TSTP Solution File: GRP383-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP383-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:41:08 EDT 2023
% Result : Unsatisfiable 22.29s 11.62s
% Output : CNFRefutation 22.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 592 ( 470 unt; 11 typ; 0 def)
% Number of atoms : 809 ( 782 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 457 ( 229 ~; 228 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 279 (; 279 !; 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_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_203,axiom,
! [X5,X3,X1,X2,X4] :
( ( inverse(sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( inverse(X3) != sk_c8 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( multiply(X4,X5) != sk_c7 )
| ( inverse(X4) != X5 )
| ( multiply(X5,sk_c8) != sk_c7 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( inverse(X1) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( inverse(X2) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_158,axiom,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_155,axiom,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_164,axiom,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_161,axiom,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_100488,plain,
! [X_682,Y_683,Z_684] : ( multiply(multiply(X_682,Y_683),Z_684) = multiply(X_682,multiply(Y_683,Z_684)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_100521,plain,
! [X_2,Z_684] : ( multiply(inverse(X_2),multiply(X_2,Z_684)) = multiply(identity,Z_684) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_100488]) ).
tff(c_100899,plain,
! [X_693,Z_694] : ( multiply(inverse(X_693),multiply(X_693,Z_694)) = Z_694 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100521]) ).
tff(c_100534,plain,
! [X_2,Z_684] : ( multiply(inverse(X_2),multiply(X_2,Z_684)) = Z_684 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100521]) ).
tff(c_101677,plain,
! [X_709,Z_710] : ( multiply(inverse(inverse(X_709)),Z_710) = multiply(X_709,Z_710) ),
inference(superposition,[status(thm),theory(equality)],[c_100899,c_100534]) ).
tff(c_100929,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_100899]) ).
tff(c_101684,plain,
! [X_709] : ( multiply(X_709,identity) = X_709 ),
inference(superposition,[status(thm),theory(equality)],[c_101677,c_100929]) ).
tff(c_101698,plain,
! [X_709] : ( multiply(X_709,inverse(X_709)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_101677,c_4]) ).
tff(c_101094,plain,
! [X_696,Z_697] : ( multiply(inverse(inverse(X_696)),Z_697) = multiply(X_696,Z_697) ),
inference(superposition,[status(thm),theory(equality)],[c_100534,c_100899]) ).
tff(c_101101,plain,
! [X_696] : ( multiply(X_696,identity) = X_696 ),
inference(superposition,[status(thm),theory(equality)],[c_101094,c_100929]) ).
tff(c_83396,plain,
! [X_532,Y_533,Z_534] : ( multiply(multiply(X_532,Y_533),Z_534) = multiply(X_532,multiply(Y_533,Z_534)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_83429,plain,
! [X_2,Z_534] : ( multiply(inverse(X_2),multiply(X_2,Z_534)) = multiply(identity,Z_534) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_83396]) ).
tff(c_83662,plain,
! [X_540,Z_541] : ( multiply(inverse(X_540),multiply(X_540,Z_541)) = Z_541 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83429]) ).
tff(c_83442,plain,
! [X_2,Z_534] : ( multiply(inverse(X_2),multiply(X_2,Z_534)) = Z_534 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83429]) ).
tff(c_84749,plain,
! [X_561,Z_562] : ( multiply(inverse(inverse(X_561)),Z_562) = multiply(X_561,Z_562) ),
inference(superposition,[status(thm),theory(equality)],[c_83662,c_83442]) ).
tff(c_83716,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_83662]) ).
tff(c_84766,plain,
! [X_561] : ( multiply(X_561,identity) = X_561 ),
inference(superposition,[status(thm),theory(equality)],[c_84749,c_83716]) ).
tff(c_84780,plain,
! [X_561] : ( multiply(X_561,inverse(X_561)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_84749,c_4]) ).
tff(c_84094,plain,
! [X_548,Z_549] : ( multiply(inverse(inverse(X_548)),Z_549) = multiply(X_548,Z_549) ),
inference(superposition,[status(thm),theory(equality)],[c_83442,c_83662]) ).
tff(c_84114,plain,
! [X_548] : ( multiply(X_548,identity) = X_548 ),
inference(superposition,[status(thm),theory(equality)],[c_84094,c_83716]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_119,plain,
inverse(sk_c1) = sk_c8,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_124,plain,
multiply(sk_c8,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_119,c_4]) ).
tff(c_10,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_107,plain,
inverse(sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_111,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_107,c_4]) ).
tff(c_82748,plain,
! [X_515,Y_516,Z_517] : ( multiply(multiply(X_515,Y_516),Z_517) = multiply(X_515,multiply(Y_516,Z_517)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_82781,plain,
! [Z_517] : ( multiply(sk_c7,multiply(sk_c8,Z_517)) = multiply(identity,Z_517) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_82748]) ).
tff(c_82826,plain,
! [Z_519] : ( multiply(sk_c7,multiply(sk_c8,Z_519)) = Z_519 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82781]) ).
tff(c_82847,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_82826]) ).
tff(c_48,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_82316,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_48]) ).
tff(c_82317,plain,
multiply(sk_c2,sk_c3) = sk_c7,
inference(splitLeft,[status(thm)],[c_82316]) ).
tff(c_64,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_95,plain,
inverse(sk_c2) = sk_c3,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_99,plain,
multiply(sk_c3,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_95,c_4]) ).
tff(c_82349,plain,
! [X_505,Y_506,Z_507] : ( multiply(multiply(X_505,Y_506),Z_507) = multiply(X_505,multiply(Y_506,Z_507)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_82388,plain,
! [Z_507] : ( multiply(sk_c3,multiply(sk_c2,Z_507)) = multiply(identity,Z_507) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_82349]) ).
tff(c_82409,plain,
! [Z_508] : ( multiply(sk_c3,multiply(sk_c2,Z_508)) = Z_508 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82388]) ).
tff(c_82421,plain,
multiply(sk_c3,sk_c7) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_82317,c_82409]) ).
tff(c_82391,plain,
! [X_2,Z_507] : ( multiply(inverse(X_2),multiply(X_2,Z_507)) = multiply(identity,Z_507) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_82349]) ).
tff(c_82526,plain,
! [X_512,Z_513] : ( multiply(inverse(X_512),multiply(X_512,Z_513)) = Z_513 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82391]) ).
tff(c_82556,plain,
multiply(inverse(sk_c3),sk_c3) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_82421,c_82526]) ).
tff(c_82607,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_82556]) ).
tff(c_82385,plain,
! [Z_507] : ( multiply(sk_c7,multiply(sk_c8,Z_507)) = multiply(identity,Z_507) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_82349]) ).
tff(c_82474,plain,
! [Z_511] : ( multiply(sk_c7,multiply(sk_c8,Z_511)) = Z_511 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82385]) ).
tff(c_82498,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_82474]) ).
tff(c_82615,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82607,c_82498]) ).
tff(c_82627,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82615]) ).
tff(c_24073,plain,
! [X_229,Y_230,Z_231] : ( multiply(multiply(X_229,Y_230),Z_231) = multiply(X_229,multiply(Y_230,Z_231)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_24115,plain,
! [X_2,Z_231] : ( multiply(inverse(X_2),multiply(X_2,Z_231)) = multiply(identity,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_24073]) ).
tff(c_24504,plain,
! [X_238,Z_239] : ( multiply(inverse(X_238),multiply(X_238,Z_239)) = Z_239 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24115]) ).
tff(c_24130,plain,
! [X_2,Z_231] : ( multiply(inverse(X_2),multiply(X_2,Z_231)) = Z_231 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24115]) ).
tff(c_26092,plain,
! [X_265,Z_266] : ( multiply(inverse(inverse(X_265)),Z_266) = multiply(X_265,Z_266) ),
inference(superposition,[status(thm),theory(equality)],[c_24504,c_24130]) ).
tff(c_26116,plain,
! [X_265] : ( multiply(X_265,inverse(X_265)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_26092,c_4]) ).
tff(c_24549,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_24504]) ).
tff(c_26102,plain,
! [X_265] : ( multiply(X_265,identity) = X_265 ),
inference(superposition,[status(thm),theory(equality)],[c_26092,c_24549]) ).
tff(c_24797,plain,
! [X_243,Z_244] : ( multiply(inverse(inverse(X_243)),Z_244) = multiply(X_243,Z_244) ),
inference(superposition,[status(thm),theory(equality)],[c_24130,c_24504]) ).
tff(c_24807,plain,
! [X_243] : ( multiply(X_243,identity) = X_243 ),
inference(superposition,[status(thm),theory(equality)],[c_24797,c_24549]) ).
tff(c_24109,plain,
! [Z_231] : ( multiply(sk_c7,multiply(sk_c8,Z_231)) = multiply(identity,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_24073]) ).
tff(c_24440,plain,
! [Z_237] : ( multiply(sk_c7,multiply(sk_c8,Z_237)) = Z_237 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24109]) ).
tff(c_24461,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_24440]) ).
tff(c_22881,plain,
! [X_203,Y_204,Z_205] : ( multiply(multiply(X_203,Y_204),Z_205) = multiply(X_203,multiply(Y_204,Z_205)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22917,plain,
! [Z_205] : ( multiply(sk_c7,multiply(sk_c8,Z_205)) = multiply(identity,Z_205) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_22881]) ).
tff(c_23019,plain,
! [Z_209] : ( multiply(sk_c7,multiply(sk_c8,Z_209)) = Z_209 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22917]) ).
tff(c_23046,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_23019]) ).
tff(c_44,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_22824,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_22914,plain,
! [Z_205] : ( multiply(sk_c8,multiply(sk_c1,Z_205)) = multiply(identity,Z_205) ),
inference(superposition,[status(thm),theory(equality)],[c_124,c_22881]) ).
tff(c_22954,plain,
! [Z_207] : ( multiply(sk_c8,multiply(sk_c1,Z_207)) = Z_207 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22914]) ).
tff(c_22966,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22824,c_22954]) ).
tff(c_22977,plain,
! [Z_208] : ( multiply(sk_c1,multiply(sk_c7,Z_208)) = multiply(sk_c8,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_22824,c_22881]) ).
tff(c_22995,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c1,identity),
inference(superposition,[status(thm),theory(equality)],[c_111,c_22977]) ).
tff(c_22999,plain,
multiply(sk_c1,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22966,c_22995]) ).
tff(c_22934,plain,
! [Z_205] : ( multiply(sk_c8,multiply(sk_c1,Z_205)) = Z_205 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22914]) ).
tff(c_23003,plain,
multiply(sk_c8,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22999,c_22934]) ).
tff(c_22923,plain,
! [X_2,Z_205] : ( multiply(inverse(X_2),multiply(X_2,Z_205)) = multiply(identity,Z_205) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22881]) ).
tff(c_23062,plain,
! [X_210,Z_211] : ( multiply(inverse(X_210),multiply(X_210,Z_211)) = Z_211 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22923]) ).
tff(c_23086,plain,
multiply(inverse(sk_c8),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23003,c_23062]) ).
tff(c_23156,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_23046,c_107,c_23086]) ).
tff(c_22394,plain,
! [X_194,Y_195,Z_196] : ( multiply(multiply(X_194,Y_195),Z_196) = multiply(X_194,multiply(Y_195,Z_196)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22433,plain,
! [Z_196] : ( multiply(sk_c7,multiply(sk_c8,Z_196)) = multiply(identity,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_22394]) ).
tff(c_22482,plain,
! [Z_198] : ( multiply(sk_c7,multiply(sk_c8,Z_198)) = Z_198 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22433]) ).
tff(c_22503,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_22482]) ).
tff(c_180,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_216,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_180]) ).
tff(c_459,plain,
! [X_22,Z_23] : ( multiply(inverse(X_22),multiply(X_22,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_216]) ).
tff(c_519,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_459]) ).
tff(c_227,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_216]) ).
tff(c_770,plain,
! [X_27,Z_28] : ( multiply(inverse(inverse(X_27)),Z_28) = multiply(X_27,Z_28) ),
inference(superposition,[status(thm),theory(equality)],[c_459,c_227]) ).
tff(c_804,plain,
! [X_2] : ( multiply(X_2,identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_519,c_770]) ).
tff(c_795,plain,
! [X_27] : ( multiply(X_27,inverse(X_27)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_770,c_4]) ).
tff(c_50,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_154,plain,
multiply(sk_c2,sk_c3) = sk_c7,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_213,plain,
! [Z_15] : ( multiply(sk_c3,multiply(sk_c2,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_180]) ).
tff(c_420,plain,
! [Z_20] : ( multiply(sk_c3,multiply(sk_c2,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_213]) ).
tff(c_432,plain,
multiply(sk_c3,sk_c7) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_154,c_420]) ).
tff(c_480,plain,
multiply(inverse(sk_c3),sk_c3) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_432,c_459]) ).
tff(c_527,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_480]) ).
tff(c_20,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_140,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_78,plain,
! [X2_9,X1_8,X4_10,X3_7] :
( ( multiply(X2_9,sk_c6) != sk_c7 )
| ( inverse(X2_9) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_230,plain,
! [X2_9,X1_8,X4_10,X3_7] :
( ( multiply(X2_9,sk_c6) != sk_c7 )
| ( inverse(X2_9) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( sk_c6 != identity )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_107,c_140,c_111,c_78]) ).
tff(c_231,plain,
sk_c6 != identity,
inference(splitLeft,[status(thm)],[c_230]) ).
tff(c_232,plain,
! [Z_16] : ( multiply(sk_c3,multiply(sk_c2,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_213]) ).
tff(c_244,plain,
multiply(sk_c3,sk_c7) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_154,c_232]) ).
tff(c_278,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_216]) ).
tff(c_302,plain,
multiply(inverse(sk_c3),sk_c3) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_244,c_278]) ).
tff(c_350,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_302]) ).
tff(c_360,plain,
multiply(identity,sk_c6) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_350,c_140]) ).
tff(c_364,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_360]) ).
tff(c_363,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_350,c_107]) ).
tff(c_376,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_364,c_363]) ).
tff(c_383,plain,
multiply(identity,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_376,c_4]) ).
tff(c_390,plain,
multiply(inverse(identity),identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_383,c_227]) ).
tff(c_402,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_390]) ).
tff(c_404,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_231,c_402]) ).
tff(c_406,plain,
sk_c6 = identity,
inference(splitRight,[status(thm)],[c_230]) ).
tff(c_407,plain,
multiply(sk_c7,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_406,c_140]) ).
tff(c_501,plain,
multiply(inverse(sk_c8),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_459]) ).
tff(c_530,plain,
sk_c8 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_407,c_107,c_501]) ).
tff(c_538,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_530,c_119]) ).
tff(c_540,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_530,c_107]) ).
tff(c_573,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_538,c_527,c_540]) ).
tff(c_576,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_573,c_530]) ).
tff(c_405,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X2_9,sk_c6) != sk_c7 )
| ( inverse(X2_9) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_230]) ).
tff(c_822,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_527,c_527,c_406,c_576,c_576,c_527,c_527,c_576,c_527,c_576,c_576,c_527,c_405]) ).
tff(c_823,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_822]) ).
tff(c_1155,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_804,c_823]) ).
tff(c_575,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_573,c_573,c_538]) ).
tff(c_1157,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1155,c_575]) ).
tff(c_1158,plain,
! [X1_8,X4_10,X3_7] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity ) ),
inference(splitRight,[status(thm)],[c_822]) ).
tff(c_22316,plain,
! [X1_8,X4_10,X3_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity )
| ( identity != X3_7 )
| ( inverse(X3_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_804,c_795,c_804,c_804,c_1158]) ).
tff(c_22318,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22316]) ).
tff(c_22320,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22318,c_575]) ).
tff(c_22321,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_22316]) ).
tff(c_22323,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22321]) ).
tff(c_22325,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22323,c_575]) ).
tff(c_22326,plain,
! [X4_10] : ( inverse(X4_10) != identity ),
inference(splitRight,[status(thm)],[c_22321]) ).
tff(c_22329,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22326,c_575]) ).
tff(c_22331,plain,
multiply(sk_c2,sk_c3) != sk_c7,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_22371,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_48]) ).
tff(c_22372,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_22331,c_22371]) ).
tff(c_22373,plain,
multiply(sk_c7,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_22372,c_140]) ).
tff(c_22507,plain,
sk_c8 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22503,c_22373]) ).
tff(c_22525,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22507,c_119]) ).
tff(c_22527,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22507,c_107]) ).
tff(c_22599,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22525,c_22527]) ).
tff(c_54,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_22343,plain,
inverse(sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22331,c_54]) ).
tff(c_56,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_22382,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22372,c_56]) ).
tff(c_22383,plain,
multiply(sk_c5,identity) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22331,c_22382]) ).
tff(c_22439,plain,
! [X_2,Z_196] : ( multiply(inverse(X_2),multiply(X_2,Z_196)) = multiply(identity,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22394]) ).
tff(c_22539,plain,
! [X_199,Z_200] : ( multiply(inverse(X_199),multiply(X_199,Z_200)) = Z_200 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22439]) ).
tff(c_22566,plain,
multiply(inverse(sk_c5),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22383,c_22539]) ).
tff(c_22588,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22343,c_22566]) ).
tff(c_22641,plain,
multiply(sk_c1,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22599,c_22599,c_22588]) ).
tff(c_22330,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_22521,plain,
inverse(sk_c4) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22507,c_22330]) ).
tff(c_52,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_22389,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_22331,c_52]) ).
tff(c_22519,plain,
multiply(sk_c4,sk_c7) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22507,c_22389]) ).
tff(c_22667,plain,
multiply(sk_c4,sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22599,c_22519]) ).
tff(c_22454,plain,
! [X_2,Z_196] : ( multiply(inverse(X_2),multiply(X_2,Z_196)) = Z_196 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22439]) ).
tff(c_22671,plain,
multiply(inverse(sk_c4),sk_c1) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_22667,c_22454]) ).
tff(c_22677,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22641,c_22521,c_22671]) ).
tff(c_22684,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22677,c_22599]) ).
tff(c_22687,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22677,c_22507]) ).
tff(c_70,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_135,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_22427,plain,
! [Z_196] : ( multiply(sk_c3,multiply(sk_c8,Z_196)) = multiply(sk_c7,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_22394]) ).
tff(c_22776,plain,
! [Z_202] : ( multiply(sk_c3,Z_202) = Z_202 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22684,c_2,c_22687,c_22427]) ).
tff(c_22788,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_22776,c_99]) ).
tff(c_22614,plain,
multiply(sk_c2,sk_c3) != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_22599,c_22331]) ).
tff(c_22758,plain,
multiply(sk_c2,sk_c3) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22677,c_22614]) ).
tff(c_22798,plain,
multiply(identity,sk_c3) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22788,c_22758]) ).
tff(c_22801,plain,
sk_c3 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22798]) ).
tff(c_22335,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22330,c_4]) ).
tff(c_22500,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_22335,c_22482]) ).
tff(c_22654,plain,
multiply(sk_c1,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_22599,c_22500]) ).
tff(c_22680,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_22677,c_22654]) ).
tff(c_22688,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22680]) ).
tff(c_22686,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22677,c_22521]) ).
tff(c_22721,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22688,c_22686]) ).
tff(c_22800,plain,
inverse(identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_22788,c_95]) ).
tff(c_22803,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22721,c_22800]) ).
tff(c_22810,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22801,c_22803]) ).
tff(c_22812,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_24,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_22835,plain,
inverse(sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22812,c_24]) ).
tff(c_18,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_22860,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_18]) ).
tff(c_22861,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_22812,c_22860]) ).
tff(c_22862,plain,
multiply(sk_c7,identity) != sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_22861,c_22812]) ).
tff(c_26,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_22870,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( multiply(sk_c7,identity) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22861,c_22861,c_26]) ).
tff(c_22871,plain,
multiply(sk_c5,identity) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22862,c_22870]) ).
tff(c_23107,plain,
multiply(inverse(sk_c5),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22871,c_23062]) ).
tff(c_23161,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22835,c_23107]) ).
tff(c_23232,plain,
multiply(sk_c1,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23156,c_23156,c_23161]) ).
tff(c_23095,plain,
multiply(inverse(sk_c8),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_22966,c_23062]) ).
tff(c_23159,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_107,c_23095]) ).
tff(c_23265,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23232,c_23156,c_23156,c_23159]) ).
tff(c_23050,plain,
sk_c8 != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_23046,c_22862]) ).
tff(c_23268,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_23265,c_23050]) ).
tff(c_22811,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_22816,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22811,c_4]) ).
tff(c_23122,plain,
multiply(inverse(sk_c8),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_22816,c_23062]) ).
tff(c_23164,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_23046,c_107,c_23122]) ).
tff(c_23043,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_22816,c_23019]) ).
tff(c_23248,plain,
multiply(sk_c1,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_23156,c_23164,c_23043]) ).
tff(c_23190,plain,
multiply(sk_c1,sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23156,c_111]) ).
tff(c_23346,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23248,c_23265,c_23190]) ).
tff(c_23347,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23268,c_23346]) ).
tff(c_23349,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_23864,plain,
! [X_223,Y_224,Z_225] : ( multiply(multiply(X_223,Y_224),Z_225) = multiply(X_223,multiply(Y_224,Z_225)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_23897,plain,
! [Z_225] : ( multiply(sk_c7,multiply(sk_c8,Z_225)) = multiply(identity,Z_225) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_23864]) ).
tff(c_23934,plain,
! [Z_227] : ( multiply(sk_c7,multiply(sk_c8,Z_227)) = Z_227 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23897]) ).
tff(c_23952,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_23934]) ).
tff(c_23949,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_22816,c_23934]) ).
tff(c_23987,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_23952,c_23949]) ).
tff(c_42,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_23832,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_23349,c_42]) ).
tff(c_23988,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_23987,c_23832]) ).
tff(c_23992,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23349,c_23988]) ).
tff(c_23994,plain,
multiply(sk_c3,sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_68,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_24050,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_68]) ).
tff(c_24051,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_23994,c_24050]) ).
tff(c_22,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_24033,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_24052,plain,
multiply(sk_c7,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_24051,c_24033]) ).
tff(c_24465,plain,
sk_c8 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24461,c_24052]) ).
tff(c_24483,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24465,c_119]) ).
tff(c_24485,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_24465,c_107]) ).
tff(c_24557,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24483,c_24485]) ).
tff(c_74,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_24009,plain,
inverse(sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_23994,c_74]) ).
tff(c_76,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_24062,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_24051,c_76]) ).
tff(c_24063,plain,
multiply(sk_c5,identity) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_23994,c_24062]) ).
tff(c_24534,plain,
multiply(inverse(sk_c5),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_24063,c_24504]) ).
tff(c_24556,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24009,c_24534]) ).
tff(c_24576,plain,
multiply(sk_c1,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24557,c_24557,c_24556]) ).
tff(c_23993,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_24481,plain,
inverse(sk_c4) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24465,c_23993]) ).
tff(c_72,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_24038,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_23994,c_72]) ).
tff(c_24478,plain,
multiply(sk_c4,sk_c7) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24465,c_24038]) ).
tff(c_24603,plain,
multiply(sk_c4,sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24557,c_24478]) ).
tff(c_24607,plain,
multiply(inverse(sk_c4),sk_c1) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_24603,c_24130]) ).
tff(c_24613,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24576,c_24481,c_24607]) ).
tff(c_24619,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24613,c_24557]) ).
tff(c_24622,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24613,c_24465]) ).
tff(c_24158,plain,
! [Z_233] : ( multiply(sk_c7,multiply(sk_c8,Z_233)) = Z_233 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24109]) ).
tff(c_24179,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_24158]) ).
tff(c_24183,plain,
sk_c8 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24179,c_24052]) ).
tff(c_24201,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24183,c_119]) ).
tff(c_24203,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_24183,c_107]) ).
tff(c_24275,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24201,c_24203]) ).
tff(c_24222,plain,
! [X_234,Z_235] : ( multiply(inverse(X_234),multiply(X_234,Z_235)) = Z_235 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24115]) ).
tff(c_24252,plain,
multiply(inverse(sk_c5),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_24063,c_24222]) ).
tff(c_24274,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24009,c_24252]) ).
tff(c_24294,plain,
multiply(sk_c1,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24275,c_24275,c_24274]) ).
tff(c_24199,plain,
inverse(sk_c4) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24183,c_23993]) ).
tff(c_24196,plain,
multiply(sk_c4,sk_c7) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24183,c_24038]) ).
tff(c_24321,plain,
multiply(sk_c4,sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_24275,c_24196]) ).
tff(c_24325,plain,
multiply(inverse(sk_c4),sk_c1) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_24321,c_24130]) ).
tff(c_24331,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24294,c_24199,c_24325]) ).
tff(c_23998,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_23993,c_4]) ).
tff(c_24176,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_23998,c_24158]) ).
tff(c_24308,plain,
multiply(sk_c1,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_24275,c_24176]) ).
tff(c_24334,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_24331,c_24308]) ).
tff(c_24341,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24334]) ).
tff(c_24339,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24331,c_24199]) ).
tff(c_24374,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24341,c_24339]) ).
tff(c_24340,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24331,c_24183]) ).
tff(c_24337,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24331,c_24275]) ).
tff(c_24156,plain,
! [X2_9,X1_8,X4_10,X3_7] :
( ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_107,c_24052,c_24051,c_24051,c_111,c_24051,c_78]) ).
tff(c_24157,plain,
! [X3_7] :
( ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_24156]) ).
tff(c_24356,plain,
! [X3_236] :
( ( multiply(X3_236,identity) != sk_c8 )
| ( inverse(X3_236) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_24337,c_24157]) ).
tff(c_24368,plain,
( ( sk_c8 != identity )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_24356]) ).
tff(c_24438,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24374,c_24340,c_24340,c_24368]) ).
tff(c_24439,plain,
! [X4_10,X1_8,X2_9] :
( ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_24156]) ).
tff(c_24701,plain,
! [X4_10,X1_8,X2_9] :
( ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_24619,c_24619,c_24622,c_24622,c_24619,c_24619,c_24622,c_24619,c_24439]) ).
tff(c_24702,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_24701]) ).
tff(c_25988,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_24807,c_24702]) ).
tff(c_24458,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_23998,c_24440]) ).
tff(c_24590,plain,
multiply(sk_c1,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_24557,c_24458]) ).
tff(c_24616,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_24613,c_24590]) ).
tff(c_24623,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24616]) ).
tff(c_24621,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24613,c_24481]) ).
tff(c_24660,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24623,c_24621]) ).
tff(c_25990,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25988,c_24660]) ).
tff(c_25991,plain,
! [X1_8,X4_10] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity ) ),
inference(splitRight,[status(thm)],[c_24701]) ).
tff(c_82300,plain,
! [X1_8,X4_10] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26116,c_26102,c_26102,c_25991]) ).
tff(c_82301,plain,
! [X4_10] : ( inverse(X4_10) != identity ),
inference(splitLeft,[status(thm)],[c_82300]) ).
tff(c_82303,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_82301,c_24660]) ).
tff(c_82305,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_82300]) ).
tff(c_82307,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_82305,c_24660]) ).
tff(c_82309,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_82322,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_18]) ).
tff(c_82323,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_82309,c_82322]) ).
tff(c_82324,plain,
multiply(sk_c7,identity) != sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_82323,c_82309]) ).
tff(c_82502,plain,
sk_c8 != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82498,c_82324]) ).
tff(c_82633,plain,
sk_c8 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_82627,c_82502]) ).
tff(c_82586,plain,
multiply(inverse(sk_c7),identity) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_111,c_82526]) ).
tff(c_82715,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_82607,c_82586]) ).
tff(c_82716,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_82633,c_82715]) ).
tff(c_82717,plain,
sk_c6 = identity,
inference(splitRight,[status(thm)],[c_82316]) ).
tff(c_46,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_82732,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_82717,c_46]) ).
tff(c_82733,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_82732]) ).
tff(c_82778,plain,
! [Z_517] : ( multiply(sk_c8,multiply(sk_c1,Z_517)) = multiply(identity,Z_517) ),
inference(superposition,[status(thm),theory(equality)],[c_124,c_82748]) ).
tff(c_82803,plain,
! [Z_518] : ( multiply(sk_c8,multiply(sk_c1,Z_518)) = Z_518 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82778]) ).
tff(c_82815,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_82733,c_82803]) ).
tff(c_82844,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_23998,c_82826]) ).
tff(c_82862,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82847,c_82844]) ).
tff(c_82308,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_82769,plain,
! [Z_517] : ( multiply(sk_c4,multiply(sk_c7,Z_517)) = multiply(sk_c8,Z_517) ),
inference(superposition,[status(thm),theory(equality)],[c_82308,c_82748]) ).
tff(c_82894,plain,
! [Z_521] : ( multiply(sk_c1,multiply(sk_c7,Z_521)) = multiply(sk_c8,Z_521) ),
inference(demodulation,[status(thm),theory(equality)],[c_82862,c_82769]) ).
tff(c_82921,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c1,identity),
inference(superposition,[status(thm),theory(equality)],[c_111,c_82894]) ).
tff(c_82925,plain,
multiply(sk_c1,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_82815,c_82921]) ).
tff(c_82798,plain,
! [Z_517] : ( multiply(sk_c8,multiply(sk_c1,Z_517)) = Z_517 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82778]) ).
tff(c_82929,plain,
multiply(sk_c8,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_82925,c_82798]) ).
tff(c_82799,plain,
! [Z_517] : ( multiply(sk_c7,multiply(sk_c8,Z_517)) = Z_517 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82781]) ).
tff(c_82940,plain,
multiply(sk_c7,identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_82929,c_82799]) ).
tff(c_82946,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82847,c_82940]) ).
tff(c_82838,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_82815,c_82826]) ).
tff(c_82952,plain,
multiply(sk_c1,sk_c1) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_82946,c_82946,c_82838]) ).
tff(c_82960,plain,
inverse(sk_c5) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82946,c_24009]) ).
tff(c_82734,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_82717,c_76]) ).
tff(c_82735,plain,
multiply(sk_c5,identity) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_23994,c_82734]) ).
tff(c_82957,plain,
multiply(sk_c5,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82946,c_82735]) ).
tff(c_82787,plain,
! [X_2,Z_517] : ( multiply(inverse(X_2),multiply(X_2,Z_517)) = multiply(identity,Z_517) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_82748]) ).
tff(c_82801,plain,
! [X_2,Z_517] : ( multiply(inverse(X_2),multiply(X_2,Z_517)) = Z_517 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_82787]) ).
tff(c_83100,plain,
multiply(inverse(sk_c5),sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_82957,c_82801]) ).
tff(c_83106,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_82952,c_82960,c_83100]) ).
tff(c_82955,plain,
multiply(sk_c8,sk_c8) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82946,c_82815]) ).
tff(c_83109,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_83106,c_83106,c_82955]) ).
tff(c_83117,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83109]) ).
tff(c_82719,plain,
multiply(sk_c7,identity) != sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_82717,c_82309]) ).
tff(c_82851,plain,
sk_c8 != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_82847,c_82719]) ).
tff(c_83113,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_83106,c_82851]) ).
tff(c_83170,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_83117,c_83113]) ).
tff(c_83172,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_82732]) ).
tff(c_83183,plain,
! [X_525,Y_526,Z_527] : ( multiply(multiply(X_525,Y_526),Z_527) = multiply(X_525,multiply(Y_526,Z_527)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_83213,plain,
! [Z_527] : ( multiply(sk_c7,multiply(sk_c8,Z_527)) = multiply(identity,Z_527) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_83183]) ).
tff(c_83263,plain,
! [Z_530] : ( multiply(sk_c7,multiply(sk_c8,Z_530)) = Z_530 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83213]) ).
tff(c_83281,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_124,c_83263]) ).
tff(c_83278,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_23998,c_83263]) ).
tff(c_83319,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_83281,c_83278]) ).
tff(c_83321,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_83319,c_82308]) ).
tff(c_83325,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_83172,c_83321]) ).
tff(c_83327,plain,
inverse(sk_c1) != sk_c8,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_34,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_83339,plain,
inverse(sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_83327,c_34]) ).
tff(c_28,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_83367,plain,
( ( sk_c6 = identity )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_111,c_28]) ).
tff(c_83368,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_83327,c_83367]) ).
tff(c_36,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_83375,plain,
( ( multiply(sk_c5,identity) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_83368,c_36]) ).
tff(c_83376,plain,
multiply(sk_c5,identity) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_83327,c_83375]) ).
tff(c_83485,plain,
! [X_537,Z_538] : ( multiply(inverse(X_537),multiply(X_537,Z_538)) = Z_538 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83429]) ).
tff(c_83515,plain,
multiply(inverse(sk_c5),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_83376,c_83485]) ).
tff(c_83552,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83339,c_83515]) ).
tff(c_83326,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_32,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_83359,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_83327,c_32]) ).
tff(c_83518,plain,
multiply(inverse(sk_c4),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_83359,c_83485]) ).
tff(c_83553,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_83326,c_83518]) ).
tff(c_83571,plain,
multiply(inverse(sk_c8),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_83553,c_83442]) ).
tff(c_83580,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83552,c_107,c_83571]) ).
tff(c_83583,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_83580,c_83580,c_83553]) ).
tff(c_83592,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83583]) ).
tff(c_83331,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_83326,c_4]) ).
tff(c_83423,plain,
! [Z_534] : ( multiply(sk_c7,multiply(sk_c8,Z_534)) = multiply(identity,Z_534) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_83396]) ).
tff(c_83447,plain,
! [Z_535] : ( multiply(sk_c7,multiply(sk_c8,Z_535)) = Z_535 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83423]) ).
tff(c_83459,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_83331,c_83447]) ).
tff(c_83636,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83592,c_83459]) ).
tff(c_83641,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_83636]) ).
tff(c_83445,plain,
! [X2_9,X1_8,X4_10,X3_7] :
( ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(sk_c7,identity) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_107,c_83368,c_83368,c_111,c_83368,c_78]) ).
tff(c_83446,plain,
multiply(sk_c7,identity) != sk_c8,
inference(splitLeft,[status(thm)],[c_83445]) ).
tff(c_83463,plain,
sk_c8 != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83459,c_83446]) ).
tff(c_83584,plain,
sk_c4 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_83580,c_83463]) ).
tff(c_83651,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_83641,c_83584]) ).
tff(c_83653,plain,
multiply(sk_c7,identity) = sk_c8,
inference(splitRight,[status(thm)],[c_83445]) ).
tff(c_83698,plain,
multiply(inverse(sk_c8),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_83331,c_83662]) ).
tff(c_83725,plain,
sk_c8 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83653,c_107,c_83698]) ).
tff(c_83730,plain,
inverse(sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83725,c_83326]) ).
tff(c_83732,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_83725,c_107]) ).
tff(c_83759,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83730,c_83732]) ).
tff(c_83726,plain,
multiply(sk_c7,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83725,c_83653]) ).
tff(c_83825,plain,
multiply(sk_c4,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_83759,c_83726]) ).
tff(c_83743,plain,
multiply(sk_c4,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_83730,c_4]) ).
tff(c_83414,plain,
! [Z_534] : ( multiply(sk_c4,multiply(sk_c7,Z_534)) = multiply(sk_c8,Z_534) ),
inference(superposition,[status(thm),theory(equality)],[c_83359,c_83396]) ).
tff(c_83791,plain,
! [Z_534] : ( multiply(sk_c4,multiply(sk_c4,Z_534)) = multiply(sk_c4,Z_534) ),
inference(demodulation,[status(thm),theory(equality)],[c_83759,c_83725,c_83414]) ).
tff(c_83829,plain,
multiply(sk_c4,sk_c4) = multiply(sk_c4,identity),
inference(superposition,[status(thm),theory(equality)],[c_83825,c_83791]) ).
tff(c_83838,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83825,c_83743,c_83829]) ).
tff(c_83846,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83838,c_83759]) ).
tff(c_83850,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83838,c_83725]) ).
tff(c_83652,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_83445]) ).
tff(c_83885,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_83846,c_83846,c_83850,c_83850,c_83846,c_83846,c_83850,c_83846,c_83850,c_83850,c_83846,c_83652]) ).
tff(c_83886,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_83885]) ).
tff(c_84558,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_84114,c_83886]) ).
tff(c_83848,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_83838,c_83838,c_83730]) ).
tff(c_84560,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_84558,c_83848]) ).
tff(c_84561,plain,
! [X1_8,X4_10,X3_7] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity ) ),
inference(splitRight,[status(thm)],[c_83885]) ).
tff(c_99169,plain,
! [X1_8,X4_10,X3_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity )
| ( identity != X3_7 )
| ( inverse(X3_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_84766,c_84780,c_84766,c_84766,c_84561]) ).
tff(c_99171,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_99169]) ).
tff(c_99173,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_99171,c_83848]) ).
tff(c_99174,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_99169]) ).
tff(c_99176,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_99174]) ).
tff(c_99178,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_99176,c_83848]) ).
tff(c_99179,plain,
! [X4_10] : ( inverse(X4_10) != identity ),
inference(splitRight,[status(thm)],[c_99174]) ).
tff(c_99896,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_99179,c_83848]) ).
tff(c_99898,plain,
inverse(sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_16,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_99926,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_99898,c_16]) ).
tff(c_14,plain,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_99910,plain,
inverse(sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_99898,c_14]) ).
tff(c_99914,plain,
multiply(sk_c7,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_99910,c_4]) ).
tff(c_99966,plain,
! [X_670,Y_671,Z_672] : ( multiply(multiply(X_670,Y_671),Z_672) = multiply(X_670,multiply(Y_671,Z_672)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_99990,plain,
! [Z_672] : ( multiply(sk_c7,multiply(sk_c5,Z_672)) = multiply(identity,Z_672) ),
inference(superposition,[status(thm),theory(equality)],[c_99914,c_99966]) ).
tff(c_100014,plain,
! [Z_673] : ( multiply(sk_c7,multiply(sk_c5,Z_673)) = Z_673 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_99990]) ).
tff(c_100026,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_99926,c_100014]) ).
tff(c_12,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_99938,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_99898,c_12]) ).
tff(c_99897,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_99902,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_99897,c_4]) ).
tff(c_99993,plain,
! [Z_672] : ( multiply(sk_c8,multiply(sk_c4,Z_672)) = multiply(identity,Z_672) ),
inference(superposition,[status(thm),theory(equality)],[c_99902,c_99966]) ).
tff(c_100050,plain,
! [Z_675] : ( multiply(sk_c8,multiply(sk_c4,Z_675)) = Z_675 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_99993]) ).
tff(c_100062,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_99938,c_100050]) ).
tff(c_8,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_99933,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_99898,c_8]) ).
tff(c_100265,plain,
! [Z_680] : ( multiply(sk_c7,multiply(sk_c8,Z_680)) = multiply(sk_c6,Z_680) ),
inference(superposition,[status(thm),theory(equality)],[c_99933,c_99966]) ).
tff(c_100280,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_100062,c_100265]) ).
tff(c_100290,plain,
multiply(sk_c6,sk_c8) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_100026,c_100280]) ).
tff(c_99999,plain,
! [X_2,Z_672] : ( multiply(inverse(X_2),multiply(X_2,Z_672)) = multiply(identity,Z_672) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_99966]) ).
tff(c_100010,plain,
! [X_2,Z_672] : ( multiply(inverse(X_2),multiply(X_2,Z_672)) = Z_672 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_99999]) ).
tff(c_100294,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_100290,c_100010]) ).
tff(c_100300,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_100294]) ).
tff(c_100073,plain,
! [X_676,Z_677] : ( multiply(inverse(X_676),multiply(X_676,Z_677)) = Z_677 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_99999]) ).
tff(c_100124,plain,
multiply(inverse(sk_c8),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_99902,c_100073]) ).
tff(c_100305,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_100300,c_100124]) ).
tff(c_100315,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_100305]) ).
tff(c_100313,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_100300,c_99897]) ).
tff(c_100367,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_100315,c_100313]) ).
tff(c_100307,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100300,c_100300,c_100062]) ).
tff(c_100316,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100307]) ).
tff(c_100312,plain,
inverse(identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100300,c_99898]) ).
tff(c_100389,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_100367,c_100316,c_100312]) ).
tff(c_100391,plain,
inverse(sk_c2) != sk_c3,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_100399,plain,
inverse(sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_100403,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_100399,c_4]) ).
tff(c_58,plain,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_100461,plain,
( ( sk_c6 = identity )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_100403,c_58]) ).
tff(c_100462,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_100391,c_100461]) ).
tff(c_66,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_100454,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_100391,c_66]) ).
tff(c_100463,plain,
multiply(sk_c5,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100462,c_100454]) ).
tff(c_100390,plain,
inverse(sk_c5) = sk_c7,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_100395,plain,
multiply(sk_c7,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_100390,c_4]) ).
tff(c_100518,plain,
! [Z_684] : ( multiply(sk_c7,multiply(sk_c5,Z_684)) = multiply(identity,Z_684) ),
inference(superposition,[status(thm),theory(equality)],[c_100395,c_100488]) ).
tff(c_100559,plain,
! [Z_686] : ( multiply(sk_c7,multiply(sk_c5,Z_686)) = Z_686 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100518]) ).
tff(c_100571,plain,
multiply(sk_c7,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_100463,c_100559]) ).
tff(c_100503,plain,
! [Z_684] : ( multiply(sk_c5,multiply(identity,Z_684)) = multiply(sk_c7,Z_684) ),
inference(superposition,[status(thm),theory(equality)],[c_100463,c_100488]) ).
tff(c_100785,plain,
! [Z_691] : ( multiply(sk_c7,Z_691) = multiply(sk_c5,Z_691) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100503]) ).
tff(c_100529,plain,
! [Z_684] : ( multiply(sk_c7,Z_684) = multiply(sk_c5,Z_684) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100503]) ).
tff(c_100584,plain,
! [X2_9,X1_8,X4_10,X3_7] :
( ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(sk_c7,identity) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_100399,c_100462,c_100462,c_100403,c_100462,c_78]) ).
tff(c_100585,plain,
multiply(sk_c7,identity) != sk_c8,
inference(splitLeft,[status(thm)],[c_100584]) ).
tff(c_100586,plain,
multiply(sk_c5,identity) != sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_100529,c_100585]) ).
tff(c_100587,plain,
sk_c8 != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100463,c_100586]) ).
tff(c_100588,plain,
! [Z_687] : ( multiply(sk_c7,Z_687) = multiply(sk_c5,Z_687) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100503]) ).
tff(c_100603,plain,
multiply(sk_c5,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_100588,c_100403]) ).
tff(c_100685,plain,
! [X_689,Z_690] : ( multiply(inverse(X_689),multiply(X_689,Z_690)) = Z_690 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100521]) ).
tff(c_100709,plain,
multiply(inverse(sk_c5),identity) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_100603,c_100685]) ).
tff(c_100772,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100463,c_100529,c_100390,c_100709]) ).
tff(c_100774,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_100587,c_100772]) ).
tff(c_100776,plain,
multiply(sk_c7,identity) = sk_c8,
inference(splitRight,[status(thm)],[c_100584]) ).
tff(c_100791,plain,
multiply(sk_c5,identity) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_100785,c_100776]) ).
tff(c_100826,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100463,c_100791]) ).
tff(c_62,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_100447,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_100391,c_62]) ).
tff(c_60,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c2) = sk_c3 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_100423,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_100391,c_60]) ).
tff(c_100427,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_100423,c_4]) ).
tff(c_100512,plain,
! [Z_684] : ( multiply(sk_c8,multiply(sk_c4,Z_684)) = multiply(identity,Z_684) ),
inference(superposition,[status(thm),theory(equality)],[c_100427,c_100488]) ).
tff(c_100536,plain,
! [Z_685] : ( multiply(sk_c8,multiply(sk_c4,Z_685)) = Z_685 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_100512]) ).
tff(c_100548,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_100447,c_100536]) ).
tff(c_100831,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100826,c_100826,c_100548]) ).
tff(c_100840,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_100571,c_100831]) ).
tff(c_100865,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_100840,c_100826]) ).
tff(c_100775,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(inverse(X4_10),sk_c8) != sk_c7 )
| ( multiply(X4_10,inverse(X4_10)) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c8 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X2_9,identity) != sk_c7 )
| ( inverse(X2_9) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_100584]) ).
tff(c_101011,plain,
! [X3_7,X4_10,X1_8,X2_9] :
( ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_100840,c_100840,c_100865,c_100865,c_100840,c_100840,c_100865,c_100840,c_100865,c_100865,c_100840,c_100775]) ).
tff(c_101012,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_101011]) ).
tff(c_101594,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_101101,c_101012]) ).
tff(c_100839,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_100826,c_100399]) ).
tff(c_100882,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_100840,c_100840,c_100839]) ).
tff(c_101596,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_101594,c_100882]) ).
tff(c_101597,plain,
! [X1_8,X4_10,X3_7] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(inverse(X4_10),identity) != identity )
| ( multiply(X4_10,inverse(X4_10)) != identity )
| ( multiply(X3_7,identity) != identity )
| ( inverse(X3_7) != identity ) ),
inference(splitRight,[status(thm)],[c_101011]) ).
tff(c_109574,plain,
! [X1_8,X4_10,X3_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity )
| ( identity != X3_7 )
| ( inverse(X3_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_101684,c_101698,c_101684,c_101684,c_101597]) ).
tff(c_109576,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_109574]) ).
tff(c_109578,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_109576,c_100882]) ).
tff(c_109579,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_109574]) ).
tff(c_109581,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_109579]) ).
tff(c_109583,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_109581,c_100882]) ).
tff(c_109584,plain,
! [X4_10] : ( inverse(X4_10) != identity ),
inference(splitRight,[status(thm)],[c_109579]) ).
tff(c_109587,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_109584,c_100882]) ).
tff(c_109589,plain,
inverse(sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_109612,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_109589,c_16]) ).
tff(c_110214,plain,
! [X_810,Y_811,Z_812] : ( multiply(multiply(X_810,Y_811),Z_812) = multiply(X_810,multiply(Y_811,Z_812)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_110241,plain,
! [Z_812] : ( multiply(sk_c7,multiply(sk_c5,Z_812)) = multiply(identity,Z_812) ),
inference(superposition,[status(thm),theory(equality)],[c_100395,c_110214]) ).
tff(c_110281,plain,
! [Z_814] : ( multiply(sk_c7,multiply(sk_c5,Z_814)) = Z_814 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_110241]) ).
tff(c_110293,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_109612,c_110281]) ).
tff(c_110244,plain,
! [X_2,Z_812] : ( multiply(inverse(X_2),multiply(X_2,Z_812)) = multiply(identity,Z_812) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_110214]) ).
tff(c_110304,plain,
! [X_815,Z_816] : ( multiply(inverse(X_815),multiply(X_815,Z_816)) = Z_816 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_110244]) ).
tff(c_110322,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_110293,c_110304]) ).
tff(c_110182,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_109589,c_8]) ).
tff(c_110337,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_110182,c_110304]) ).
tff(c_110437,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_110322,c_110337]) ).
tff(c_109620,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_109589,c_12]) ).
tff(c_109588,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_109593,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_109588,c_4]) ).
tff(c_110238,plain,
! [Z_812] : ( multiply(sk_c8,multiply(sk_c4,Z_812)) = multiply(identity,Z_812) ),
inference(superposition,[status(thm),theory(equality)],[c_109593,c_110214]) ).
tff(c_110256,plain,
! [Z_813] : ( multiply(sk_c8,multiply(sk_c4,Z_813)) = Z_813 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_110238]) ).
tff(c_110268,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_109620,c_110256]) ).
tff(c_110449,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_110437,c_110437,c_110268]) ).
tff(c_110457,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_110293,c_110449]) ).
tff(c_110485,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_110457,c_110457,c_110322]) ).
tff(c_110492,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_110485]) ).
tff(c_110502,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_110492,c_110457]) ).
tff(c_110455,plain,
inverse(sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_110437,c_109589]) ).
tff(c_110532,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_110502,c_110502,c_110455]) ).
tff(c_110456,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_110437,c_109588]) ).
tff(c_110533,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_110502,c_110456]) ).
tff(c_110358,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_110304]) ).
tff(c_110537,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_110533,c_110358]) ).
tff(c_110546,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_110537]) ).
tff(c_110549,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_110546,c_110533]) ).
tff(c_110551,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_110532,c_110549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP383-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % 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 : Thu Aug 3 22:29:01 EDT 2023
% 0.12/0.34 % CPUTime :
% 22.29/11.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.44/11.72
% 22.44/11.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.91/11.80
% 22.91/11.80 Inference rules
% 22.91/11.80 ----------------------
% 22.91/11.80 #Ref : 0
% 22.91/11.80 #Sup : 26369
% 22.91/11.80 #Fact : 0
% 22.91/11.80 #Define : 0
% 22.91/11.80 #Split : 34
% 22.91/11.80 #Chain : 0
% 22.91/11.80 #Close : 0
% 22.91/11.80
% 22.91/11.80 Ordering : KBO
% 22.91/11.80
% 22.91/11.80 Simplification rules
% 22.91/11.80 ----------------------
% 22.91/11.80 #Subsume : 10
% 22.91/11.80 #Demod : 84079
% 22.91/11.80 #Tautology : 21325
% 22.91/11.80 #SimpNegUnit : 93
% 22.91/11.80 #BackRed : 451
% 22.91/11.80
% 22.91/11.80 #Partial instantiations: 0
% 22.91/11.80 #Strategies tried : 1
% 22.91/11.80
% 22.91/11.80 Timing (in seconds)
% 22.91/11.80 ----------------------
% 22.91/11.80 Preprocessing : 0.54
% 22.91/11.80 Parsing : 0.21
% 22.91/11.80 CNF conversion : 0.03
% 22.91/11.80 Main loop : 9.99
% 22.91/11.80 Inferencing : 1.97
% 22.91/11.80 Reduction : 6.46
% 22.91/11.80 Demodulation : 6.05
% 22.91/11.80 BG Simplification : 0.17
% 22.91/11.80 Subsumption : 0.96
% 22.91/11.80 Abstraction : 0.45
% 22.91/11.80 MUC search : 0.00
% 22.91/11.80 Cooper : 0.00
% 22.91/11.80 Total : 10.72
% 22.91/11.80 Index Insertion : 0.00
% 22.91/11.80 Index Deletion : 0.00
% 22.91/11.80 Index Matching : 0.00
% 22.91/11.80 BG Taut test : 0.00
%------------------------------------------------------------------------------