c_31145,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_31199,plain,
! [Z_364] : ( multiply(sk_c7,multiply(sk_c1,Z_364)) = multiply(identity,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_31166]) ).
tff(c_31219,plain,
! [Z_365] : ( multiply(sk_c7,multiply(sk_c1,Z_365)) = Z_365 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31199]) ).
tff(c_31231,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_31145,c_31219]) ).
tff(c_31235,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31231,c_31110]) ).
tff(c_31459,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_31453,c_31235]) ).
tff(c_31462,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31453,c_98]) ).
tff(c_31279,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31274,c_31145]) ).
tff(c_31505,plain,
multiply(sk_c1,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31453,c_31279]) ).
tff(c_31509,plain,
multiply(inverse(sk_c1),sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31505,c_31217]) ).
tff(c_31515,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31462,c_31509]) ).
tff(c_31517,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31459,c_31515]) ).
tff(c_31518,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_31109,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_31114,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31109,c_4]) ).
tff(c_31539,plain,
! [X_372,Y_373,Z_374] : ( multiply(multiply(X_372,Y_373),Z_374) = multiply(X_372,multiply(Y_373,Z_374)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_31563,plain,
! [Z_374] : ( multiply(sk_c8,multiply(sk_c5,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_31114,c_31539]) ).
tff(c_31617,plain,
! [Z_377] : ( multiply(sk_c8,multiply(sk_c5,Z_377)) = Z_377 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31563]) ).
tff(c_31629,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31518,c_31617]) ).
tff(c_31575,plain,
! [X_2,Z_374] : ( multiply(inverse(X_2),multiply(X_2,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31539]) ).
tff(c_31657,plain,
! [X_379,Z_380] : ( multiply(inverse(X_379),multiply(X_379,Z_380)) = Z_380 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31575]) ).
tff(c_31678,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31629,c_31657]) ).
tff(c_31733,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_31678]) ).
tff(c_31696,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31140,c_31657]) ).
tff(c_31735,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31135,c_16828,c_31696]) ).
tff(c_31747,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31735,c_31135]) ).
tff(c_31839,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31733,c_2,c_31733,c_31747]) ).
tff(c_31749,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31735,c_31110]) ).
tff(c_31876,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31839,c_31733,c_31733,c_31749]) ).
tff(c_31878,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_28,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_31920,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_31878,c_28]) ).
tff(c_30,plain,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_31897,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_31878,c_30]) ).
tff(c_31877,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_31882,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31877,c_4]) ).
tff(c_31943,plain,
! [X_383,Y_384,Z_385] : ( multiply(multiply(X_383,Y_384),Z_385) = multiply(X_383,multiply(Y_384,Z_385)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_31967,plain,
! [Z_385] : ( multiply(sk_c8,multiply(sk_c4,Z_385)) = multiply(identity,Z_385) ),
inference(superposition,[status(thm),theory(equality)],[c_31882,c_31943]) ).
tff(c_32900,plain,
! [Z_402] : ( multiply(sk_c8,multiply(sk_c4,Z_402)) = Z_402 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31967]) ).
tff(c_32912,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31897,c_32900]) ).
tff(c_32916,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_32912]) ).
tff(c_32921,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32916,c_31920]) ).
tff(c_31976,plain,
! [X_2,Z_385] : ( multiply(inverse(X_2),multiply(X_2,Z_385)) = multiply(identity,Z_385) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31943]) ).
tff(c_33050,plain,
! [X_404,Z_405] : ( multiply(inverse(X_404),multiply(X_404,Z_405)) = Z_405 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31976]) ).
tff(c_33074,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32921,c_33050]) ).
tff(c_33113,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33074]) ).
tff(c_34,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_31911,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_31878,c_34]) ).
tff(c_36,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_31886,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_31887,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31878,c_31886]) ).
tff(c_31888,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_31893,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31888,c_4]) ).
tff(c_31964,plain,
! [Z_385] : ( multiply(sk_c8,multiply(sk_c5,Z_385)) = multiply(identity,Z_385) ),
inference(superposition,[status(thm),theory(equality)],[c_31893,c_31943]) ).
tff(c_31989,plain,
! [Z_386] : ( multiply(sk_c8,multiply(sk_c5,Z_386)) = Z_386 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31964]) ).
tff(c_32001,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31911,c_31989]) ).
tff(c_32918,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32916,c_32916,c_32001]) ).
tff(c_33068,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32918,c_33050]) ).
tff(c_33111,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33068]) ).
tff(c_32927,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32916,c_31877]) ).
tff(c_32925,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32916,c_31897]) ).
tff(c_32790,plain,
! [Z_400] : ( multiply(sk_c8,multiply(sk_c4,Z_400)) = Z_400 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31967]) ).
tff(c_32802,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31897,c_32790]) ).
tff(c_32806,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_32802]) ).
tff(c_32817,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32806,c_31877]) ).
tff(c_32815,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32806,c_31897]) ).
tff(c_32479,plain,
! [Z_395] : ( multiply(sk_c8,multiply(sk_c4,Z_395)) = Z_395 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31967]) ).
tff(c_32491,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31897,c_32479]) ).
tff(c_32495,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_32491]) ).
tff(c_32498,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32495,c_32495,c_32001]) ).
tff(c_32649,plain,
! [X_398,Z_399] : ( multiply(inverse(X_398),multiply(X_398,Z_399)) = Z_399 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31976]) ).
tff(c_32685,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32498,c_32649]) ).
tff(c_32715,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32685]) ).
tff(c_32507,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32495,c_31877]) ).
tff(c_32545,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32507,c_4]) ).
tff(c_32748,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32715,c_32545]) ).
tff(c_32735,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32715,c_32507]) ).
tff(c_32753,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32748,c_32735]) ).
tff(c_32501,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32495,c_31920]) ).
tff(c_32667,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32501,c_32649]) ).
tff(c_32713,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32667]) ).
tff(c_32313,plain,
! [Z_391] : ( multiply(sk_c8,multiply(sk_c4,Z_391)) = Z_391 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31967]) ).
tff(c_32325,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31897,c_32313]) ).
tff(c_32329,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_32325]) ).
tff(c_32339,plain,
inverse(sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32329,c_31888]) ).
tff(c_32335,plain,
multiply(sk_c5,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32329,c_31911]) ).
tff(c_32015,plain,
! [Z_387] : ( multiply(sk_c8,multiply(sk_c4,Z_387)) = Z_387 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31967]) ).
tff(c_32027,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31897,c_32015]) ).
tff(c_32031,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_32027]) ).
tff(c_32075,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32031,c_31920]) ).
tff(c_32116,plain,
! [X_389,Z_390] : ( multiply(inverse(X_389),multiply(X_389,Z_390)) = Z_390 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31976]) ).
tff(c_32134,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32075,c_32116]) ).
tff(c_32156,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32134]) ).
tff(c_32006,plain,
! [X2_9,X1_8,X5_6,X3_7] :
( ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_31920,c_68]) ).
tff(c_32007,plain,
multiply(sk_c7,sk_c8) != sk_c6,
inference(splitLeft,[status(thm)],[c_32006]) ).
tff(c_32073,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32031,c_32007]) ).
tff(c_32295,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32156,c_32073]) ).
tff(c_32296,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_32006]) ).
tff(c_32305,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c8 )
| ( multiply(X2_9,sk_c8) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_32296]) ).
tff(c_32396,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32329,c_32329,c_32305]) ).
tff(c_32447,plain,
inverse(sk_c5) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32335,c_32396]) ).
tff(c_32456,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32339,c_32447]) ).
tff(c_32457,plain,
! [X1_8,X5_6,X3_7] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_32296]) ).
tff(c_32465,plain,
! [X3_7] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_32457]) ).
tff(c_32567,plain,
! [X3_7] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32495,c_32465]) ).
tff(c_32645,plain,
inverse(sk_c6) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32501,c_32567]) ).
tff(c_32717,plain,
inverse(sk_c6) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_32713,c_32645]) ).
tff(c_32787,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32753,c_32715,c_32717]) ).
tff(c_32788,plain,
! [X5_6,X1_8] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_32457]) ).
tff(c_32789,plain,
! [X1_8] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_32788]) ).
tff(c_32876,plain,
! [X1_401] :
( ( inverse(X1_401) != sk_c6 )
| ( multiply(X1_401,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32806,c_32806,c_32789]) ).
tff(c_32879,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32815,c_32876]) ).
tff(c_32898,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32817,c_32879]) ).
tff(c_32899,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_32788]) ).
tff(c_32986,plain,
! [X5_403] :
( ( inverse(X5_403) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_403,sk_c6)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32916,c_32916,c_32916,c_32899]) ).
tff(c_32989,plain,
( ( inverse(sk_c4) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_32925,c_32986]) ).
tff(c_33006,plain,
multiply(sk_c6,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32927,c_32989]) ).
tff(c_33048,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32921,c_33006]) ).
tff(c_33115,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_33111,c_33048]) ).
tff(c_33141,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_33113,c_33115]) ).
tff(c_33143,plain,
inverse(sk_c2) != sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_58,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_33205,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_33143,c_58]) ).
tff(c_60,plain,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_33189,plain,
multiply(sk_c4,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_33143,c_60]) ).
tff(c_62,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_33144,plain,
inverse(sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_62]) ).
tff(c_33152,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_33143,c_33144]) ).
tff(c_33153,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_33158,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33153,c_4]) ).
tff(c_33258,plain,
! [Z_408] : ( multiply(sk_c8,multiply(sk_c4,Z_408)) = multiply(identity,Z_408) ),
inference(superposition,[status(thm),theory(equality)],[c_33158,c_33228]) ).
tff(c_33297,plain,
! [Z_410] : ( multiply(sk_c8,multiply(sk_c4,Z_410)) = Z_410 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33258]) ).
tff(c_33309,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_33189,c_33297]) ).
tff(c_33313,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33205,c_33309]) ).
tff(c_64,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_33200,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_33143,c_64]) ).
tff(c_33142,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_33165,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33142,c_4]) ).
tff(c_33255,plain,
! [Z_408] : ( multiply(sk_c8,multiply(sk_c5,Z_408)) = multiply(identity,Z_408) ),
inference(superposition,[status(thm),theory(equality)],[c_33165,c_33228]) ).
tff(c_33274,plain,
! [Z_409] : ( multiply(sk_c8,multiply(sk_c5,Z_409)) = Z_409 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33255]) ).
tff(c_33286,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_33200,c_33274]) ).
tff(c_33315,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33313,c_33313,c_33286]) ).
tff(c_33620,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_33315,c_33272]) ).
tff(c_33626,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33620]) ).
tff(c_33317,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33313,c_33205]) ).
tff(c_33590,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_33317,c_33272]) ).
tff(c_33596,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33590]) ).
tff(c_33390,plain,
! [X_411,Z_412] : ( multiply(inverse(X_411),multiply(X_411,Z_412)) = Z_412 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33261]) ).
tff(c_33423,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_33317,c_33390]) ).
tff(c_33451,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33423]) ).
tff(c_33411,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_33315,c_33390]) ).
tff(c_33449,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33411]) ).
tff(c_33336,plain,
! [X2_9,X1_8,X5_6,X3_7] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_33313,c_33313,c_33313,c_33313,c_33313,c_33313,c_33313,c_33313,c_33313,c_33313,c_68]) ).
tff(c_33337,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(splitLeft,[status(thm)],[c_33336]) ).
tff(c_33516,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33451,c_33449,c_33449,c_33337]) ).
tff(c_33517,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_33336]) ).
tff(c_40194,plain,
! [X3_7,X5_6,X1_8,X2_9] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_33770,c_33626,c_33626,c_33626,c_33770,c_33626,c_33596,c_33626,c_33770,c_33626,c_2,c_33626,c_33596,c_33626,c_33770,c_33626,c_33596,c_33596,c_33626,c_2,c_33626,c_33596,c_33517]) ).
tff(c_40196,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_40194]) ).
tff(c_33323,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33313,c_33153]) ).
tff(c_33562,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33323,c_4]) ).
tff(c_33672,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33626,c_33562]) ).
tff(c_33630,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33626,c_33323]) ).
tff(c_33677,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33672,c_33630]) ).
tff(c_40198,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40196,c_33677]) ).
tff(c_40199,plain,
! [X1_8,X5_6,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(splitRight,[status(thm)],[c_40194]) ).
tff(c_42821,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_40199]) ).
tff(c_42823,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42821,c_33677]) ).
tff(c_42824,plain,
! [X5_6,X1_8] :
( ( inverse(X5_6) != identity )
| ( identity != X5_6 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_40199]) ).
tff(c_42826,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_42824]) ).
tff(c_42828,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42826,c_33677]) ).
tff(c_43240,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_42824]) ).
tff(c_43242,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43240,c_33677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP323-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:42:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 14.73/5.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.73/5.13
% 14.73/5.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------