TSTP Solution File: GRP058-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP058-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n029.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 10:39:45 EDT 2023
% Result : Unsatisfiable 49.88s 24.21s
% Output : CNFRefutation 50.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of formulae : 207 ( 195 unt; 9 typ; 0 def)
% Number of atoms : 203 ( 200 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 17 ( 3 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 642 (; 642 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > c3 > b3 > b2 > b1 > a3 > a2 > a1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a1,type,
a1: $i ).
tff(a3,type,
a3: $i ).
tff(c3,type,
c3: $i ).
tff(b2,type,
b2: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b1,type,
b1: $i ).
tff(b3,type,
b3: $i ).
tff(a2,type,
a2: $i ).
tff(f_27,axiom,
! [X,Y,Z,U] : ( multiply(X,inverse(multiply(Y,multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(U,Y))),X)))) = U ),
file(unknown,unknown) ).
tff(f_35,axiom,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1,Y_2,Z_3,U_4] : ( multiply(X_1,inverse(multiply(Y_2,multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2))),X_1)))) = U_4 ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_5,plain,
! [X_5,Y_6,Z_7,U_8] : ( multiply(X_5,inverse(multiply(Y_6,multiply(multiply(multiply(Z_7,inverse(Z_7)),inverse(multiply(U_8,Y_6))),X_5)))) = U_8 ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_22,plain,
! [U_4,Z_3,X_1,X_5,Z_7,Y_2] : ( multiply(X_5,inverse(multiply(inverse(multiply(Y_2,multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2))),X_1))),multiply(multiply(multiply(Z_7,inverse(Z_7)),inverse(U_4)),X_5)))) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_36,plain,
! [Y_12,Z_10,Z_11,X_13,U_9] : ( multiply(X_13,inverse(multiply(multiply(multiply(multiply(Z_10,inverse(Z_10)),inverse(multiply(U_9,Y_12))),multiply(Z_11,inverse(Z_11))),multiply(U_9,X_13)))) = Y_12 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_141465,plain,
! [X_854,Z_851,Z_853,U_852,Y_856,Z_855] : ( multiply(multiply(multiply(Z_851,inverse(Z_851)),inverse(multiply(U_852,Y_856))),multiply(Z_853,inverse(Z_853))) = multiply(X_854,inverse(multiply(multiply(U_852,multiply(Z_855,inverse(Z_855))),multiply(Y_856,X_854)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_36]) ).
tff(c_141624,plain,
! [X_854,Z_853,U_852,Y_856,Z_855] : ( multiply(multiply(Z_853,inverse(Z_853)),inverse(multiply(Y_856,multiply(X_854,inverse(multiply(multiply(U_852,multiply(Z_855,inverse(Z_855))),multiply(Y_856,X_854))))))) = U_852 ),
inference(superposition,[status(thm),theory(equality)],[c_141465,c_2]) ).
tff(c_12,plain,
! [Z_3,Y_6,X_1,U_8,Z_7] : ( multiply(X_1,inverse(multiply(multiply(multiply(multiply(Z_7,inverse(Z_7)),inverse(multiply(U_8,Y_6))),multiply(Z_3,inverse(Z_3))),multiply(U_8,X_1)))) = Y_6 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_141967,plain,
! [U_862,Y_866,X_865,Z_864,Z_863] : ( multiply(multiply(Z_863,inverse(Z_863)),inverse(multiply(Y_866,multiply(X_865,inverse(multiply(multiply(U_862,multiply(Z_864,inverse(Z_864))),multiply(Y_866,X_865))))))) = U_862 ),
inference(superposition,[status(thm),theory(equality)],[c_141465,c_2]) ).
tff(c_142106,plain,
! [Z_870,U_868,Y_869,Z_867] : ( multiply(multiply(Z_870,inverse(Z_870)),inverse(multiply(U_868,Y_869))) = multiply(multiply(Z_867,inverse(Z_867)),inverse(multiply(U_868,Y_869))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_141967]) ).
tff(c_142621,plain,
! [X_854,Z_853,U_852,Z_867,Z_870,Y_856,Z_855] : ( multiply(multiply(Z_870,inverse(Z_870)),inverse(U_852)) = multiply(multiply(Z_867,inverse(Z_867)),inverse(multiply(multiply(Z_853,inverse(Z_853)),inverse(multiply(Y_856,multiply(X_854,inverse(multiply(multiply(U_852,multiply(Z_855,inverse(Z_855))),multiply(Y_856,X_854))))))))) ),
inference(superposition,[status(thm),theory(equality)],[c_141624,c_142106]) ).
tff(c_142839,plain,
! [Z_873,U_872,Z_871] : ( multiply(multiply(Z_873,inverse(Z_873)),inverse(U_872)) = multiply(multiply(Z_871,inverse(Z_871)),inverse(U_872)) ),
inference(demodulation,[status(thm),theory(equality)],[c_141624,c_142621]) ).
tff(c_143834,plain,
! [U_880,Z_881,Z_882] : ( multiply(inverse(U_880),inverse(multiply(inverse(Z_881),multiply(multiply(Z_882,inverse(Z_882)),inverse(U_880))))) = Z_881 ),
inference(superposition,[status(thm),theory(equality)],[c_142839,c_2]) ).
tff(c_143964,plain,
! [Y_883,Z_884,Z_885,X_886] : ( multiply(Y_883,multiply(multiply(multiply(Z_884,inverse(Z_884)),inverse(multiply(multiply(Z_885,inverse(Z_885)),Y_883))),X_886)) = X_886 ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_143834]) ).
tff(c_144272,plain,
! [Z_887,X_888] : ( multiply(Z_887,inverse(Z_887)) = multiply(X_888,inverse(X_888)) ),
inference(superposition,[status(thm),theory(equality)],[c_143964,c_2]) ).
tff(c_143900,plain,
! [Y_2,Z_3,Z_7,X_1] : ( multiply(Y_2,multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(multiply(Z_7,inverse(Z_7)),Y_2))),X_1)) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_143834]) ).
tff(c_144292,plain,
! [Z_7,Z_887,X_1] : ( multiply(inverse(multiply(Z_7,inverse(Z_7))),multiply(multiply(Z_887,inverse(Z_887)),X_1)) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_144272,c_143900]) ).
tff(c_144312,plain,
! [Y_2,X_888,Z_3,Z_7] : ( multiply(Y_2,multiply(X_888,inverse(X_888))) = inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(multiply(Z_7,inverse(Z_7)),Y_2)))) ),
inference(superposition,[status(thm),theory(equality)],[c_144272,c_143900]) ).
tff(c_144922,plain,
! [X_892,Z_893,X_894] : ( multiply(X_892,inverse(multiply(inverse(Z_893),multiply(multiply(X_894,inverse(X_894)),X_892)))) = Z_893 ),
inference(superposition,[status(thm),theory(equality)],[c_144272,c_2]) ).
tff(c_145053,plain,
! [X_1,X_894,Z_3,Z_893] : ( multiply(X_1,inverse(multiply(multiply(multiply(X_894,inverse(X_894)),multiply(Z_3,inverse(Z_3))),multiply(Z_893,X_1)))) = inverse(Z_893) ),
inference(superposition,[status(thm),theory(equality)],[c_144922,c_2]) ).
tff(c_145176,plain,
! [X_895,X_896,Z_897,Z_898] : ( multiply(X_895,inverse(multiply(multiply(multiply(X_896,inverse(X_896)),multiply(Z_897,inverse(Z_897))),multiply(Z_898,X_895)))) = inverse(Z_898) ),
inference(superposition,[status(thm),theory(equality)],[c_144922,c_2]) ).
tff(c_155855,plain,
! [Z_966,U_967,X_968,Z_969] : ( inverse(multiply(multiply(Z_966,inverse(Z_966)),inverse(multiply(U_967,multiply(multiply(X_968,inverse(X_968)),multiply(Z_969,inverse(Z_969))))))) = U_967 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_145176]) ).
tff(c_158396,plain,
! [X_973,Z_974,X_975] : ( multiply(multiply(X_973,inverse(X_973)),multiply(Z_974,inverse(Z_974))) = inverse(inverse(multiply(X_975,inverse(X_975)))) ),
inference(superposition,[status(thm),theory(equality)],[c_145053,c_155855]) ).
tff(c_159951,plain,
! [X_978,X_979,Z_980] : ( multiply(X_978,inverse(multiply(inverse(inverse(multiply(X_979,inverse(X_979)))),multiply(Z_980,X_978)))) = inverse(Z_980) ),
inference(superposition,[status(thm),theory(equality)],[c_158396,c_145053]) ).
tff(c_160161,plain,
! [Z_3,U_4,X_979] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(inverse(multiply(X_979,inverse(X_979)))))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_159951,c_2]) ).
tff(c_161358,plain,
! [Z_984,U_985,X_986] : ( inverse(multiply(multiply(Z_984,inverse(Z_984)),inverse(multiply(U_985,inverse(inverse(multiply(X_986,inverse(X_986)))))))) = U_985 ),
inference(superposition,[status(thm),theory(equality)],[c_159951,c_2]) ).
tff(c_162135,plain,
! [X_987,X_988,Z_989] : ( multiply(inverse(inverse(multiply(X_987,inverse(X_987)))),multiply(X_988,inverse(X_988))) = multiply(Z_989,inverse(Z_989)) ),
inference(superposition,[status(thm),theory(equality)],[c_161358,c_144312]) ).
tff(c_144664,plain,
! [Z_3,U_4,Y_2,X_888] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2)))),inverse(multiply(Y_2,multiply(X_888,inverse(X_888))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_144272,c_2]) ).
tff(c_162365,plain,
! [Z_3,U_4,X_987,Z_989] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(inverse(multiply(X_987,inverse(X_987)))))))),inverse(multiply(Z_989,inverse(Z_989)))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_162135,c_144664]) ).
tff(c_162942,plain,
! [U_990,Z_991] : ( multiply(U_990,inverse(multiply(Z_991,inverse(Z_991)))) = U_990 ),
inference(demodulation,[status(thm),theory(equality)],[c_160161,c_162365]) ).
tff(c_164484,plain,
! [U_996,Z_997,X_998] : ( multiply(U_996,multiply(inverse(multiply(Z_997,inverse(Z_997))),multiply(X_998,inverse(X_998)))) = U_996 ),
inference(superposition,[status(thm),theory(equality)],[c_144312,c_162942]) ).
tff(c_164584,plain,
! [Z_853,X_998,U_852,Z_997,Z_855] : ( multiply(multiply(Z_853,inverse(Z_853)),inverse(multiply(inverse(multiply(Z_997,inverse(Z_997))),multiply(multiply(X_998,inverse(X_998)),inverse(multiply(U_852,multiply(Z_855,inverse(Z_855)))))))) = U_852 ),
inference(superposition,[status(thm),theory(equality)],[c_164484,c_141624]) ).
tff(c_164900,plain,
! [Z_999,U_1000,Z_1001] : ( multiply(multiply(Z_999,inverse(Z_999)),inverse(inverse(multiply(U_1000,multiply(Z_1001,inverse(Z_1001)))))) = U_1000 ),
inference(demodulation,[status(thm),theory(equality)],[c_144292,c_164584]) ).
tff(c_165236,plain,
! [U_1002,Z_1003,Z_1004] : ( multiply(inverse(inverse(multiply(U_1002,multiply(Z_1003,inverse(Z_1003))))),inverse(multiply(inverse(Z_1004),U_1002))) = Z_1004 ),
inference(superposition,[status(thm),theory(equality)],[c_164900,c_2]) ).
tff(c_162929,plain,
! [U_4,Z_989] : ( multiply(U_4,inverse(multiply(Z_989,inverse(Z_989)))) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_160161,c_162365]) ).
tff(c_165642,plain,
! [Z_1005,Z_1006] : ( inverse(inverse(multiply(inverse(inverse(Z_1005)),multiply(Z_1006,inverse(Z_1006))))) = Z_1005 ),
inference(superposition,[status(thm),theory(equality)],[c_165236,c_162929]) ).
tff(c_164854,plain,
! [Z_853,U_852,Z_855] : ( multiply(multiply(Z_853,inverse(Z_853)),inverse(inverse(multiply(U_852,multiply(Z_855,inverse(Z_855)))))) = U_852 ),
inference(demodulation,[status(thm),theory(equality)],[c_144292,c_164584]) ).
tff(c_165672,plain,
! [Z_853,Z_1005] : ( multiply(multiply(Z_853,inverse(Z_853)),Z_1005) = inverse(inverse(Z_1005)) ),
inference(superposition,[status(thm),theory(equality)],[c_165642,c_164854]) ).
tff(c_55342,plain,
! [Y_372,X_370,Z_371,Z_367,Z_369,U_368] : ( multiply(multiply(multiply(Z_367,inverse(Z_367)),inverse(multiply(U_368,Y_372))),multiply(Z_369,inverse(Z_369))) = multiply(X_370,inverse(multiply(multiply(U_368,multiply(Z_371,inverse(Z_371))),multiply(Y_372,X_370)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_36]) ).
tff(c_55469,plain,
! [Y_372,X_370,Z_371,Z_369,U_368] : ( multiply(multiply(Z_369,inverse(Z_369)),inverse(multiply(Y_372,multiply(X_370,inverse(multiply(multiply(U_368,multiply(Z_371,inverse(Z_371))),multiply(Y_372,X_370))))))) = U_368 ),
inference(superposition,[status(thm),theory(equality)],[c_55342,c_2]) ).
tff(c_55725,plain,
! [Y_381,X_378,Z_379,U_380,Z_382] : ( multiply(multiply(Z_379,inverse(Z_379)),inverse(multiply(Y_381,multiply(X_378,inverse(multiply(multiply(U_380,multiply(Z_382,inverse(Z_382))),multiply(Y_381,X_378))))))) = U_380 ),
inference(superposition,[status(thm),theory(equality)],[c_55342,c_2]) ).
tff(c_55841,plain,
! [Z_386,U_384,Y_385,Z_383] : ( multiply(multiply(Z_386,inverse(Z_386)),inverse(multiply(U_384,Y_385))) = multiply(multiply(Z_383,inverse(Z_383)),inverse(multiply(U_384,Y_385))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_55725]) ).
tff(c_56252,plain,
! [Y_372,X_370,Z_383,Z_371,Z_369,Z_386,U_368] : ( multiply(multiply(Z_386,inverse(Z_386)),inverse(U_368)) = multiply(multiply(Z_383,inverse(Z_383)),inverse(multiply(multiply(Z_369,inverse(Z_369)),inverse(multiply(Y_372,multiply(X_370,inverse(multiply(multiply(U_368,multiply(Z_371,inverse(Z_371))),multiply(Y_372,X_370))))))))) ),
inference(superposition,[status(thm),theory(equality)],[c_55469,c_55841]) ).
tff(c_56406,plain,
! [Z_389,U_388,Z_387] : ( multiply(multiply(Z_389,inverse(Z_389)),inverse(U_388)) = multiply(multiply(Z_387,inverse(Z_387)),inverse(U_388)) ),
inference(demodulation,[status(thm),theory(equality)],[c_55469,c_56252]) ).
tff(c_57214,plain,
! [U_396,Z_397,Z_398] : ( multiply(inverse(U_396),inverse(multiply(inverse(Z_397),multiply(multiply(Z_398,inverse(Z_398)),inverse(U_396))))) = Z_397 ),
inference(superposition,[status(thm),theory(equality)],[c_56406,c_2]) ).
tff(c_8,plain,
! [Z_3,Y_6,X_1,U_8,X_5,Z_7] : ( multiply(X_1,inverse(multiply(inverse(multiply(Y_6,multiply(multiply(multiply(Z_7,inverse(Z_7)),inverse(multiply(U_8,Y_6))),X_5))),multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(U_8)),X_1)))) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).
tff(c_57334,plain,
! [Y_399,Z_400,Z_401,X_402] : ( multiply(Y_399,multiply(multiply(multiply(Z_400,inverse(Z_400)),inverse(multiply(multiply(Z_401,inverse(Z_401)),Y_399))),X_402)) = X_402 ),
inference(superposition,[status(thm),theory(equality)],[c_57214,c_8]) ).
tff(c_57602,plain,
! [Z_403,X_404] : ( multiply(Z_403,inverse(Z_403)) = multiply(X_404,inverse(X_404)) ),
inference(superposition,[status(thm),theory(equality)],[c_57334,c_2]) ).
tff(c_57224,plain,
! [Y_6,Z_7,Z_3,X_5] : ( multiply(Y_6,multiply(multiply(multiply(Z_7,inverse(Z_7)),inverse(multiply(multiply(Z_3,inverse(Z_3)),Y_6))),X_5)) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_57214,c_8]) ).
tff(c_57638,plain,
! [Z_3,X_404,X_5] : ( multiply(inverse(multiply(Z_3,inverse(Z_3))),multiply(multiply(X_404,inverse(X_404)),X_5)) = X_5 ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_57224]) ).
tff(c_57463,plain,
! [Z_401,X_402] : ( multiply(Z_401,inverse(Z_401)) = multiply(X_402,inverse(X_402)) ),
inference(superposition,[status(thm),theory(equality)],[c_57334,c_2]) ).
tff(c_58483,plain,
! [Z_412,X_413,X_414] : ( multiply(inverse(multiply(Z_412,inverse(Z_412))),multiply(multiply(X_413,inverse(X_413)),X_414)) = X_414 ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_57224]) ).
tff(c_58579,plain,
! [Z_412,Z_401,X_413] : ( multiply(inverse(multiply(Z_412,inverse(Z_412))),multiply(Z_401,inverse(Z_401))) = inverse(multiply(X_413,inverse(X_413))) ),
inference(superposition,[status(thm),theory(equality)],[c_57463,c_58483]) ).
tff(c_57999,plain,
! [X_405,Z_406,X_407] : ( multiply(X_405,inverse(multiply(inverse(Z_406),multiply(multiply(X_407,inverse(X_407)),X_405)))) = Z_406 ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_2]) ).
tff(c_58114,plain,
! [X_1,X_407,Z_3,Z_406] : ( multiply(X_1,inverse(multiply(multiply(multiply(X_407,inverse(X_407)),multiply(Z_3,inverse(Z_3))),multiply(Z_406,X_1)))) = inverse(Z_406) ),
inference(superposition,[status(thm),theory(equality)],[c_57999,c_2]) ).
tff(c_58226,plain,
! [X_408,X_409,Z_410,Z_411] : ( multiply(X_408,inverse(multiply(multiply(multiply(X_409,inverse(X_409)),multiply(Z_410,inverse(Z_410))),multiply(Z_411,X_408)))) = inverse(Z_411) ),
inference(superposition,[status(thm),theory(equality)],[c_57999,c_2]) ).
tff(c_68396,plain,
! [Z_482,U_483,X_484,Z_485] : ( inverse(multiply(multiply(Z_482,inverse(Z_482)),inverse(multiply(U_483,multiply(multiply(X_484,inverse(X_484)),multiply(Z_485,inverse(Z_485))))))) = U_483 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_58226]) ).
tff(c_70780,plain,
! [X_489,Z_490,X_491] : ( multiply(multiply(X_489,inverse(X_489)),multiply(Z_490,inverse(Z_490))) = inverse(inverse(multiply(X_491,inverse(X_491)))) ),
inference(superposition,[status(thm),theory(equality)],[c_58114,c_68396]) ).
tff(c_58473,plain,
! [Z_3,U_4,X_409,Z_410] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,multiply(multiply(X_409,inverse(X_409)),multiply(Z_410,inverse(Z_410))))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_58226]) ).
tff(c_70816,plain,
! [Z_3,U_4,X_491] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(inverse(multiply(X_491,inverse(X_491)))))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_70780,c_58473]) ).
tff(c_74957,plain,
! [Z_507,U_508,X_509] : ( inverse(multiply(multiply(Z_507,inverse(Z_507)),inverse(multiply(U_508,inverse(inverse(multiply(X_509,inverse(X_509)))))))) = U_508 ),
inference(superposition,[status(thm),theory(equality)],[c_70780,c_58473]) ).
tff(c_57626,plain,
! [Y_6,Z_403,Z_7,Z_3] : ( multiply(Y_6,multiply(Z_403,inverse(Z_403))) = inverse(multiply(multiply(Z_7,inverse(Z_7)),inverse(multiply(multiply(Z_3,inverse(Z_3)),Y_6)))) ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_57224]) ).
tff(c_75729,plain,
! [X_510,Z_511,Z_512] : ( multiply(inverse(inverse(multiply(X_510,inverse(X_510)))),multiply(Z_511,inverse(Z_511))) = multiply(Z_512,inverse(Z_512)) ),
inference(superposition,[status(thm),theory(equality)],[c_74957,c_57626]) ).
tff(c_57921,plain,
! [Z_3,U_4,Y_2,Z_403] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2)))),inverse(multiply(Y_2,multiply(Z_403,inverse(Z_403))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_2]) ).
tff(c_75962,plain,
! [Z_3,U_4,X_510,Z_512] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(inverse(multiply(X_510,inverse(X_510)))))))),inverse(multiply(Z_512,inverse(Z_512)))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_75729,c_57921]) ).
tff(c_76547,plain,
! [U_513,Z_514] : ( multiply(U_513,inverse(multiply(Z_514,inverse(Z_514)))) = U_513 ),
inference(demodulation,[status(thm),theory(equality)],[c_70816,c_75962]) ).
tff(c_77620,plain,
! [U_517,Z_518,Z_519] : ( multiply(U_517,multiply(inverse(multiply(Z_518,inverse(Z_518))),multiply(Z_519,inverse(Z_519)))) = U_517 ),
inference(superposition,[status(thm),theory(equality)],[c_58579,c_76547]) ).
tff(c_77723,plain,
! [Z_371,Z_519,Z_518,Z_369,U_368] : ( multiply(multiply(Z_369,inverse(Z_369)),inverse(multiply(inverse(multiply(Z_518,inverse(Z_518))),multiply(multiply(Z_519,inverse(Z_519)),inverse(multiply(U_368,multiply(Z_371,inverse(Z_371)))))))) = U_368 ),
inference(superposition,[status(thm),theory(equality)],[c_77620,c_55469]) ).
tff(c_78033,plain,
! [Z_520,U_521,Z_522] : ( multiply(multiply(Z_520,inverse(Z_520)),inverse(inverse(multiply(U_521,multiply(Z_522,inverse(Z_522)))))) = U_521 ),
inference(demodulation,[status(thm),theory(equality)],[c_57638,c_77723]) ).
tff(c_79290,plain,
! [Z_526,U_527,Z_528] : ( multiply(inverse(multiply(Z_526,inverse(Z_526))),U_527) = inverse(inverse(multiply(U_527,multiply(Z_528,inverse(Z_528))))) ),
inference(superposition,[status(thm),theory(equality)],[c_78033,c_57638]) ).
tff(c_77985,plain,
! [Z_369,U_368,Z_371] : ( multiply(multiply(Z_369,inverse(Z_369)),inverse(inverse(multiply(U_368,multiply(Z_371,inverse(Z_371)))))) = U_368 ),
inference(demodulation,[status(thm),theory(equality)],[c_57638,c_77723]) ).
tff(c_79341,plain,
! [Z_369,Z_526,U_527] : ( multiply(multiply(Z_369,inverse(Z_369)),multiply(inverse(multiply(Z_526,inverse(Z_526))),U_527)) = U_527 ),
inference(superposition,[status(thm),theory(equality)],[c_79290,c_77985]) ).
tff(c_76533,plain,
! [U_4,Z_512] : ( multiply(U_4,inverse(multiply(Z_512,inverse(Z_512)))) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_70816,c_75962]) ).
tff(c_80709,plain,
! [Z_529,Z_530,U_531] : ( multiply(multiply(Z_529,inverse(Z_529)),multiply(inverse(multiply(Z_530,inverse(Z_530))),U_531)) = U_531 ),
inference(superposition,[status(thm),theory(equality)],[c_79290,c_77985]) ).
tff(c_80837,plain,
! [Z_530,Z_371,Z_369,Z_529,U_368] : ( multiply(multiply(Z_369,inverse(Z_369)),inverse(inverse(multiply(multiply(U_368,multiply(Z_371,inverse(Z_371))),multiply(multiply(Z_529,inverse(Z_529)),inverse(multiply(Z_530,inverse(Z_530)))))))) = U_368 ),
inference(superposition,[status(thm),theory(equality)],[c_80709,c_55469]) ).
tff(c_81247,plain,
! [U_368,Z_371] : ( multiply(U_368,multiply(Z_371,inverse(Z_371))) = U_368 ),
inference(demodulation,[status(thm),theory(equality)],[c_77985,c_76533,c_80837]) ).
tff(c_81316,plain,
! [Z_3,U_4] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(U_4))) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_81247,c_81247,c_58473]) ).
tff(c_82303,plain,
! [Z_539,U_540] : ( inverse(multiply(multiply(Z_539,inverse(Z_539)),inverse(U_540))) = U_540 ),
inference(demodulation,[status(thm),theory(equality)],[c_81247,c_81247,c_58473]) ).
tff(c_83978,plain,
! [Z_546,Z_547] : ( multiply(Z_546,inverse(Z_546)) = inverse(multiply(Z_547,inverse(Z_547))) ),
inference(superposition,[status(thm),theory(equality)],[c_57463,c_82303]) ).
tff(c_84500,plain,
! [Z_3,U_4,Y_2,Z_547] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2)))),inverse(multiply(Y_2,inverse(multiply(Z_547,inverse(Z_547)))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_83978,c_2]) ).
tff(c_84744,plain,
! [U_548,Y_549] : ( multiply(multiply(U_548,Y_549),inverse(Y_549)) = U_548 ),
inference(demodulation,[status(thm),theory(equality)],[c_81316,c_76533,c_84500]) ).
tff(c_84729,plain,
! [U_4,Y_2] : ( multiply(multiply(U_4,Y_2),inverse(Y_2)) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_81316,c_76533,c_84500]) ).
tff(c_85029,plain,
! [U_550,Y_551] : ( multiply(U_550,inverse(inverse(Y_551))) = multiply(U_550,Y_551) ),
inference(superposition,[status(thm),theory(equality)],[c_84744,c_84729]) ).
tff(c_85103,plain,
! [Z_369,Z_526,Y_551] : ( multiply(multiply(Z_369,inverse(Z_369)),multiply(inverse(multiply(Z_526,inverse(Z_526))),Y_551)) = inverse(inverse(Y_551)) ),
inference(superposition,[status(thm),theory(equality)],[c_85029,c_79341]) ).
tff(c_85451,plain,
! [Y_551] : ( inverse(inverse(Y_551)) = Y_551 ),
inference(demodulation,[status(thm),theory(equality)],[c_79341,c_85103]) ).
tff(c_57930,plain,
! [X_1,Z_3,X_404] : ( multiply(X_1,inverse(multiply(inverse(Z_3),multiply(multiply(X_404,inverse(X_404)),X_1)))) = Z_3 ),
inference(superposition,[status(thm),theory(equality)],[c_57602,c_2]) ).
tff(c_52,plain,
! [Y_12,Z_10,Z_3,Z_11,X_1,X_13,U_9] : ( multiply(X_1,inverse(multiply(inverse(multiply(multiply(multiply(multiply(Z_10,inverse(Z_10)),inverse(multiply(U_9,Y_12))),multiply(Z_11,inverse(Z_11))),multiply(U_9,X_13))),multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(Y_12)),X_1)))) = X_13 ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_2]) ).
tff(c_85694,plain,
! [X_557,U_554,Z_553,Y_555,Z_556,X_558] : ( multiply(X_557,inverse(multiply(inverse(multiply(multiply(multiply(Z_556,inverse(Z_556)),inverse(multiply(U_554,Y_555))),multiply(U_554,X_558))),multiply(multiply(multiply(Z_553,inverse(Z_553)),inverse(Y_555)),X_557)))) = X_558 ),
inference(demodulation,[status(thm),theory(equality)],[c_81247,c_52]) ).
tff(c_86237,plain,
! [X_557,Z_553,X_404,Z_3,Z_556,X_558] : ( multiply(X_557,inverse(multiply(inverse(multiply(Z_3,multiply(inverse(Z_3),X_558))),multiply(multiply(multiply(Z_553,inverse(Z_553)),inverse(multiply(multiply(X_404,inverse(X_404)),multiply(Z_556,inverse(Z_556))))),X_557)))) = X_558 ),
inference(superposition,[status(thm),theory(equality)],[c_57930,c_85694]) ).
tff(c_86485,plain,
! [Z_3,X_558] : ( multiply(Z_3,multiply(inverse(Z_3),X_558)) = X_558 ),
inference(demodulation,[status(thm),theory(equality)],[c_57930,c_76533,c_81247,c_86237]) ).
tff(c_81313,plain,
! [Z_369,U_368] : ( multiply(multiply(Z_369,inverse(Z_369)),inverse(inverse(U_368))) = U_368 ),
inference(demodulation,[status(thm),theory(equality)],[c_81247,c_77985]) ).
tff(c_56386,plain,
! [Z_386,U_368,Z_383] : ( multiply(multiply(Z_386,inverse(Z_386)),inverse(U_368)) = multiply(multiply(Z_383,inverse(Z_383)),inverse(U_368)) ),
inference(demodulation,[status(thm),theory(equality)],[c_55469,c_56252]) ).
tff(c_68628,plain,
! [Z_485,Z_383,U_483,Z_386,X_484,Z_482] : ( multiply(multiply(Z_386,inverse(Z_386)),U_483) = multiply(multiply(Z_383,inverse(Z_383)),inverse(multiply(multiply(Z_482,inverse(Z_482)),inverse(multiply(U_483,multiply(multiply(X_484,inverse(X_484)),multiply(Z_485,inverse(Z_485)))))))) ),
inference(superposition,[status(thm),theory(equality)],[c_68396,c_56386]) ).
tff(c_68951,plain,
! [Z_386,U_483,Z_383] : ( multiply(multiply(Z_386,inverse(Z_386)),U_483) = multiply(multiply(Z_383,inverse(Z_383)),U_483) ),
inference(demodulation,[status(thm),theory(equality)],[c_58473,c_68628]) ).
tff(c_85417,plain,
! [Z_386,Y_551,Z_383] : ( multiply(multiply(Z_386,inverse(Z_386)),Y_551) = multiply(multiply(Z_383,inverse(Z_383)),inverse(inverse(Y_551))) ),
inference(superposition,[status(thm),theory(equality)],[c_68951,c_85029]) ).
tff(c_85469,plain,
! [Z_386,Y_551] : ( multiply(multiply(Z_386,inverse(Z_386)),Y_551) = Y_551 ),
inference(demodulation,[status(thm),theory(equality)],[c_81313,c_85417]) ).
tff(c_84994,plain,
! [U_4,Y_2,Z_3,X_1] : ( multiply(U_4,inverse(inverse(multiply(Y_2,multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2))),X_1))))) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_84744]) ).
tff(c_101228,plain,
! [U_649,Y_650,X_651] : ( multiply(U_649,multiply(Y_650,multiply(inverse(multiply(U_649,Y_650)),X_651))) = X_651 ),
inference(demodulation,[status(thm),theory(equality)],[c_85469,c_85451,c_84994]) ).
tff(c_101736,plain,
! [U_649,Y_650,X_558] : ( multiply(inverse(inverse(multiply(U_649,Y_650))),X_558) = multiply(U_649,multiply(Y_650,X_558)) ),
inference(superposition,[status(thm),theory(equality)],[c_86485,c_101228]) ).
tff(c_101882,plain,
! [U_649,Y_650,X_558] : ( multiply(multiply(U_649,Y_650),X_558) = multiply(U_649,multiply(Y_650,X_558)) ),
inference(demodulation,[status(thm),theory(equality)],[c_85451,c_101736]) ).
tff(c_4752,plain,
! [Z_84,Z_87,Z_89,X_88,Z_83,U_85,Y_86] : ( multiply(X_88,inverse(multiply(multiply(Y_86,multiply(Z_84,inverse(Z_84))),multiply(multiply(multiply(multiply(Z_87,inverse(Z_87)),inverse(multiply(U_85,Y_86))),multiply(Z_89,inverse(Z_89))),X_88)))) = multiply(U_85,multiply(Z_83,inverse(Z_83))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_12]) ).
tff(c_43,plain,
! [Y_12,Z_10,Z_3,Z_11,X_1,U_9,Z_7] : ( multiply(X_1,inverse(multiply(multiply(Y_12,multiply(Z_3,inverse(Z_3))),multiply(multiply(multiply(multiply(Z_10,inverse(Z_10)),inverse(multiply(U_9,Y_12))),multiply(Z_11,inverse(Z_11))),X_1)))) = multiply(U_9,multiply(Z_7,inverse(Z_7))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_12]) ).
tff(c_4787,plain,
! [U_85,Z_83,Z_7] : ( multiply(U_85,multiply(Z_83,inverse(Z_83))) = multiply(U_85,multiply(Z_7,inverse(Z_7))) ),
inference(superposition,[status(thm),theory(equality)],[c_4752,c_43]) ).
tff(c_2152,plain,
! [Y_57,Z_53,X_55,U_54,X_56,Z_52] : ( multiply(X_56,inverse(multiply(inverse(multiply(Y_57,multiply(multiply(multiply(Z_53,inverse(Z_53)),inverse(multiply(U_54,Y_57))),X_55))),multiply(multiply(multiply(Z_52,inverse(Z_52)),inverse(U_54)),X_56)))) = X_55 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_7162,plain,
! [Z_108,Y_106,Z_103,X_105,X_107,Z_102,U_104] : ( multiply(X_105,inverse(multiply(multiply(multiply(multiply(Z_102,inverse(Z_102)),inverse(U_104)),multiply(Z_103,inverse(Z_103))),multiply(X_107,X_105)))) = inverse(multiply(Y_106,multiply(multiply(multiply(Z_108,inverse(Z_108)),inverse(multiply(U_104,Y_106))),X_107))) ),
inference(superposition,[status(thm),theory(equality)],[c_2152,c_2]) ).
tff(c_8238,plain,
! [Y_106,Z_108,U_8,Y_6] : ( inverse(multiply(Y_106,multiply(multiply(multiply(Z_108,inverse(Z_108)),inverse(multiply(multiply(U_8,Y_6),Y_106))),U_8))) = Y_6 ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_7162]) ).
tff(c_11840,plain,
! [Y_133,Z_134,U_135,Y_136] : ( inverse(multiply(Y_133,multiply(multiply(multiply(Z_134,inverse(Z_134)),inverse(multiply(multiply(U_135,Y_136),Y_133))),U_135))) = Y_136 ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_7162]) ).
tff(c_158,plain,
! [Z_25,Z_20,Y_22,Z_23,U_21,X_24] : ( multiply(multiply(multiply(Z_23,inverse(Z_23)),inverse(multiply(U_21,Y_22))),multiply(Z_25,inverse(Z_25))) = multiply(X_24,inverse(multiply(multiply(U_21,multiply(Z_20,inverse(Z_20))),multiply(Y_22,X_24)))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_2]) ).
tff(c_257,plain,
! [Z_25,Z_20,Y_22,U_21,X_24] : ( multiply(multiply(Z_25,inverse(Z_25)),inverse(multiply(Y_22,multiply(X_24,inverse(multiply(multiply(U_21,multiply(Z_20,inverse(Z_20))),multiply(Y_22,X_24))))))) = U_21 ),
inference(superposition,[status(thm),theory(equality)],[c_158,c_2]) ).
tff(c_438,plain,
! [U_31,X_32,Z_34,Z_33,Y_35] : ( multiply(multiply(Z_34,inverse(Z_34)),inverse(multiply(Y_35,multiply(X_32,inverse(multiply(multiply(U_31,multiply(Z_33,inverse(Z_33))),multiply(Y_35,X_32))))))) = U_31 ),
inference(superposition,[status(thm),theory(equality)],[c_158,c_2]) ).
tff(c_1140,plain,
! [Z_48,U_46,Y_47,Z_45] : ( multiply(multiply(Z_48,inverse(Z_48)),inverse(multiply(U_46,Y_47))) = multiply(multiply(Z_45,inverse(Z_45)),inverse(multiply(U_46,Y_47))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_438]) ).
tff(c_1591,plain,
! [Z_25,Z_20,Y_22,Z_48,Z_45,U_21,X_24] : ( multiply(multiply(Z_48,inverse(Z_48)),inverse(U_21)) = multiply(multiply(Z_45,inverse(Z_45)),inverse(multiply(multiply(Z_25,inverse(Z_25)),inverse(multiply(Y_22,multiply(X_24,inverse(multiply(multiply(U_21,multiply(Z_20,inverse(Z_20))),multiply(Y_22,X_24))))))))) ),
inference(superposition,[status(thm),theory(equality)],[c_257,c_1140]) ).
tff(c_1679,plain,
! [Z_48,U_21,Z_45] : ( multiply(multiply(Z_48,inverse(Z_48)),inverse(U_21)) = multiply(multiply(Z_45,inverse(Z_45)),inverse(U_21)) ),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_1591]) ).
tff(c_12069,plain,
! [Z_134,Y_136,U_135,Z_48,Z_45,Y_133] : ( multiply(multiply(Z_48,inverse(Z_48)),Y_136) = multiply(multiply(Z_45,inverse(Z_45)),inverse(multiply(Y_133,multiply(multiply(multiply(Z_134,inverse(Z_134)),inverse(multiply(multiply(U_135,Y_136),Y_133))),U_135)))) ),
inference(superposition,[status(thm),theory(equality)],[c_11840,c_1679]) ).
tff(c_12599,plain,
! [Z_139,Y_138,Z_137] : ( multiply(multiply(Z_139,inverse(Z_139)),Y_138) = multiply(multiply(Z_137,inverse(Z_137)),Y_138) ),
inference(demodulation,[status(thm),theory(equality)],[c_8238,c_12069]) ).
tff(c_14811,plain,
! [Y_142,Y_143,Z_144] : ( inverse(multiply(inverse(multiply(Y_142,Y_143)),multiply(multiply(Z_144,inverse(Z_144)),Y_142))) = Y_143 ),
inference(superposition,[status(thm),theory(equality)],[c_12599,c_8238]) ).
tff(c_15280,plain,
! [Z_144,Y_143,Z_7] : ( inverse(multiply(inverse(multiply(inverse(multiply(Z_144,inverse(Z_144))),Y_143)),multiply(Z_7,inverse(Z_7)))) = Y_143 ),
inference(superposition,[status(thm),theory(equality)],[c_4787,c_14811]) ).
tff(c_12667,plain,
! [Y_138,Y_6,Z_137] : ( inverse(multiply(inverse(multiply(Y_138,Y_6)),multiply(multiply(Z_137,inverse(Z_137)),Y_138))) = Y_6 ),
inference(superposition,[status(thm),theory(equality)],[c_12599,c_8238]) ).
tff(c_20748,plain,
! [Z_165,Y_166,Z_167] : ( inverse(multiply(inverse(multiply(inverse(multiply(Z_165,inverse(Z_165))),Y_166)),multiply(Z_167,inverse(Z_167)))) = Y_166 ),
inference(superposition,[status(thm),theory(equality)],[c_4787,c_14811]) ).
tff(c_21490,plain,
! [Z_168,Y_169,Z_170] : ( multiply(multiply(Z_168,inverse(Z_168)),Y_169) = inverse(multiply(inverse(Y_169),multiply(Z_170,inverse(Z_170)))) ),
inference(superposition,[status(thm),theory(equality)],[c_12667,c_20748]) ).
tff(c_25546,plain,
! [Y_180,Z_181,Z_182] : ( multiply(Y_180,inverse(multiply(inverse(Z_181),inverse(multiply(inverse(Y_180),multiply(Z_182,inverse(Z_182))))))) = Z_181 ),
inference(superposition,[status(thm),theory(equality)],[c_21490,c_2]) ).
tff(c_5452,plain,
! [U_90,Z_92,Z_91] : ( multiply(U_90,multiply(Z_92,inverse(Z_92))) = multiply(U_90,multiply(Z_91,inverse(Z_91))) ),
inference(superposition,[status(thm),theory(equality)],[c_4752,c_43]) ).
tff(c_5836,plain,
! [Z_3,U_4,U_90,Z_91] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,U_90)))),inverse(multiply(U_90,multiply(Z_91,inverse(Z_91))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_5452,c_2]) ).
tff(c_25705,plain,
! [Z_181,Z_3,Z_182,Z_91] : ( multiply(inverse(Z_181),inverse(multiply(inverse(multiply(inverse(multiply(Z_3,inverse(Z_3))),multiply(Z_182,inverse(Z_182)))),multiply(Z_91,inverse(Z_91))))) = inverse(Z_181) ),
inference(superposition,[status(thm),theory(equality)],[c_25546,c_5836]) ).
tff(c_26149,plain,
! [Z_181,Z_182] : ( multiply(inverse(Z_181),multiply(Z_182,inverse(Z_182))) = inverse(Z_181) ),
inference(demodulation,[status(thm),theory(equality)],[c_15280,c_25705]) ).
tff(c_22640,plain,
! [Y_169,Z_3,Z_170] : ( multiply(Y_169,inverse(multiply(inverse(Z_3),inverse(multiply(inverse(Y_169),multiply(Z_170,inverse(Z_170))))))) = Z_3 ),
inference(superposition,[status(thm),theory(equality)],[c_21490,c_2]) ).
tff(c_26170,plain,
! [Y_169,Z_3] : ( multiply(Y_169,inverse(multiply(inverse(Z_3),inverse(inverse(Y_169))))) = Z_3 ),
inference(demodulation,[status(thm),theory(equality)],[c_26149,c_22640]) ).
tff(c_21199,plain,
! [Z_137,Y_138,Z_167] : ( multiply(multiply(Z_137,inverse(Z_137)),Y_138) = inverse(multiply(inverse(Y_138),multiply(Z_167,inverse(Z_167)))) ),
inference(superposition,[status(thm),theory(equality)],[c_12667,c_20748]) ).
tff(c_26171,plain,
! [Z_137,Y_138] : ( multiply(multiply(Z_137,inverse(Z_137)),Y_138) = inverse(inverse(Y_138)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26149,c_21199]) ).
tff(c_23029,plain,
! [Z_171,Z_172,Y_173] : ( multiply(multiply(Z_171,inverse(Z_171)),multiply(inverse(multiply(Z_172,inverse(Z_172))),Y_173)) = Y_173 ),
inference(superposition,[status(thm),theory(equality)],[c_21490,c_15280]) ).
tff(c_23068,plain,
! [Z_172,Y_173,Y_6] : ( inverse(multiply(inverse(multiply(multiply(inverse(multiply(Z_172,inverse(Z_172))),Y_173),Y_6)),Y_173)) = Y_6 ),
inference(superposition,[status(thm),theory(equality)],[c_23029,c_12667]) ).
tff(c_26174,plain,
! [Z_183,Z_184] : ( multiply(inverse(Z_183),multiply(Z_184,inverse(Z_184))) = inverse(Z_183) ),
inference(demodulation,[status(thm),theory(equality)],[c_15280,c_25705]) ).
tff(c_26389,plain,
! [Y_6,Z_184,Z_172,Y_173] : ( multiply(Y_6,multiply(Z_184,inverse(Z_184))) = inverse(multiply(inverse(multiply(multiply(inverse(multiply(Z_172,inverse(Z_172))),Y_173),Y_6)),Y_173)) ),
inference(superposition,[status(thm),theory(equality)],[c_23068,c_26174]) ).
tff(c_26555,plain,
! [Y_6,Z_184] : ( multiply(Y_6,multiply(Z_184,inverse(Z_184))) = Y_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_23068,c_26389]) ).
tff(c_1691,plain,
! [Z_51,U_50,Z_49] : ( multiply(multiply(Z_51,inverse(Z_51)),inverse(U_50)) = multiply(multiply(Z_49,inverse(Z_49)),inverse(U_50)) ),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_1591]) ).
tff(c_2555,plain,
! [U_58,Z_59,Z_60] : ( multiply(inverse(U_58),inverse(multiply(inverse(Z_59),multiply(multiply(Z_60,inverse(Z_60)),inverse(U_58))))) = Z_59 ),
inference(superposition,[status(thm),theory(equality)],[c_1691,c_2]) ).
tff(c_320,plain,
! [Z_28,X_29,U_26,X_27,Y_30] : ( multiply(X_29,inverse(multiply(multiply(X_27,inverse(multiply(multiply(U_26,multiply(Z_28,inverse(Z_28))),multiply(Y_30,X_27)))),multiply(U_26,X_29)))) = Y_30 ),
inference(superposition,[status(thm),theory(equality)],[c_158,c_12]) ).
tff(c_534,plain,
! [U_39,U_40,Z_36,X_37,Z_38] : ( multiply(multiply(Z_38,inverse(Z_38)),inverse(multiply(U_39,multiply(U_40,multiply(Z_36,inverse(Z_36)))))) = multiply(X_37,inverse(multiply(U_39,multiply(U_40,X_37)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_320]) ).
tff(c_430,plain,
! [Z_28,U_4,Z_3,X_29,U_26] : ( multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,multiply(U_26,multiply(Z_28,inverse(Z_28)))))) = multiply(X_29,inverse(multiply(U_4,multiply(U_26,X_29)))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_320]) ).
tff(c_547,plain,
! [X_37,U_39,U_40,X_29] : ( multiply(X_37,inverse(multiply(U_39,multiply(U_40,X_37)))) = multiply(X_29,inverse(multiply(U_39,multiply(U_40,X_29)))) ),
inference(superposition,[status(thm),theory(equality)],[c_534,c_430]) ).
tff(c_2700,plain,
! [X_61,Z_62,Z_63] : ( multiply(X_61,inverse(multiply(inverse(Z_62),multiply(multiply(Z_63,inverse(Z_63)),X_61)))) = Z_62 ),
inference(superposition,[status(thm),theory(equality)],[c_2555,c_547]) ).
tff(c_3828,plain,
! [X_73,Z_74,Z_75,Z_76] : ( multiply(X_73,inverse(multiply(multiply(multiply(Z_74,inverse(Z_74)),multiply(Z_75,inverse(Z_75))),multiply(Z_76,X_73)))) = inverse(Z_76) ),
inference(superposition,[status(thm),theory(equality)],[c_2700,c_2]) ).
tff(c_4108,plain,
! [Z_3,U_4,Z_74,Z_75] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,multiply(multiply(Z_74,inverse(Z_74)),multiply(Z_75,inverse(Z_75))))))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3828]) ).
tff(c_26571,plain,
! [Z_3,U_4] : ( inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(U_4))) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_26555,c_26555,c_4108]) ).
tff(c_27934,plain,
! [U_4] : ( inverse(inverse(inverse(inverse(U_4)))) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_26171,c_26571]) ).
tff(c_2538,plain,
! [Y_57,U_4,Z_3,Z_53,X_55,X_56,Y_2,Z_52] : ( multiply(X_56,inverse(multiply(inverse(multiply(Y_57,multiply(multiply(multiply(Z_53,inverse(Z_53)),inverse(multiply(multiply(Y_2,multiply(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,Y_2))),multiply(Z_52,inverse(Z_52)))),Y_57))),X_55))),multiply(U_4,X_56)))) = X_55 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_2152]) ).
tff(c_28827,plain,
! [X_206,U_205,Y_209,Y_207,X_208] : ( multiply(X_206,inverse(multiply(inverse(multiply(Y_207,multiply(inverse(inverse(inverse(multiply(multiply(Y_209,inverse(inverse(inverse(multiply(U_205,Y_209))))),Y_207)))),X_208))),multiply(U_205,X_206)))) = X_208 ),
inference(demodulation,[status(thm),theory(equality)],[c_26171,c_26171,c_26555,c_2538]) ).
tff(c_28963,plain,
! [X_206,Z_137,Y_138,Y_207,X_208] : ( multiply(X_206,inverse(multiply(inverse(multiply(Y_207,multiply(inverse(inverse(inverse(multiply(multiply(Y_138,inverse(inverse(inverse(inverse(inverse(Y_138)))))),Y_207)))),X_208))),multiply(multiply(Z_137,inverse(Z_137)),X_206)))) = X_208 ),
inference(superposition,[status(thm),theory(equality)],[c_26171,c_28827]) ).
tff(c_29247,plain,
! [Y_210,X_211] : ( multiply(Y_210,multiply(inverse(Y_210),X_211)) = X_211 ),
inference(demodulation,[status(thm),theory(equality)],[c_26170,c_27934,c_26171,c_27934,c_26171,c_28963]) ).
tff(c_27935,plain,
! [U_195] : ( inverse(inverse(inverse(inverse(U_195)))) = U_195 ),
inference(demodulation,[status(thm),theory(equality)],[c_26171,c_26571]) ).
tff(c_27953,plain,
! [Y_6,U_195] : ( multiply(Y_6,multiply(inverse(inverse(inverse(U_195))),U_195)) = Y_6 ),
inference(superposition,[status(thm),theory(equality)],[c_27935,c_26555]) ).
tff(c_29272,plain,
! [X_211] : ( inverse(inverse(X_211)) = X_211 ),
inference(superposition,[status(thm),theory(equality)],[c_29247,c_27953]) ).
tff(c_2934,plain,
! [Y_64,Z_65,Z_66,X_67] : ( multiply(Y_64,multiply(multiply(multiply(Z_65,inverse(Z_65)),inverse(multiply(multiply(Z_66,inverse(Z_66)),Y_64))),X_67)) = X_67 ),
inference(superposition,[status(thm),theory(equality)],[c_2555,c_22]) ).
tff(c_2571,plain,
! [X_29,Z_59,Z_60] : ( multiply(X_29,inverse(multiply(inverse(Z_59),multiply(multiply(Z_60,inverse(Z_60)),X_29)))) = Z_59 ),
inference(superposition,[status(thm),theory(equality)],[c_2555,c_547]) ).
tff(c_2953,plain,
! [Z_66,X_67] : ( multiply(Z_66,inverse(Z_66)) = multiply(X_67,inverse(X_67)) ),
inference(superposition,[status(thm),theory(equality)],[c_2934,c_2571]) ).
tff(c_28648,plain,
! [Y_203,Z_204] : ( multiply(Y_203,inverse(multiply(inverse(Z_204),inverse(inverse(Y_203))))) = Z_204 ),
inference(demodulation,[status(thm),theory(equality)],[c_26149,c_22640]) ).
tff(c_33277,plain,
! [Z_248,X_249] : ( multiply(Z_248,inverse(multiply(X_249,inverse(X_249)))) = Z_248 ),
inference(superposition,[status(thm),theory(equality)],[c_2953,c_28648]) ).
tff(c_38422,plain,
! [Z_279,X_280] : ( multiply(Z_279,inverse(multiply(inverse(X_280),X_280))) = Z_279 ),
inference(superposition,[status(thm),theory(equality)],[c_29272,c_33277]) ).
tff(c_26146,plain,
! [Z_3,U_4,Y_180] : ( multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(Y_180)))) = multiply(Y_180,inverse(U_4)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_25546]) ).
tff(c_26383,plain,
! [Z_3,U_4,Z_183] : ( multiply(inverse(multiply(multiply(Z_3,inverse(Z_3)),inverse(multiply(U_4,inverse(Z_183))))),inverse(inverse(Z_183))) = U_4 ),
inference(superposition,[status(thm),theory(equality)],[c_26174,c_2]) ).
tff(c_33012,plain,
! [Z_183,U_4] : ( multiply(inverse(multiply(Z_183,inverse(U_4))),Z_183) = U_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_29272,c_26146,c_26383]) ).
tff(c_33287,plain,
! [Z_248,X_249] : ( multiply(inverse(Z_248),Z_248) = multiply(X_249,inverse(X_249)) ),
inference(superposition,[status(thm),theory(equality)],[c_33277,c_33012]) ).
tff(c_43996,plain,
! [Z_307,X_308] : ( multiply(inverse(Z_307),Z_307) = multiply(inverse(X_308),X_308) ),
inference(superposition,[status(thm),theory(equality)],[c_38422,c_33287]) ).
tff(c_4,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 )
| ( multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_87,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(splitLeft,[status(thm)],[c_4]) ).
tff(c_44512,plain,
! [Z_307] : ( multiply(inverse(a1),a1) != multiply(inverse(Z_307),Z_307) ),
inference(superposition,[status(thm),theory(equality)],[c_43996,c_87]) ).
tff(c_55062,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_44512]) ).
tff(c_55063,plain,
( ( multiply(multiply(inverse(b2),b2),a2) != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(splitRight,[status(thm)],[c_4]) ).
tff(c_55078,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(splitLeft,[status(thm)],[c_55063]) ).
tff(c_140920,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_101882,c_55078]) ).
tff(c_140922,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(splitRight,[status(thm)],[c_55063]) ).
tff(c_143434,plain,
! [X_877,Z_874,X_878,Z_875,Y_879,U_876] : ( multiply(X_878,inverse(multiply(inverse(multiply(Y_879,multiply(multiply(multiply(Z_875,inverse(Z_875)),inverse(multiply(U_876,Y_879))),X_877))),multiply(multiply(multiply(Z_874,inverse(Z_874)),inverse(U_876)),X_878)))) = X_877 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5]) ).
tff(c_143786,plain,
! [X_878,Z_875,X_877,Z_874] : ( multiply(X_878,inverse(multiply(inverse(multiply(c3,multiply(multiply(multiply(Z_875,inverse(Z_875)),inverse(multiply(a3,multiply(b3,c3)))),X_877))),multiply(multiply(multiply(Z_874,inverse(Z_874)),inverse(multiply(a3,b3))),X_878)))) = X_877 ),
inference(superposition,[status(thm),theory(equality)],[c_140922,c_143434]) ).
tff(c_167504,plain,
! [X_878,X_877] : ( multiply(X_878,inverse(multiply(inverse(multiply(c3,multiply(inverse(inverse(inverse(multiply(a3,multiply(b3,c3))))),X_877))),multiply(inverse(inverse(inverse(multiply(a3,b3)))),X_878)))) = X_877 ),
inference(demodulation,[status(thm),theory(equality)],[c_165672,c_165672,c_143786]) ).
tff(c_163616,plain,
! [U_990,Z_7,X_888] : ( multiply(U_990,multiply(inverse(multiply(Z_7,inverse(Z_7))),multiply(X_888,inverse(X_888)))) = U_990 ),
inference(superposition,[status(thm),theory(equality)],[c_144312,c_162942]) ).
tff(c_161477,plain,
! [X_986,X_888,Z_7] : ( multiply(inverse(inverse(multiply(X_986,inverse(X_986)))),multiply(X_888,inverse(X_888))) = multiply(Z_7,inverse(Z_7)) ),
inference(superposition,[status(thm),theory(equality)],[c_161358,c_144312]) ).
tff(c_166783,plain,
! [X_1011,Z_1012] : ( multiply(X_1011,inverse(X_1011)) = inverse(inverse(multiply(Z_1012,inverse(Z_1012)))) ),
inference(superposition,[status(thm),theory(equality)],[c_161477,c_165642]) ).
tff(c_152261,plain,
! [Y_951,X_952,Z_953,Z_954] : ( multiply(Y_951,multiply(X_952,inverse(X_952))) = inverse(multiply(multiply(Z_953,inverse(Z_953)),inverse(multiply(multiply(Z_954,inverse(Z_954)),Y_951)))) ),
inference(superposition,[status(thm),theory(equality)],[c_144272,c_143900]) ).
tff(c_152276,plain,
! [Y_951,X_952,X_888] : ( multiply(Y_951,multiply(X_952,inverse(X_952))) = multiply(Y_951,multiply(X_888,inverse(X_888))) ),
inference(superposition,[status(thm),theory(equality)],[c_152261,c_144312]) ).
tff(c_166957,plain,
! [Y_951,Z_1012,X_1011,X_952] : ( multiply(Y_951,multiply(inverse(multiply(Z_1012,inverse(Z_1012))),multiply(X_1011,inverse(X_1011)))) = multiply(Y_951,multiply(X_952,inverse(X_952))) ),
inference(superposition,[status(thm),theory(equality)],[c_166783,c_152276]) ).
tff(c_167252,plain,
! [Y_951,X_952] : ( multiply(Y_951,multiply(X_952,inverse(X_952))) = Y_951 ),
inference(demodulation,[status(thm),theory(equality)],[c_163616,c_166957]) ).
tff(c_165246,plain,
! [Z_1004,Z_1003] : ( inverse(inverse(multiply(inverse(inverse(Z_1004)),multiply(Z_1003,inverse(Z_1003))))) = Z_1004 ),
inference(superposition,[status(thm),theory(equality)],[c_165236,c_162929]) ).
tff(c_166826,plain,
! [Z_1004,Z_1012,X_1011] : ( inverse(inverse(multiply(inverse(inverse(Z_1004)),multiply(inverse(multiply(Z_1012,inverse(Z_1012))),multiply(X_1011,inverse(X_1011)))))) = Z_1004 ),
inference(superposition,[status(thm),theory(equality)],[c_166783,c_165246]) ).
tff(c_167240,plain,
! [Z_1004] : ( inverse(inverse(inverse(inverse(Z_1004)))) = Z_1004 ),
inference(demodulation,[status(thm),theory(equality)],[c_163616,c_166826]) ).
tff(c_142809,plain,
! [Z_870,U_852,Z_867] : ( multiply(multiply(Z_870,inverse(Z_870)),inverse(U_852)) = multiply(multiply(Z_867,inverse(Z_867)),inverse(U_852)) ),
inference(demodulation,[status(thm),theory(equality)],[c_141624,c_142621]) ).
tff(c_144688,plain,
! [Z_867,Z_870,Z_887] : ( multiply(multiply(Z_867,inverse(Z_867)),inverse(multiply(Z_870,inverse(Z_870)))) = multiply(Z_887,inverse(Z_887)) ),
inference(superposition,[status(thm),theory(equality)],[c_142809,c_144272]) ).
tff(c_167833,plain,
! [X_1018,Y_1019,U_1020] : ( multiply(X_1018,inverse(multiply(Y_1019,multiply(inverse(inverse(inverse(multiply(U_1020,Y_1019)))),X_1018)))) = U_1020 ),
inference(demodulation,[status(thm),theory(equality)],[c_165672,c_2]) ).
tff(c_167994,plain,
! [U_1020,Y_1019,Z_867,Z_870] : ( multiply(inverse(inverse(inverse(inverse(multiply(U_1020,Y_1019))))),inverse(multiply(Y_1019,multiply(multiply(Z_867,inverse(Z_867)),inverse(multiply(Z_870,inverse(Z_870))))))) = U_1020 ),
inference(superposition,[status(thm),theory(equality)],[c_144688,c_167833]) ).
tff(c_168042,plain,
! [U_1021,Y_1022] : ( multiply(multiply(U_1021,Y_1022),inverse(Y_1022)) = U_1021 ),
inference(demodulation,[status(thm),theory(equality)],[c_167252,c_167240,c_162929,c_167994]) ).
tff(c_168038,plain,
! [U_1020,Y_1019] : ( multiply(multiply(U_1020,Y_1019),inverse(Y_1019)) = U_1020 ),
inference(demodulation,[status(thm),theory(equality)],[c_167252,c_167240,c_162929,c_167994]) ).
tff(c_168189,plain,
! [U_1023,Y_1024] : ( multiply(U_1023,inverse(inverse(Y_1024))) = multiply(U_1023,Y_1024) ),
inference(superposition,[status(thm),theory(equality)],[c_168042,c_168038]) ).
tff(c_168214,plain,
! [X_878,Y_1024] : ( multiply(X_878,inverse(multiply(inverse(multiply(c3,multiply(inverse(inverse(inverse(multiply(a3,multiply(b3,c3))))),Y_1024))),multiply(inverse(inverse(inverse(multiply(a3,b3)))),X_878)))) = inverse(inverse(Y_1024)) ),
inference(superposition,[status(thm),theory(equality)],[c_168189,c_167504]) ).
tff(c_168395,plain,
! [Y_1024] : ( inverse(inverse(Y_1024)) = Y_1024 ),
inference(demodulation,[status(thm),theory(equality)],[c_167504,c_168214]) ).
tff(c_168924,plain,
! [Z_1030,Z_1031] : ( multiply(multiply(Z_1030,inverse(Z_1030)),Z_1031) = Z_1031 ),
inference(demodulation,[status(thm),theory(equality)],[c_168395,c_165672]) ).
tff(c_169052,plain,
! [Y_1024,Z_1031] : ( multiply(multiply(inverse(Y_1024),Y_1024),Z_1031) = Z_1031 ),
inference(superposition,[status(thm),theory(equality)],[c_168395,c_168924]) ).
tff(c_140921,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(splitRight,[status(thm)],[c_55063]) ).
tff(c_169317,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_169052,c_140921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP058-1 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.12/0.34 % Computer : n029.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 : Thu Aug 3 22:33:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 49.88/24.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.04/24.24
% 50.04/24.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.04/24.29
% 50.04/24.29 Inference rules
% 50.04/24.29 ----------------------
% 50.04/24.29 #Ref : 1
% 50.04/24.29 #Sup : 46148
% 50.04/24.29 #Fact : 0
% 50.04/24.29 #Define : 0
% 50.04/24.29 #Split : 2
% 50.04/24.29 #Chain : 0
% 50.04/24.29 #Close : 0
% 50.04/24.29
% 50.04/24.29 Ordering : KBO
% 50.04/24.30
% 50.04/24.30 Simplification rules
% 50.04/24.30 ----------------------
% 50.04/24.30 #Subsume : 4182
% 50.04/24.30 #Demod : 30235
% 50.04/24.30 #Tautology : 8126
% 50.04/24.30 #SimpNegUnit : 0
% 50.04/24.30 #BackRed : 204
% 50.04/24.30
% 50.04/24.30 #Partial instantiations: 0
% 50.04/24.30 #Strategies tried : 1
% 50.04/24.30
% 50.04/24.30 Timing (in seconds)
% 50.04/24.30 ----------------------
% 50.04/24.30 Preprocessing : 0.41
% 50.04/24.30 Parsing : 0.21
% 50.04/24.30 CNF conversion : 0.02
% 50.04/24.30 Main loop : 22.71
% 50.04/24.30 Inferencing : 5.27
% 50.04/24.30 Reduction : 13.06
% 50.04/24.30 Demodulation : 12.34
% 50.04/24.30 BG Simplification : 0.93
% 50.04/24.30 Subsumption : 1.98
% 50.04/24.30 Abstraction : 1.51
% 50.04/24.30 MUC search : 0.00
% 50.04/24.30 Cooper : 0.00
% 50.04/24.30 Total : 23.23
% 50.04/24.30 Index Insertion : 0.00
% 50.04/24.30 Index Deletion : 0.00
% 50.04/24.30 Index Matching : 0.00
% 50.04/24.30 BG Taut test : 0.00
%------------------------------------------------------------------------------