TSTP Solution File: GRP381-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP381-1 : 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 : n008.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 15.07s 6.24s
% Output : CNFRefutation 15.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 39
% Syntax : Number of formulae : 526 ( 435 unt; 10 typ; 0 def)
% Number of atoms : 698 ( 672 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 379 ( 197 ~; 182 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 247 (; 247 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
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,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X3,X4,X1,X2] :
( ( inverse(sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_44,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_111,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_115,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_111,c_4]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_98,plain,
inverse(sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_102,plain,
multiply(sk_c6,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_18795,plain,
! [X_212,Y_213,Z_214] : ( multiply(multiply(X_212,Y_213),Z_214) = multiply(X_212,multiply(Y_213,Z_214)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18825,plain,
! [Z_214] : ( multiply(sk_c6,multiply(sk_c7,Z_214)) = multiply(identity,Z_214) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_18795]) ).
tff(c_18875,plain,
! [Z_217] : ( multiply(sk_c6,multiply(sk_c7,Z_217)) = Z_217 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18825]) ).
tff(c_18893,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_18875]) ).
tff(c_30,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_17459,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_18089,plain,
! [X_196,Y_197,Z_198] : ( multiply(multiply(X_196,Y_197),Z_198) = multiply(X_196,multiply(Y_197,Z_198)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18119,plain,
! [Z_198] : ( multiply(sk_c7,multiply(sk_c1,Z_198)) = multiply(identity,Z_198) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_18089]) ).
tff(c_18144,plain,
! [Z_199] : ( multiply(sk_c7,multiply(sk_c1,Z_199)) = Z_199 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18119]) ).
tff(c_18156,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17459,c_18144]) ).
tff(c_18122,plain,
! [Z_198] : ( multiply(sk_c6,multiply(sk_c7,Z_198)) = multiply(identity,Z_198) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_18089]) ).
tff(c_18182,plain,
! [Z_201] : ( multiply(sk_c6,multiply(sk_c7,Z_201)) = Z_201 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18122]) ).
tff(c_18194,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18156,c_18182]) ).
tff(c_18207,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_18194]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_125,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_64,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_85,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_89,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_17167,plain,
! [X_173,Y_174,Z_175] : ( multiply(multiply(X_173,Y_174),Z_175) = multiply(X_173,multiply(Y_174,Z_175)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17203,plain,
! [Z_175] : ( multiply(sk_c6,multiply(sk_c2,Z_175)) = multiply(identity,Z_175) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_17167]) ).
tff(c_17345,plain,
! [Z_179] : ( multiply(sk_c6,multiply(sk_c2,Z_179)) = Z_179 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17203]) ).
tff(c_17366,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_125,c_17345]) ).
tff(c_17371,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_17366]) ).
tff(c_17200,plain,
! [Z_175] : ( multiply(sk_c6,multiply(sk_c7,Z_175)) = multiply(identity,Z_175) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_17167]) ).
tff(c_17235,plain,
! [Z_177] : ( multiply(sk_c6,multiply(sk_c7,Z_177)) = Z_177 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17200]) ).
tff(c_17253,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_17235]) ).
tff(c_17378,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_17371,c_17253]) ).
tff(c_17391,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17378]) ).
tff(c_16770,plain,
! [X_165,Y_166,Z_167] : ( multiply(multiply(X_165,Y_166),Z_167) = multiply(X_165,multiply(Y_166,Z_167)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16806,plain,
! [Z_167] : ( multiply(sk_c6,multiply(sk_c7,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_16770]) ).
tff(c_16842,plain,
! [Z_169] : ( multiply(sk_c6,multiply(sk_c7,Z_169)) = Z_169 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16806]) ).
tff(c_16860,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_16842]) ).
tff(c_16553,plain,
! [X_160,Y_161,Z_162] : ( multiply(multiply(X_160,Y_161),Z_162) = multiply(X_160,multiply(Y_161,Z_162)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16592,plain,
! [Z_162] : ( multiply(sk_c6,multiply(sk_c2,Z_162)) = multiply(identity,Z_162) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_16553]) ).
tff(c_16613,plain,
! [Z_163] : ( multiply(sk_c6,multiply(sk_c2,Z_163)) = Z_163 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16592]) ).
tff(c_16625,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_125,c_16613]) ).
tff(c_16629,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_16625]) ).
tff(c_160,plain,
! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_193,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_160]) ).
tff(c_204,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_193]) ).
tff(c_454,plain,
! [X_21,Z_22] : ( multiply(inverse(X_21),multiply(X_21,Z_22)) = Z_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_193]) ).
tff(c_774,plain,
! [X_30,Z_31] : ( multiply(inverse(inverse(X_30)),Z_31) = multiply(X_30,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_204,c_454]) ).
tff(c_481,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_454]) ).
tff(c_795,plain,
! [X_30] : ( multiply(X_30,identity) = X_30 ),
inference(superposition,[status(thm),theory(equality)],[c_774,c_481]) ).
tff(c_34,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_131,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_184,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_160]) ).
tff(c_206,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_184]) ).
tff(c_218,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_131,c_206]) ).
tff(c_187,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c7,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_160]) ).
tff(c_229,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c7,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_187]) ).
tff(c_241,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_218,c_229]) ).
tff(c_251,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_241]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_138,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_68,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( inverse(sk_c7) != sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_253,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( sk_c5 != identity )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_138,c_102,c_68]) ).
tff(c_254,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_253]) ).
tff(c_257,plain,
multiply(identity,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_138]) ).
tff(c_264,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_257]) ).
tff(c_260,plain,
multiply(identity,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_102]) ).
tff(c_378,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_264,c_260]) ).
tff(c_379,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_254,c_378]) ).
tff(c_381,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_253]) ).
tff(c_382,plain,
multiply(sk_c6,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_381,c_138]) ).
tff(c_437,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_251,c_382]) ).
tff(c_415,plain,
inverse(sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_98]) ).
tff(c_438,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_437,c_415]) ).
tff(c_559,plain,
! [X_23] : ( multiply(inverse(inverse(X_23)),identity) = X_23 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_454]) ).
tff(c_565,plain,
! [X_23] : ( multiply(inverse(inverse(inverse(X_23))),X_23) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_559,c_204]) ).
tff(c_380,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_253]) ).
tff(c_591,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != 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_251,c_251,c_381,c_437,c_437,c_251,c_437,c_251,c_251,c_437,c_251,c_437,c_380]) ).
tff(c_621,plain,
! [X2_25] :
( ( multiply(X2_25,identity) != identity )
| ( inverse(X2_25) != identity ) ),
inference(splitLeft,[status(thm)],[c_591]) ).
tff(c_625,plain,
inverse(inverse(inverse(inverse(identity)))) != identity,
inference(superposition,[status(thm),theory(equality)],[c_565,c_621]) ).
tff(c_644,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_438,c_438,c_438,c_438,c_625]) ).
tff(c_645,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_591]) ).
tff(c_16477,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_795,c_795,c_795,c_645]) ).
tff(c_16479,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16477]) ).
tff(c_16481,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16479,c_438]) ).
tff(c_16482,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_16477]) ).
tff(c_16484,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16482]) ).
tff(c_16486,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16484,c_438]) ).
tff(c_16489,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_16482]) ).
tff(c_16491,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16489,c_438]) ).
tff(c_16493,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_16530,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_18]) ).
tff(c_16531,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_16493,c_16530]) ).
tff(c_16533,plain,
multiply(sk_c6,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_16531,c_16493]) ).
tff(c_16632,plain,
multiply(identity,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_16629,c_16533]) ).
tff(c_16642,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16632]) ).
tff(c_16638,plain,
multiply(identity,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16629,c_102]) ).
tff(c_16694,plain,
sk_c7 = identity,
inference(superposition,[status(thm),theory(equality)],[c_16638,c_2]) ).
tff(c_16702,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16642,c_16694]) ).
tff(c_16704,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_28,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_16751,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_28]) ).
tff(c_16752,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_16704,c_16751]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_16739,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_16753,plain,
multiply(sk_c6,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_16752,c_16739]) ).
tff(c_16864,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16860,c_16753]) ).
tff(c_16881,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16864,c_111]) ).
tff(c_16883,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16864,c_98]) ).
tff(c_16917,plain,
sk_c6 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16881,c_16883]) ).
tff(c_16882,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16864,c_102]) ).
tff(c_17003,plain,
multiply(sk_c1,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16917,c_16882]) ).
tff(c_16931,plain,
inverse(sk_c2) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16917,c_85]) ).
tff(c_16879,plain,
multiply(sk_c2,sk_c6) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16864,c_125]) ).
tff(c_17044,plain,
multiply(sk_c2,sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_16917,c_16879]) ).
tff(c_16812,plain,
! [X_2,Z_167] : ( multiply(inverse(X_2),multiply(X_2,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_16770]) ).
tff(c_16827,plain,
! [X_2,Z_167] : ( multiply(inverse(X_2),multiply(X_2,Z_167)) = Z_167 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16812]) ).
tff(c_17048,plain,
multiply(inverse(sk_c2),sk_c1) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_17044,c_16827]) ).
tff(c_17054,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17003,c_16931,c_17048]) ).
tff(c_17061,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17054,c_16917]) ).
tff(c_16878,plain,
multiply(sk_c1,sk_c1) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16864,c_16704]) ).
tff(c_17139,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_17061,c_17054,c_2,c_17054,c_16878]) ).
tff(c_17141,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_17149,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_18]) ).
tff(c_17150,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_17141,c_17149]) ).
tff(c_17151,plain,
multiply(sk_c6,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17150,c_17141]) ).
tff(c_17257,plain,
sk_c7 != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_17253,c_17151]) ).
tff(c_17397,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17391,c_17257]) ).
tff(c_16718,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_16704,c_30]) ).
tff(c_16722,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16718,c_4]) ).
tff(c_17250,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_16722,c_17235]) ).
tff(c_17266,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_17253,c_17250]) ).
tff(c_32,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_17142,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_16704,c_32]) ).
tff(c_17267,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17266,c_17142]) ).
tff(c_17197,plain,
! [Z_175] : ( multiply(sk_c7,multiply(sk_c1,Z_175)) = multiply(identity,Z_175) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_17167]) ).
tff(c_17217,plain,
! [Z_175] : ( multiply(sk_c7,multiply(sk_c1,Z_175)) = Z_175 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17197]) ).
tff(c_17281,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17267,c_17217]) ).
tff(c_17218,plain,
! [Z_175] : ( multiply(sk_c6,multiply(sk_c7,Z_175)) = Z_175 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17200]) ).
tff(c_17291,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17281,c_17218]) ).
tff(c_17375,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17371,c_17371,c_17291]) ).
tff(c_17390,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17375]) ).
tff(c_17438,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17397,c_17390]) ).
tff(c_17440,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_48,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_18070,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_18071,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_17440,c_18070]) ).
tff(c_17512,plain,
! [X_182,Y_183,Z_184] : ( multiply(multiply(X_182,Y_183),Z_184) = multiply(X_182,multiply(Y_183,Z_184)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17545,plain,
! [Z_184] : ( multiply(sk_c7,multiply(sk_c1,Z_184)) = multiply(identity,Z_184) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_17512]) ).
tff(c_17571,plain,
! [Z_185] : ( multiply(sk_c7,multiply(sk_c1,Z_185)) = Z_185 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17545]) ).
tff(c_17583,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17459,c_17571]) ).
tff(c_17548,plain,
! [Z_184] : ( multiply(sk_c6,multiply(sk_c7,Z_184)) = multiply(identity,Z_184) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_17512]) ).
tff(c_17812,plain,
! [Z_192] : ( multiply(sk_c6,multiply(sk_c7,Z_192)) = Z_192 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17548]) ).
tff(c_17824,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17583,c_17812]) ).
tff(c_17837,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_17824]) ).
tff(c_17881,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17837,c_85]) ).
tff(c_17916,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17881,c_4]) ).
tff(c_17554,plain,
! [X_2,Z_184] : ( multiply(inverse(X_2),multiply(X_2,Z_184)) = multiply(identity,Z_184) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17512]) ).
tff(c_17569,plain,
! [X_2,Z_184] : ( multiply(inverse(X_2),multiply(X_2,Z_184)) = Z_184 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17554]) ).
tff(c_18029,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_17916,c_17569]) ).
tff(c_18041,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18029]) ).
tff(c_17485,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_17486,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_17440,c_17485]) ).
tff(c_17480,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_17487,plain,
multiply(sk_c6,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17486,c_17480]) ).
tff(c_17872,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17837,c_17487]) ).
tff(c_17883,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17872]) ).
tff(c_17876,plain,
multiply(sk_c2,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17837,c_17440]) ).
tff(c_18056,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18041,c_17883,c_17876]) ).
tff(c_18058,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_18073,plain,
multiply(sk_c6,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18071,c_18058]) ).
tff(c_18211,plain,
multiply(identity,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18207,c_18073]) ).
tff(c_18222,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18211]) ).
tff(c_18219,plain,
inverse(sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18207,c_98]) ).
tff(c_18277,plain,
multiply(identity,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18219,c_4]) ).
tff(c_18128,plain,
! [X_2,Z_198] : ( multiply(inverse(X_2),multiply(X_2,Z_198)) = multiply(identity,Z_198) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18089]) ).
tff(c_18142,plain,
! [X_2,Z_198] : ( multiply(inverse(X_2),multiply(X_2,Z_198)) = Z_198 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18128]) ).
tff(c_18304,plain,
multiply(inverse(identity),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18277,c_18142]) ).
tff(c_18316,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18304]) ).
tff(c_18318,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18222,c_18316]) ).
tff(c_18319,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_18324,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18319,c_4]) ).
tff(c_18890,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_18324,c_18875]) ).
tff(c_18937,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18893,c_18890]) ).
tff(c_18377,plain,
! [X_204,Y_205,Z_206] : ( multiply(multiply(X_204,Y_205),Z_206) = multiply(X_204,multiply(Y_205,Z_206)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18410,plain,
! [Z_206] : ( multiply(sk_c6,multiply(sk_c7,Z_206)) = multiply(identity,Z_206) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_18377]) ).
tff(c_18446,plain,
! [Z_208] : ( multiply(sk_c6,multiply(sk_c7,Z_208)) = Z_208 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18410]) ).
tff(c_18464,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_18446]) ).
tff(c_18359,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_18360,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_17440,c_18359]) ).
tff(c_18344,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_18361,plain,
multiply(sk_c6,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18360,c_18344]) ).
tff(c_18468,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18464,c_18361]) ).
tff(c_18485,plain,
inverse(sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18468,c_111]) ).
tff(c_18487,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18468,c_98]) ).
tff(c_18521,plain,
sk_c6 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18485,c_18487]) ).
tff(c_18534,plain,
multiply(sk_c1,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18521,c_89]) ).
tff(c_18530,plain,
multiply(sk_c1,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18521,c_18464]) ).
tff(c_18461,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_18324,c_18446]) ).
tff(c_18594,plain,
multiply(sk_c1,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_18521,c_18461]) ).
tff(c_18652,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18530,c_18594]) ).
tff(c_18320,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_18352,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_18320,c_32]) ).
tff(c_18398,plain,
! [Z_206] : ( multiply(sk_c3,multiply(sk_c6,Z_206)) = multiply(sk_c7,Z_206) ),
inference(superposition,[status(thm),theory(equality)],[c_18352,c_18377]) ).
tff(c_18674,plain,
! [Z_206] : ( multiply(sk_c1,multiply(sk_c1,Z_206)) = multiply(sk_c1,Z_206) ),
inference(demodulation,[status(thm),theory(equality)],[c_18652,c_18521,c_18468,c_18398]) ).
tff(c_18712,plain,
multiply(sk_c1,sk_c2) = multiply(sk_c1,identity),
inference(superposition,[status(thm),theory(equality)],[c_18534,c_18674]) ).
tff(c_18721,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18534,c_18530,c_18712]) ).
tff(c_18525,plain,
multiply(sk_c1,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18485,c_4]) ).
tff(c_18481,plain,
multiply(sk_c1,sk_c1) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18468,c_18320]) ).
tff(c_18708,plain,
multiply(sk_c1,sk_c1) != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18521,c_18481]) ).
tff(c_18725,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_18525,c_18708]) ).
tff(c_18766,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18721,c_18725]) ).
tff(c_18767,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_18939,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18937,c_18767]) ).
tff(c_18822,plain,
! [Z_214] : ( multiply(sk_c7,multiply(sk_c1,Z_214)) = multiply(identity,Z_214) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_18795]) ).
tff(c_18842,plain,
! [Z_214] : ( multiply(sk_c7,multiply(sk_c1,Z_214)) = Z_214 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18822]) ).
tff(c_18951,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18939,c_18842]) ).
tff(c_18843,plain,
! [Z_214] : ( multiply(sk_c6,multiply(sk_c7,Z_214)) = Z_214 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18825]) ).
tff(c_18961,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18951,c_18843]) ).
tff(c_17439,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_18773,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_18774,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_17440,c_18773]) ).
tff(c_36,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_18338,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18320,c_36]) ).
tff(c_18776,plain,
multiply(sk_c4,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18774,c_18338]) ).
tff(c_18831,plain,
! [X_2,Z_214] : ( multiply(inverse(X_2),multiply(X_2,Z_214)) = multiply(identity,Z_214) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18795]) ).
tff(c_18975,plain,
! [X_219,Z_220] : ( multiply(inverse(X_219),multiply(X_219,Z_220)) = Z_220 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18831]) ).
tff(c_19017,plain,
multiply(inverse(sk_c4),sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18776,c_18975]) ).
tff(c_19054,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18961,c_17439,c_19017]) ).
tff(c_18768,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_18775,plain,
multiply(sk_c6,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18774,c_18768]) ).
tff(c_18897,plain,
sk_c7 != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_18893,c_18775]) ).
tff(c_19062,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19054,c_18897]) ).
tff(c_19060,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_19054,c_19054,c_18951]) ).
tff(c_19071,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19060]) ).
tff(c_19077,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_19071,c_18893]) ).
tff(c_19084,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19077]) ).
tff(c_19125,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19062,c_19084]) ).
tff(c_19127,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_40,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_19139,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19127,c_40]) ).
tff(c_19143,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19139,c_4]) ).
tff(c_19193,plain,
! [X_222,Y_223,Z_224] : ( multiply(multiply(X_222,Y_223),Z_224) = multiply(X_222,multiply(Y_223,Z_224)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_19220,plain,
! [Z_224] : ( multiply(sk_c6,multiply(sk_c7,Z_224)) = multiply(identity,Z_224) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_19193]) ).
tff(c_19241,plain,
! [Z_225] : ( multiply(sk_c6,multiply(sk_c7,Z_225)) = Z_225 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19220]) ).
tff(c_19253,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_19143,c_19241]) ).
tff(c_42,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_19174,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19127,c_42]) ).
tff(c_19214,plain,
! [Z_224] : ( multiply(sk_c7,multiply(sk_c3,Z_224)) = multiply(identity,Z_224) ),
inference(superposition,[status(thm),theory(equality)],[c_19143,c_19193]) ).
tff(c_19281,plain,
! [Z_227] : ( multiply(sk_c7,multiply(sk_c3,Z_227)) = Z_227 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19214]) ).
tff(c_19296,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_19174,c_19281]) ).
tff(c_19310,plain,
! [Z_228] : ( multiply(sk_c3,multiply(sk_c6,Z_228)) = multiply(sk_c7,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_19174,c_19193]) ).
tff(c_19337,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c3,identity),
inference(superposition,[status(thm),theory(equality)],[c_102,c_19310]) ).
tff(c_19344,plain,
multiply(sk_c3,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_19296,c_19337]) ).
tff(c_19235,plain,
! [Z_224] : ( multiply(sk_c7,multiply(sk_c3,Z_224)) = Z_224 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19214]) ).
tff(c_19348,plain,
multiply(sk_c7,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19344,c_19235]) ).
tff(c_19237,plain,
! [Z_224] : ( multiply(sk_c6,multiply(sk_c7,Z_224)) = Z_224 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19220]) ).
tff(c_19369,plain,
multiply(sk_c6,identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_19348,c_19237]) ).
tff(c_19375,plain,
sk_c6 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19253,c_19369]) ).
tff(c_19303,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19296,c_19237]) ).
tff(c_19379,plain,
multiply(sk_c3,sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19375,c_19375,c_19303]) ).
tff(c_19126,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_19389,plain,
inverse(sk_c4) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19375,c_19126]) ).
tff(c_38,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_19167,plain,
( ( sk_c5 = identity )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_38]) ).
tff(c_19168,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_19127,c_19167]) ).
tff(c_46,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_19152,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_19127,c_46]) ).
tff(c_19169,plain,
multiply(sk_c4,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_19168,c_19152]) ).
tff(c_19386,plain,
multiply(sk_c4,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19375,c_19169]) ).
tff(c_19226,plain,
! [X_2,Z_224] : ( multiply(inverse(X_2),multiply(X_2,Z_224)) = multiply(identity,Z_224) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19193]) ).
tff(c_19239,plain,
! [X_2,Z_224] : ( multiply(inverse(X_2),multiply(X_2,Z_224)) = Z_224 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19226]) ).
tff(c_19528,plain,
multiply(inverse(sk_c4),sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19386,c_19239]) ).
tff(c_19534,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19379,c_19389,c_19528]) ).
tff(c_19382,plain,
multiply(sk_c7,sk_c7) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19375,c_19296]) ).
tff(c_19573,plain,
multiply(identity,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19534,c_19534,c_19382]) ).
tff(c_19582,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19573]) ).
tff(c_19279,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( sk_c7 != sk_c3 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_19253,c_19168,c_19168,c_102,c_19168,c_68]) ).
tff(c_19280,plain,
sk_c7 != sk_c3,
inference(splitLeft,[status(thm)],[c_19279]) ).
tff(c_19578,plain,
sk_c3 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19534,c_19280]) ).
tff(c_19607,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19582,c_19578]) ).
tff(c_19609,plain,
sk_c7 = sk_c3,
inference(splitRight,[status(thm)],[c_19279]) ).
tff(c_19613,plain,
inverse(sk_c3) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19609,c_19139]) ).
tff(c_19616,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_19609,c_98]) ).
tff(c_19628,plain,
sk_c6 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19613,c_19616]) ).
tff(c_19611,plain,
multiply(sk_c3,sk_c6) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19609,c_19174]) ).
tff(c_19691,plain,
multiply(sk_c3,sk_c3) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_19628,c_19611]) ).
tff(c_19695,plain,
multiply(inverse(sk_c3),sk_c3) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_19691,c_19239]) ).
tff(c_19701,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19695]) ).
tff(c_19719,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19701,c_19628]) ).
tff(c_19640,plain,
! [X_232,Z_233] : ( multiply(inverse(X_232),multiply(X_232,Z_233)) = Z_233 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19226]) ).
tff(c_19817,plain,
! [X_235,Z_236] : ( multiply(inverse(inverse(X_235)),Z_236) = multiply(X_235,Z_236) ),
inference(superposition,[status(thm),theory(equality)],[c_19239,c_19640]) ).
tff(c_19664,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19640]) ).
tff(c_19824,plain,
! [X_235] : ( multiply(X_235,identity) = X_235 ),
inference(superposition,[status(thm),theory(equality)],[c_19817,c_19664]) ).
tff(c_19722,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19701,c_19609]) ).
tff(c_19608,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_19279]) ).
tff(c_27461,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19719,c_19824,c_19719,c_19722,c_19824,c_19719,c_19722,c_19824,c_19719,c_19722,c_19719,c_19824,c_19719,c_19722,c_19722,c_19608]) ).
tff(c_27463,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_27461]) ).
tff(c_19721,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19701,c_19701,c_19613]) ).
tff(c_27465,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_27463,c_19721]) ).
tff(c_27466,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_27461]) ).
tff(c_31097,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_27466]) ).
tff(c_31099,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31097,c_19721]) ).
tff(c_31100,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_27466]) ).
tff(c_31102,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_31100]) ).
tff(c_31104,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31102,c_19721]) ).
tff(c_31720,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_31100]) ).
tff(c_31722,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31720,c_19721]) ).
tff(c_31724,plain,
inverse(sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_31767,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_31724,c_16]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_31749,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_31724,c_14]) ).
tff(c_31753,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31749,c_4]) ).
tff(c_31797,plain,
! [X_352,Y_353,Z_354] : ( multiply(multiply(X_352,Y_353),Z_354) = multiply(X_352,multiply(Y_353,Z_354)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_31818,plain,
! [Z_354] : ( multiply(sk_c6,multiply(sk_c4,Z_354)) = multiply(identity,Z_354) ),
inference(superposition,[status(thm),theory(equality)],[c_31753,c_31797]) ).
tff(c_31862,plain,
! [Z_356] : ( multiply(sk_c6,multiply(sk_c4,Z_356)) = Z_356 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31818]) ).
tff(c_31874,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_31767,c_31862]) ).
tff(c_12,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_31757,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_31724,c_12]) ).
tff(c_31723,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_31728,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31723,c_4]) ).
tff(c_31827,plain,
! [Z_354] : ( multiply(sk_c7,multiply(sk_c3,Z_354)) = multiply(identity,Z_354) ),
inference(superposition,[status(thm),theory(equality)],[c_31728,c_31797]) ).
tff(c_31916,plain,
! [Z_358] : ( multiply(sk_c7,multiply(sk_c3,Z_358)) = Z_358 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31827]) ).
tff(c_31931,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31757,c_31916]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_31775,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_31724,c_8]) ).
tff(c_32257,plain,
! [Z_364] : ( multiply(sk_c6,multiply(sk_c7,Z_364)) = multiply(sk_c5,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_31775,c_31797]) ).
tff(c_32275,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_31931,c_32257]) ).
tff(c_32282,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_31874,c_32275]) ).
tff(c_31833,plain,
! [X_2,Z_354] : ( multiply(inverse(X_2),multiply(X_2,Z_354)) = multiply(identity,Z_354) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31797]) ).
tff(c_31845,plain,
! [X_2,Z_354] : ( multiply(inverse(X_2),multiply(X_2,Z_354)) = Z_354 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31833]) ).
tff(c_32311,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32282,c_31845]) ).
tff(c_32318,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32311]) ).
tff(c_31737,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_31741,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31737,c_4]) ).
tff(c_31969,plain,
! [X_359,Z_360] : ( multiply(inverse(X_359),multiply(X_359,Z_360)) = Z_360 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31833]) ).
tff(c_32032,plain,
multiply(inverse(sk_c7),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_31741,c_31969]) ).
tff(c_32342,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_32318,c_32032]) ).
tff(c_32345,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32342]) ).
tff(c_32344,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32318,c_31737]) ).
tff(c_32410,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32345,c_32344]) ).
tff(c_32044,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_89,c_31969]) ).
tff(c_32023,plain,
multiply(inverse(sk_c6),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_31753,c_31969]) ).
tff(c_32160,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_32044,c_32023]) ).
tff(c_32174,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32160,c_31767]) ).
tff(c_31815,plain,
! [Z_354] : ( multiply(sk_c4,multiply(sk_c5,Z_354)) = multiply(sk_c6,Z_354) ),
inference(superposition,[status(thm),theory(equality)],[c_31767,c_31797]) ).
tff(c_32200,plain,
! [Z_354] : ( multiply(sk_c2,multiply(sk_c5,Z_354)) = multiply(sk_c6,Z_354) ),
inference(demodulation,[status(thm),theory(equality)],[c_32160,c_31815]) ).
tff(c_32308,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c2,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_32282,c_32200]) ).
tff(c_32317,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_32174,c_31775,c_32308]) ).
tff(c_32332,plain,
inverse(sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_32317,c_31724]) ).
tff(c_32396,plain,
inverse(identity) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_32318,c_32332]) ).
tff(c_32411,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_32410,c_32396]) ).
tff(c_32329,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_32317,c_32317,c_31874]) ).
tff(c_32436,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_32329,c_31845]) ).
tff(c_32443,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32436]) ).
tff(c_32445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32411,c_32443]) ).
tff(c_32447,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_32476,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_32447,c_46]) ).
tff(c_32446,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_32451,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32446,c_4]) ).
tff(c_32500,plain,
! [X_367,Y_368,Z_369] : ( multiply(multiply(X_367,Y_368),Z_369) = multiply(X_367,multiply(Y_368,Z_369)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_32524,plain,
! [Z_369] : ( multiply(sk_c6,multiply(sk_c4,Z_369)) = multiply(identity,Z_369) ),
inference(superposition,[status(thm),theory(equality)],[c_32451,c_32500]) ).
tff(c_32546,plain,
! [Z_370] : ( multiply(sk_c6,multiply(sk_c4,Z_370)) = Z_370 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32524]) ).
tff(c_32558,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_32476,c_32546]) ).
tff(c_32467,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_32447,c_42]) ).
tff(c_32527,plain,
! [Z_369] : ( multiply(sk_c7,multiply(sk_c3,Z_369)) = multiply(identity,Z_369) ),
inference(superposition,[status(thm),theory(equality)],[c_31728,c_32500]) ).
tff(c_32571,plain,
! [Z_371] : ( multiply(sk_c7,multiply(sk_c3,Z_371)) = Z_371 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32527]) ).
tff(c_32583,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32467,c_32571]) ).
tff(c_32462,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_31724,c_8]) ).
tff(c_32900,plain,
! [Z_379] : ( multiply(sk_c6,multiply(sk_c7,Z_379)) = multiply(sk_c5,Z_379) ),
inference(superposition,[status(thm),theory(equality)],[c_32462,c_32500]) ).
tff(c_32921,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_32583,c_32900]) ).
tff(c_32931,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_32558,c_32921]) ).
tff(c_32533,plain,
! [X_2,Z_369] : ( multiply(inverse(X_2),multiply(X_2,Z_369)) = multiply(identity,Z_369) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_32500]) ).
tff(c_32544,plain,
! [X_2,Z_369] : ( multiply(inverse(X_2),multiply(X_2,Z_369)) = Z_369 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32533]) ).
tff(c_32935,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32931,c_32544]) ).
tff(c_32941,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32935]) ).
tff(c_32949,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32941,c_32941,c_32583]) ).
tff(c_32960,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32949]) ).
tff(c_32955,plain,
inverse(identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_32941,c_31724]) ).
tff(c_33021,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_32960,c_32955]) ).
tff(c_32623,plain,
! [X_374,Z_375] : ( multiply(inverse(X_374),multiply(X_374,Z_375)) = Z_375 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32533]) ).
tff(c_32683,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_89,c_32623]) ).
tff(c_32993,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_32960,c_32683]) ).
tff(c_32999,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32993]) ).
tff(c_32997,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32960,c_85]) ).
tff(c_33022,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32999,c_32997]) ).
tff(c_33023,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_33021,c_33022]) ).
tff(c_33025,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_66,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_56892,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_33025,c_66]) ).
tff(c_33024,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_33029,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33024,c_4]) ).
tff(c_56916,plain,
! [X_578,Y_579,Z_580] : ( multiply(multiply(X_578,Y_579),Z_580) = multiply(X_578,multiply(Y_579,Z_580)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_56943,plain,
! [Z_580] : ( multiply(sk_c6,multiply(sk_c4,Z_580)) = multiply(identity,Z_580) ),
inference(superposition,[status(thm),theory(equality)],[c_33029,c_56916]) ).
tff(c_56983,plain,
! [Z_582] : ( multiply(sk_c6,multiply(sk_c4,Z_582)) = Z_582 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_56943]) ).
tff(c_56995,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_56892,c_56983]) ).
tff(c_56946,plain,
! [X_2,Z_580] : ( multiply(inverse(X_2),multiply(X_2,Z_580)) = multiply(identity,Z_580) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_56916]) ).
tff(c_57006,plain,
! [X_583,Z_584] : ( multiply(inverse(X_583),multiply(X_583,Z_584)) = Z_584 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_56946]) ).
tff(c_57024,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_56995,c_57006]) ).
tff(c_58,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_56882,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_33025,c_58]) ).
tff(c_57042,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_56882,c_57006]) ).
tff(c_57193,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_57024,c_57042]) ).
tff(c_33116,plain,
! [X_381,Y_382,Z_383] : ( multiply(multiply(X_381,Y_382),Z_383) = multiply(X_381,multiply(Y_382,Z_383)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_33149,plain,
! [X_2,Z_383] : ( multiply(inverse(X_2),multiply(X_2,Z_383)) = multiply(identity,Z_383) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_33116]) ).
tff(c_33535,plain,
! [X_393,Z_394] : ( multiply(inverse(X_393),multiply(X_393,Z_394)) = Z_394 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33149]) ).
tff(c_33162,plain,
! [X_2,Z_383] : ( multiply(inverse(X_2),multiply(X_2,Z_383)) = Z_383 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33149]) ).
tff(c_34208,plain,
! [X_409,Z_410] : ( multiply(inverse(inverse(X_409)),Z_410) = multiply(X_409,Z_410) ),
inference(superposition,[status(thm),theory(equality)],[c_33535,c_33162]) ).
tff(c_33565,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_33535]) ).
tff(c_34215,plain,
! [X_409] : ( multiply(X_409,identity) = X_409 ),
inference(superposition,[status(thm),theory(equality)],[c_34208,c_33565]) ).
tff(c_33668,plain,
! [X_396,Z_397] : ( multiply(inverse(inverse(X_396)),Z_397) = multiply(X_396,Z_397) ),
inference(superposition,[status(thm),theory(equality)],[c_33162,c_33535]) ).
tff(c_33675,plain,
! [X_396] : ( multiply(X_396,identity) = X_396 ),
inference(superposition,[status(thm),theory(equality)],[c_33668,c_33565]) ).
tff(c_33056,plain,
inverse(sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_33060,plain,
multiply(sk_c6,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33056,c_4]) ).
tff(c_33083,plain,
( ( sk_c5 = identity )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_33060,c_58]) ).
tff(c_33084,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_33025,c_33083]) ).
tff(c_33097,plain,
( ( multiply(sk_c4,identity) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_33084,c_66]) ).
tff(c_33098,plain,
multiply(sk_c4,identity) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_33025,c_33097]) ).
tff(c_33146,plain,
! [Z_383] : ( multiply(sk_c6,multiply(sk_c4,Z_383)) = multiply(identity,Z_383) ),
inference(superposition,[status(thm),theory(equality)],[c_33029,c_33116]) ).
tff(c_33187,plain,
! [Z_385] : ( multiply(sk_c6,multiply(sk_c4,Z_385)) = Z_385 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33146]) ).
tff(c_33199,plain,
multiply(sk_c6,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33098,c_33187]) ).
tff(c_62,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_33089,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_33025,c_62]) ).
tff(c_60,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_33033,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_60]) ).
tff(c_33034,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_33025,c_33033]) ).
tff(c_33035,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_60]) ).
tff(c_33040,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33035,c_4]) ).
tff(c_33143,plain,
! [Z_383] : ( multiply(sk_c7,multiply(sk_c3,Z_383)) = multiply(identity,Z_383) ),
inference(superposition,[status(thm),theory(equality)],[c_33040,c_33116]) ).
tff(c_33164,plain,
! [Z_384] : ( multiply(sk_c7,multiply(sk_c3,Z_384)) = Z_384 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33143]) ).
tff(c_33176,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_33089,c_33164]) ).
tff(c_33140,plain,
! [Z_383] : ( multiply(sk_c6,multiply(sk_c7,Z_383)) = multiply(identity,Z_383) ),
inference(superposition,[status(thm),theory(equality)],[c_33060,c_33116]) ).
tff(c_33429,plain,
! [Z_391] : ( multiply(sk_c6,multiply(sk_c7,Z_391)) = Z_391 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33140]) ).
tff(c_33444,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_33176,c_33429]) ).
tff(c_33457,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33199,c_33444]) ).
tff(c_33461,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33457,c_33457,c_33176]) ).
tff(c_33471,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33461]) ).
tff(c_33131,plain,
! [Z_383] : ( multiply(sk_c4,multiply(identity,Z_383)) = multiply(sk_c6,Z_383) ),
inference(superposition,[status(thm),theory(equality)],[c_33098,c_33116]) ).
tff(c_33157,plain,
! [Z_383] : ( multiply(sk_c6,Z_383) = multiply(sk_c4,Z_383) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33131]) ).
tff(c_33225,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c6,identity) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_33056,c_33084,c_33084,c_33060,c_33084,c_68]) ).
tff(c_33226,plain,
multiply(sk_c6,identity) != sk_c7,
inference(splitLeft,[status(thm)],[c_33225]) ).
tff(c_33227,plain,
multiply(sk_c4,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_33157,c_33226]) ).
tff(c_33228,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33098,c_33227]) ).
tff(c_33229,plain,
! [Z_387] : ( multiply(sk_c6,Z_387) = multiply(sk_c4,Z_387) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33131]) ).
tff(c_33244,plain,
multiply(sk_c4,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_33229,c_33060]) ).
tff(c_33326,plain,
! [X_389,Z_390] : ( multiply(inverse(X_389),multiply(X_389,Z_390)) = Z_390 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33149]) ).
tff(c_33350,plain,
multiply(inverse(sk_c4),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_33244,c_33326]) ).
tff(c_33416,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33098,c_33157,c_33024,c_33350]) ).
tff(c_33418,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_33228,c_33416]) ).
tff(c_33419,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_33225]) ).
tff(c_33628,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != 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_33471,c_33471,c_33457,c_33471,c_33457,c_33471,c_33457,c_33471,c_33471,c_33457,c_33457,c_33419]) ).
tff(c_33629,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_33628]) ).
tff(c_34171,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_33675,c_33629]) ).
tff(c_33467,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33457,c_33056]) ).
tff(c_33519,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33471,c_33467]) ).
tff(c_34173,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34171,c_33519]) ).
tff(c_34174,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_33628]) ).
tff(c_55945,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_34215,c_34215,c_34215,c_34174]) ).
tff(c_55947,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_55945]) ).
tff(c_55949,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_55947,c_33519]) ).
tff(c_55950,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_55945]) ).
tff(c_55952,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_55950]) ).
tff(c_55954,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_55952,c_33519]) ).
tff(c_56873,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_55950]) ).
tff(c_56875,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56873,c_33519]) ).
tff(c_56876,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_56940,plain,
! [Z_580] : ( multiply(sk_c7,multiply(sk_c3,Z_580)) = multiply(identity,Z_580) ),
inference(superposition,[status(thm),theory(equality)],[c_33040,c_56916]) ).
tff(c_56958,plain,
! [Z_581] : ( multiply(sk_c7,multiply(sk_c3,Z_581)) = Z_581 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_56940]) ).
tff(c_56970,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_56876,c_56958]) ).
tff(c_57030,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_56970,c_57006]) ).
tff(c_57204,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_57193,c_57193,c_57030]) ).
tff(c_57213,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_57204]) ).
tff(c_56877,plain,
inverse(sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_57210,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_57193,c_56877]) ).
tff(c_57268,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_57213,c_57213,c_57210]) ).
tff(c_57212,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_57193,c_33035]) ).
tff(c_57270,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_57213,c_57212]) ).
tff(c_57060,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_57006]) ).
tff(c_57274,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_57270,c_57060]) ).
tff(c_57283,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_57274]) ).
tff(c_57286,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_57283,c_57270]) ).
tff(c_57289,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57268,c_57286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP381-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 22:02:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 15.07/6.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.07/6.28
% 15.07/6.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.21/6.34
% 15.21/6.34 Inference rules
% 15.21/6.34 ----------------------
% 15.21/6.34 #Ref : 0
% 15.21/6.34 #Sup : 13916
% 15.21/6.34 #Fact : 0
% 15.21/6.34 #Define : 0
% 15.21/6.34 #Split : 29
% 15.21/6.34 #Chain : 0
% 15.21/6.34 #Close : 0
% 15.21/6.34
% 15.21/6.34 Ordering : KBO
% 15.21/6.34
% 15.21/6.34 Simplification rules
% 15.21/6.34 ----------------------
% 15.21/6.34 #Subsume : 8
% 15.21/6.34 #Demod : 42202
% 15.21/6.34 #Tautology : 11267
% 15.21/6.34 #SimpNegUnit : 81
% 15.21/6.34 #BackRed : 446
% 15.21/6.34
% 15.21/6.34 #Partial instantiations: 0
% 15.21/6.34 #Strategies tried : 1
% 15.21/6.34
% 15.21/6.34 Timing (in seconds)
% 15.21/6.34 ----------------------
% 15.21/6.35 Preprocessing : 0.50
% 15.21/6.35 Parsing : 0.21
% 15.21/6.35 CNF conversion : 0.03
% 15.21/6.35 Main loop : 4.69
% 15.21/6.35 Inferencing : 1.26
% 15.21/6.35 Reduction : 2.68
% 15.21/6.35 Demodulation : 2.46
% 15.21/6.35 BG Simplification : 0.11
% 15.21/6.35 Subsumption : 0.43
% 15.21/6.35 Abstraction : 0.28
% 15.21/6.35 MUC search : 0.00
% 15.21/6.35 Cooper : 0.00
% 15.21/6.35 Total : 5.31
% 15.21/6.35 Index Insertion : 0.00
% 15.21/6.35 Index Deletion : 0.00
% 15.21/6.35 Index Matching : 0.00
% 15.21/6.35 BG Taut test : 0.00
%------------------------------------------------------------------------------