TSTP Solution File: GRP359-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP359-1 : 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 : n032.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 10:41:03 EDT 2023
% Result : Unsatisfiable 10.85s 3.59s
% Output : CNFRefutation 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of formulae : 467 ( 379 unt; 11 typ; 0 def)
% Number of atoms : 598 ( 580 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 281 ( 139 ~; 142 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 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 : 168 (; 168 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c8 > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(sk_c8,type,
sk_c8: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X5,X3,X1,X2,X4] :
( ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c8,X3) != sk_c7 )
| ( multiply(X4,sk_c8) != X3 )
| ( inverse(X4) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,X2) != sk_c7 )
| ( multiply(X5,sk_c8) != X2 )
| ( inverse(X5) != sk_c8 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c8,sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_13016,plain,
! [X_201,Y_202,Z_203] : ( multiply(multiply(X_201,Y_202),Z_203) = multiply(X_201,multiply(Y_202,Z_203)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_13052,plain,
! [X_2,Z_203] : ( multiply(inverse(X_2),multiply(X_2,Z_203)) = multiply(identity,Z_203) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_13016]) ).
tff(c_13063,plain,
! [X_2,Z_203] : ( multiply(inverse(X_2),multiply(X_2,Z_203)) = Z_203 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13052]) ).
tff(c_14919,plain,
! [X_236,Z_237] : ( multiply(inverse(X_236),multiply(X_236,Z_237)) = Z_237 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13052]) ).
tff(c_15249,plain,
! [X_240,Z_241] : ( multiply(inverse(inverse(X_240)),Z_241) = multiply(X_240,Z_241) ),
inference(superposition,[status(thm),theory(equality)],[c_13063,c_14919]) ).
tff(c_14967,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14919]) ).
tff(c_15256,plain,
! [X_240] : ( multiply(X_240,identity) = X_240 ),
inference(superposition,[status(thm),theory(equality)],[c_15249,c_14967]) ).
tff(c_9996,plain,
! [X_144,Y_145,Z_146] : ( multiply(multiply(X_144,Y_145),Z_146) = multiply(X_144,multiply(Y_145,Z_146)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10035,plain,
! [X_2,Z_146] : ( multiply(inverse(X_2),multiply(X_2,Z_146)) = multiply(identity,Z_146) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9996]) ).
tff(c_12004,plain,
! [X_183,Z_184] : ( multiply(inverse(X_183),multiply(X_183,Z_184)) = Z_184 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10035]) ).
tff(c_10047,plain,
! [X_2,Z_146] : ( multiply(inverse(X_2),multiply(X_2,Z_146)) = Z_146 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10035]) ).
tff(c_12149,plain,
! [X_186,Z_187] : ( multiply(inverse(inverse(X_186)),Z_187) = multiply(X_186,Z_187) ),
inference(superposition,[status(thm),theory(equality)],[c_12004,c_10047]) ).
tff(c_12040,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12004]) ).
tff(c_12156,plain,
! [X_186] : ( multiply(X_186,identity) = X_186 ),
inference(superposition,[status(thm),theory(equality)],[c_12149,c_12040]) ).
tff(c_66,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_85,plain,
inverse(sk_c1) = sk_c8,
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_89,plain,
multiply(sk_c8,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_98,plain,
inverse(sk_c8) = sk_c6,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_102,plain,
multiply(sk_c6,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_10029,plain,
! [Z_146] : ( multiply(sk_c6,multiply(sk_c8,Z_146)) = multiply(identity,Z_146) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_9996]) ).
tff(c_10049,plain,
! [Z_147] : ( multiply(sk_c6,multiply(sk_c8,Z_147)) = Z_147 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10029]) ).
tff(c_10073,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_10049]) ).
tff(c_48,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_8643,plain,
multiply(sk_c1,sk_c8) = sk_c2,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_8692,plain,
! [X_115,Y_116,Z_117] : ( multiply(multiply(X_115,Y_116),Z_117) = multiply(X_115,multiply(Y_116,Z_117)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8737,plain,
! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = multiply(identity,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8692]) ).
tff(c_8878,plain,
! [X_120,Z_121] : ( multiply(inverse(X_120),multiply(X_120,Z_121)) = Z_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8737]) ).
tff(c_8914,plain,
multiply(inverse(sk_c1),sk_c2) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_8643,c_8878]) ).
tff(c_8937,plain,
multiply(sk_c8,sk_c2) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_85,c_8914]) ).
tff(c_8749,plain,
! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = Z_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8737]) ).
tff(c_8943,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_8937,c_8749]) ).
tff(c_8955,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_98,c_8943]) ).
tff(c_8731,plain,
! [Z_117] : ( multiply(sk_c6,multiply(sk_c8,Z_117)) = multiply(identity,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_8692]) ).
tff(c_8751,plain,
! [Z_118] : ( multiply(sk_c6,multiply(sk_c8,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8731]) ).
tff(c_8778,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_8751]) ).
tff(c_8448,plain,
! [X_110,Y_111,Z_112] : ( multiply(multiply(X_110,Y_111),Z_112) = multiply(X_110,multiply(Y_111,Z_112)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8487,plain,
! [Z_112] : ( multiply(sk_c6,multiply(sk_c8,Z_112)) = multiply(identity,Z_112) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_8448]) ).
tff(c_8507,plain,
! [Z_113] : ( multiply(sk_c6,multiply(sk_c8,Z_113)) = Z_113 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8487]) ).
tff(c_8534,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_8507]) ).
tff(c_149,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_179,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_149]) ).
tff(c_189,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_179]) ).
tff(c_307,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_179]) ).
tff(c_510,plain,
! [X_21,Z_22] : ( multiply(inverse(inverse(X_21)),Z_22) = multiply(X_21,Z_22) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_307]) ).
tff(c_337,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_307]) ).
tff(c_517,plain,
! [X_21] : ( multiply(X_21,identity) = X_21 ),
inference(superposition,[status(thm),theory(equality)],[c_510,c_337]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_111,plain,
multiply(sk_c8,sk_c2) = sk_c7,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_128,plain,
multiply(sk_c1,sk_c8) = sk_c2,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_176,plain,
! [Z_15] : ( multiply(sk_c8,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_149]) ).
tff(c_225,plain,
! [Z_17] : ( multiply(sk_c8,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_176]) ).
tff(c_240,plain,
multiply(sk_c8,sk_c2) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_128,c_225]) ).
tff(c_244,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_240]) ).
tff(c_68,plain,
! [X5_6,X1_8,X4_10] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 )
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_258,plain,
! [X5_6,X1_8,X4_10] :
( ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_10,sk_c7)) != sk_c7 )
| ( inverse(sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_244,c_244,c_244,c_244,c_244,c_244,c_244,c_244,c_244,c_244,c_68]) ).
tff(c_259,plain,
multiply(sk_c7,sk_c6) != sk_c7,
inference(splitLeft,[status(thm)],[c_258]) ).
tff(c_18,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_117,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_248,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_117]) ).
tff(c_297,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_259,c_248]) ).
tff(c_299,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_258]) ).
tff(c_399,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_299,c_189]) ).
tff(c_405,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_399]) ).
tff(c_250,plain,
multiply(sk_c6,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_102]) ).
tff(c_443,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_405,c_250]) ).
tff(c_173,plain,
! [Z_15] : ( multiply(sk_c6,multiply(sk_c8,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_149]) ).
tff(c_191,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c8,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_173]) ).
tff(c_206,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_191]) ).
tff(c_409,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_206]) ).
tff(c_410,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_409]) ).
tff(c_253,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_85]) ).
tff(c_416,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_410,c_253]) ).
tff(c_445,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_443,c_416]) ).
tff(c_298,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_10,sk_c7)) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c7 )
| ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_258]) ).
tff(c_8377,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_517,c_443,c_443,c_2,c_443,c_443,c_517,c_443,c_443,c_443,c_517,c_443,c_443,c_2,c_443,c_443,c_443,c_2,c_443,c_405,c_445,c_443,c_405,c_298]) ).
tff(c_8379,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8377]) ).
tff(c_8381,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8379,c_445]) ).
tff(c_8382,plain,
! [X1_8,X4_10] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 ) ),
inference(splitRight,[status(thm)],[c_8377]) ).
tff(c_8384,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8382]) ).
tff(c_8386,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8384,c_445]) ).
tff(c_8389,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_8382]) ).
tff(c_8391,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8389,c_445]) ).
tff(c_8392,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_8397,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8392,c_4]) ).
tff(c_8528,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_8397,c_8507]) ).
tff(c_8571,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_8534,c_8528]) ).
tff(c_8393,plain,
multiply(sk_c1,sk_c8) != sk_c2,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_8433,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8393,c_46]) ).
tff(c_8572,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8571,c_8433]) ).
tff(c_8597,plain,
sk_c7 != sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8572,c_8393]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_8405,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_8393,c_54]) ).
tff(c_8409,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8405,c_4]) ).
tff(c_8525,plain,
multiply(sk_c6,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_8409,c_8507]) ).
tff(c_8612,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_8534,c_8525]) ).
tff(c_8531,plain,
multiply(sk_c6,sk_c7) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_111,c_8507]) ).
tff(c_50,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_8443,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8393,c_50]) ).
tff(c_8519,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_8443,c_8507]) ).
tff(c_8563,plain,
sk_c5 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8531,c_8519]) ).
tff(c_52,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_8428,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_8393,c_52]) ).
tff(c_8565,plain,
multiply(sk_c4,sk_c8) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8563,c_8428]) ).
tff(c_8613,plain,
multiply(sk_c1,sk_c8) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8612,c_8565]) ).
tff(c_8622,plain,
sk_c7 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8613,c_8572]) ).
tff(c_8624,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8597,c_8622]) ).
tff(c_8626,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_8650,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_8626,c_12]) ).
tff(c_8654,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8650,c_4]) ).
tff(c_8769,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_8654,c_8751]) ).
tff(c_8799,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_8778,c_8769]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_8667,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8626,c_10]) ).
tff(c_8800,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8799,c_8667]) ).
tff(c_8803,plain,
sk_c7 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8643,c_8800]) ).
tff(c_8963,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8955,c_8803]) ).
tff(c_8728,plain,
! [Z_117] : ( multiply(sk_c8,multiply(sk_c2,Z_117)) = multiply(sk_c7,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_111,c_8692]) ).
tff(c_9048,plain,
! [Z_123] : ( multiply(sk_c8,Z_123) = Z_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8963,c_2,c_8955,c_8728]) ).
tff(c_9060,plain,
sk_c1 = identity,
inference(superposition,[status(thm),theory(equality)],[c_9048,c_89]) ).
tff(c_9045,plain,
! [Z_117] : ( multiply(sk_c8,Z_117) = Z_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8963,c_2,c_8955,c_8728]) ).
tff(c_8959,plain,
multiply(sk_c8,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_8955,c_8937]) ).
tff(c_9046,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9045,c_8959]) ).
tff(c_9076,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9046,c_85]) ).
tff(c_9114,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9060,c_9076]) ).
tff(c_9074,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9046,c_98]) ).
tff(c_9133,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9114,c_9074]) ).
tff(c_8841,plain,
multiply(sk_c2,sk_c6) != sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_8803,c_8626]) ).
tff(c_9148,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9133,c_9046,c_2,c_8955,c_8841]) ).
tff(c_9150,plain,
multiply(sk_c1,sk_c8) != sk_c2,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_9200,plain,
! [X_125,Y_126,Z_127] : ( multiply(multiply(X_125,Y_126),Z_127) = multiply(X_125,multiply(Y_126,Z_127)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9236,plain,
! [Z_127] : ( multiply(sk_c6,multiply(sk_c8,Z_127)) = multiply(identity,Z_127) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_9200]) ).
tff(c_9271,plain,
! [Z_129] : ( multiply(sk_c6,multiply(sk_c8,Z_129)) = Z_129 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9236]) ).
tff(c_9298,plain,
multiply(sk_c6,sk_c7) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_111,c_9271]) ).
tff(c_9170,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9150,c_50]) ).
tff(c_9289,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9170,c_9271]) ).
tff(c_9363,plain,
sk_c5 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_9298,c_9289]) ).
tff(c_9301,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_9271]) ).
tff(c_8625,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_8630,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8625,c_4]) ).
tff(c_9295,plain,
multiply(sk_c6,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_8630,c_9271]) ).
tff(c_9343,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_9301,c_9295]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_9187,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_8626,c_16]) ).
tff(c_9344,plain,
multiply(sk_c1,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9343,c_9187]) ).
tff(c_9441,plain,
multiply(sk_c1,sk_c8) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_9363,c_9344]) ).
tff(c_9442,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9150,c_9441]) ).
tff(c_9443,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_9448,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9443,c_4]) ).
tff(c_10070,plain,
multiply(sk_c6,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_9448,c_10049]) ).
tff(c_10597,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10073,c_10070]) ).
tff(c_9444,plain,
multiply(sk_c8,sk_c2) != sk_c7,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_9975,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_9444,c_40]) ).
tff(c_10598,plain,
multiply(sk_c1,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10597,c_9975]) ).
tff(c_36,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_9459,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_9444,c_36]) ).
tff(c_9463,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9459,c_4]) ).
tff(c_10067,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_9463,c_10049]) ).
tff(c_10473,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10073,c_10067]) ).
tff(c_38,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_9502,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9444,c_38]) ).
tff(c_9516,plain,
! [X_133,Y_134,Z_135] : ( multiply(multiply(X_133,Y_134),Z_135) = multiply(X_133,multiply(Y_134,Z_135)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9555,plain,
! [Z_135] : ( multiply(sk_c6,multiply(sk_c8,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_9516]) ).
tff(c_9717,plain,
! [Z_141] : ( multiply(sk_c6,multiply(sk_c8,Z_141)) = Z_141 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9555]) ).
tff(c_9741,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9502,c_9717]) ).
tff(c_32,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_9509,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9444,c_32]) ).
tff(c_9750,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_9717]) ).
tff(c_9744,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_9463,c_9717]) ).
tff(c_9783,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_9750,c_9744]) ).
tff(c_34,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_9492,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9444,c_34]) ).
tff(c_9784,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9783,c_9492]) ).
tff(c_9558,plain,
! [Z_135] : ( multiply(sk_c8,multiply(sk_c1,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_9516]) ).
tff(c_9572,plain,
! [Z_135] : ( multiply(sk_c8,multiply(sk_c1,Z_135)) = Z_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9558]) ).
tff(c_9817,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_9784,c_9572]) ).
tff(c_9823,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9509,c_9817]) ).
tff(c_9862,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9823,c_9509]) ).
tff(c_9869,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9741,c_9862]) ).
tff(c_9480,plain,
multiply(sk_c1,sk_c8) = sk_c2,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_9677,plain,
! [Z_139] : ( multiply(sk_c8,multiply(sk_c1,Z_139)) = Z_139 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9558]) ).
tff(c_9689,plain,
multiply(sk_c8,sk_c2) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_9480,c_9677]) ).
tff(c_9693,plain,
sk_c8 != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9689,c_9444]) ).
tff(c_9860,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9823,c_9693]) ).
tff(c_9886,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9869,c_9860]) ).
tff(c_9874,plain,
sk_c8 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9869,c_9823]) ).
tff(c_9747,plain,
multiply(sk_c6,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_9448,c_9717]) ).
tff(c_9794,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_9750,c_9747]) ).
tff(c_9485,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_9444,c_40]) ).
tff(c_9795,plain,
multiply(sk_c1,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9794,c_9485]) ).
tff(c_9919,plain,
multiply(sk_c1,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9874,c_9795]) ).
tff(c_9857,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9823,c_9784]) ).
tff(c_9961,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9919,c_9869,c_9857]) ).
tff(c_9962,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9886,c_9961]) ).
tff(c_9964,plain,
multiply(sk_c1,sk_c8) != sk_c2,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_9983,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9964,c_46]) ).
tff(c_10482,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10473,c_9983]) ).
tff(c_10638,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10598,c_10482]) ).
tff(c_9963,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_10652,plain,
multiply(sk_c8,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_9963]) ).
tff(c_44,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_9969,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9964,c_44]) ).
tff(c_10651,plain,
multiply(sk_c8,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_9969]) ).
tff(c_11923,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10652,c_10651]) ).
tff(c_10064,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9963,c_10049]) ).
tff(c_10649,plain,
multiply(sk_c6,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_10064]) ).
tff(c_11924,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11923,c_10649]) ).
tff(c_12022,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11924,c_12004]) ).
tff(c_12047,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12022]) ).
tff(c_11929,plain,
inverse(sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11923,c_98]) ).
tff(c_11954,plain,
multiply(sk_c5,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11929,c_4]) ).
tff(c_12073,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12047,c_11954]) ).
tff(c_10768,plain,
! [X_157,Z_158] : ( multiply(inverse(X_157),multiply(X_157,Z_158)) = Z_158 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10035]) ).
tff(c_10913,plain,
! [X_160,Z_161] : ( multiply(inverse(inverse(X_160)),Z_161) = multiply(X_160,Z_161) ),
inference(superposition,[status(thm),theory(equality)],[c_10047,c_10768]) ).
tff(c_10804,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10768]) ).
tff(c_10920,plain,
! [X_160] : ( multiply(X_160,identity) = X_160 ),
inference(superposition,[status(thm),theory(equality)],[c_10913,c_10804]) ).
tff(c_10687,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10652,c_10651]) ).
tff(c_10688,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10687,c_10649]) ).
tff(c_10786,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10688,c_10768]) ).
tff(c_10811,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10786]) ).
tff(c_10693,plain,
inverse(sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10687,c_98]) ).
tff(c_10718,plain,
multiply(sk_c5,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10693,c_4]) ).
tff(c_10837,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10811,c_10718]) ).
tff(c_10492,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10073,c_10070]) ).
tff(c_10493,plain,
multiply(sk_c1,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10492,c_9975]) ).
tff(c_10533,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10493,c_10482]) ).
tff(c_10547,plain,
multiply(sk_c8,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10533,c_9963]) ).
tff(c_10102,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10073,c_10067]) ).
tff(c_10111,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10102,c_9983]) ).
tff(c_10196,plain,
multiply(inverse(sk_c1),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_10111,c_10047]) ).
tff(c_10202,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9969,c_85,c_10196]) ).
tff(c_10207,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10202,c_9969]) ).
tff(c_10214,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10064,c_10207]) ).
tff(c_10255,plain,
sk_c8 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10214,c_10202]) ).
tff(c_10120,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10073,c_10070]) ).
tff(c_10121,plain,
multiply(sk_c1,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10120,c_9975]) ).
tff(c_10289,plain,
multiply(sk_c1,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10255,c_10121]) ).
tff(c_10204,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10202,c_10111]) ).
tff(c_10351,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10289,c_10214,c_10204]) ).
tff(c_10210,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10202,c_102]) ).
tff(c_10319,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10214,c_10214,c_10210]) ).
tff(c_10208,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10202,c_9963]) ).
tff(c_10359,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10351,c_10319,c_10214,c_10208]) ).
tff(c_10361,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10359,c_10351]) ).
tff(c_10092,plain,
! [X5_6,X1_8,X4_10] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_9969,c_68]) ).
tff(c_10093,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitLeft,[status(thm)],[c_10092]) ).
tff(c_10205,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10202,c_10093]) ).
tff(c_10455,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10361,c_10205]) ).
tff(c_10456,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_10092]) ).
tff(c_10491,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_10456]) ).
tff(c_10574,plain,
! [X5_154] :
( ( inverse(X5_154) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_154,sk_c8)) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10533,c_10491]) ).
tff(c_10577,plain,
( ( inverse(sk_c1) != sk_c8 )
| ( multiply(sk_c8,sk_c5) != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_10493,c_10574]) ).
tff(c_10595,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10547,c_85,c_10577]) ).
tff(c_10596,plain,
! [X1_8,X4_10] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_10456]) ).
tff(c_10678,plain,
! [X1_8,X4_10] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c5 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_10638,c_10596]) ).
tff(c_10679,plain,
! [X4_10] :
( ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_10678]) ).
tff(c_11912,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_10920,c_10837,c_2,c_10837,c_10811,c_10837,c_10679]) ).
tff(c_10690,plain,
multiply(sk_c5,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10687,c_10073]) ).
tff(c_10020,plain,
! [Z_146] : ( multiply(sk_c8,multiply(sk_c5,Z_146)) = multiply(sk_c7,Z_146) ),
inference(superposition,[status(thm),theory(equality)],[c_9963,c_9996]) ).
tff(c_10698,plain,
! [Z_146] : ( multiply(sk_c8,multiply(sk_c5,Z_146)) = multiply(sk_c5,Z_146) ),
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_10020]) ).
tff(c_10748,plain,
multiply(sk_c8,sk_c1) = multiply(sk_c5,identity),
inference(superposition,[status(thm),theory(equality)],[c_10690,c_10698]) ).
tff(c_10754,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10690,c_89,c_10748]) ).
tff(c_10763,plain,
inverse(identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_10754,c_85]) ).
tff(c_10850,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10837,c_10763]) ).
tff(c_11914,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11912,c_10850]) ).
tff(c_11915,plain,
! [X1_8] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_10678]) ).
tff(c_12409,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12156,c_12073,c_12047,c_12073,c_11915]) ).
tff(c_11926,plain,
multiply(sk_c5,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_11923,c_10073]) ).
tff(c_11934,plain,
! [Z_146] : ( multiply(sk_c8,multiply(sk_c5,Z_146)) = multiply(sk_c5,Z_146) ),
inference(demodulation,[status(thm),theory(equality)],[c_10638,c_10020]) ).
tff(c_11984,plain,
multiply(sk_c8,sk_c1) = multiply(sk_c5,identity),
inference(superposition,[status(thm),theory(equality)],[c_11926,c_11934]) ).
tff(c_11990,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11926,c_89,c_11984]) ).
tff(c_11999,plain,
inverse(identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_11990,c_85]) ).
tff(c_12086,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12073,c_11999]) ).
tff(c_12411,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12409,c_12086]) ).
tff(c_12413,plain,
inverse(sk_c8) != sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_26,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_12443,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12413,c_26]) ).
tff(c_28,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_12459,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_12413,c_28]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_12425,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_12413,c_30]) ).
tff(c_12429,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12425,c_4]) ).
tff(c_12479,plain,
! [X_193,Y_194,Z_195] : ( multiply(multiply(X_193,Y_194),Z_195) = multiply(X_193,multiply(Y_194,Z_195)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12506,plain,
! [Z_195] : ( multiply(sk_c8,multiply(sk_c4,Z_195)) = multiply(identity,Z_195) ),
inference(superposition,[status(thm),theory(equality)],[c_12429,c_12479]) ).
tff(c_12528,plain,
! [Z_196] : ( multiply(sk_c8,multiply(sk_c4,Z_196)) = Z_196 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12506]) ).
tff(c_12540,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_12459,c_12528]) ).
tff(c_12544,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12443,c_12540]) ).
tff(c_20,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_12453,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_12413,c_20]) ).
tff(c_12549,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12544,c_12453]) ).
tff(c_12412,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_12556,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12544,c_12412]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_12448,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12413,c_22]) ).
tff(c_12550,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12544,c_12448]) ).
tff(c_12515,plain,
! [X_2,Z_195] : ( multiply(inverse(X_2),multiply(X_2,Z_195)) = multiply(identity,Z_195) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12479]) ).
tff(c_12526,plain,
! [X_2,Z_195] : ( multiply(inverse(X_2),multiply(X_2,Z_195)) = Z_195 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12515]) ).
tff(c_12662,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12550,c_12526]) ).
tff(c_12668,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12549,c_12556,c_12662]) ).
tff(c_12671,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12668,c_12668,c_12549]) ).
tff(c_12839,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_12671,c_12526]) ).
tff(c_12846,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12839]) ).
tff(c_12558,plain,
inverse(sk_c1) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12544,c_85]) ).
tff(c_12673,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12668,c_12558]) ).
tff(c_12725,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12673,c_4]) ).
tff(c_12906,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12846,c_12725]) ).
tff(c_12856,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12846,c_12673]) ).
tff(c_12911,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12906,c_12856]) ).
tff(c_12555,plain,
inverse(sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12544,c_12413]) ).
tff(c_12675,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12668,c_12555]) ).
tff(c_12858,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12846,c_12846,c_12675]) ).
tff(c_12935,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12911,c_12858]) ).
tff(c_12937,plain,
inverse(sk_c1) != sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_56,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_12986,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_12937,c_56]) ).
tff(c_58,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_12998,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12937,c_58]) ).
tff(c_60,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_12945,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_12937,c_60]) ).
tff(c_12949,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12945,c_4]) ).
tff(c_13046,plain,
! [Z_203] : ( multiply(sk_c8,multiply(sk_c3,Z_203)) = multiply(identity,Z_203) ),
inference(superposition,[status(thm),theory(equality)],[c_12949,c_13016]) ).
tff(c_13465,plain,
! [Z_208] : ( multiply(sk_c8,multiply(sk_c3,Z_208)) = Z_208 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13046]) ).
tff(c_13477,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_12998,c_13465]) ).
tff(c_13481,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12986,c_13477]) ).
tff(c_13486,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_12986]) ).
tff(c_12971,plain,
inverse(sk_c8) = sk_c6,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_13488,plain,
inverse(sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_12971]) ).
tff(c_62,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_12966,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12937,c_62]) ).
tff(c_13489,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_12966]) ).
tff(c_14937,plain,
multiply(inverse(sk_c6),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_13489,c_14919]) ).
tff(c_14974,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_13486,c_13488,c_14937]) ).
tff(c_12936,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_13494,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_12936]) ).
tff(c_64,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_12992,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_12937,c_64]) ).
tff(c_13485,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_12992]) ).
tff(c_14943,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_13485,c_14919]) ).
tff(c_14976,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13489,c_13494,c_14943]) ).
tff(c_14987,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14974,c_14976]) ).
tff(c_12941,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12936,c_4]) ).
tff(c_13049,plain,
! [Z_203] : ( multiply(sk_c8,multiply(sk_c4,Z_203)) = multiply(identity,Z_203) ),
inference(superposition,[status(thm),theory(equality)],[c_12941,c_13016]) ).
tff(c_13068,plain,
! [Z_204] : ( multiply(sk_c8,multiply(sk_c4,Z_204)) = Z_204 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13049]) ).
tff(c_13080,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_12992,c_13068]) ).
tff(c_13084,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12966,c_13080]) ).
tff(c_13089,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13084,c_12986]) ).
tff(c_13095,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13084,c_12945]) ).
tff(c_13087,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13084,c_12998]) ).
tff(c_13216,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_13087,c_13063]) ).
tff(c_13222,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13095,c_13216]) ).
tff(c_13248,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13089,c_13222]) ).
tff(c_13091,plain,
inverse(sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13084,c_12971]) ).
tff(c_13156,plain,
multiply(sk_c6,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_13091,c_4]) ).
tff(c_13347,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13248,c_13156]) ).
tff(c_13251,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13248,c_13248,c_13089]) ).
tff(c_13363,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13347,c_13251]) ).
tff(c_13066,plain,
! [X5_6,X1_8,X4_10] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12971,c_12986,c_68]) ).
tff(c_13067,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitLeft,[status(thm)],[c_13066]) ).
tff(c_13086,plain,
multiply(sk_c7,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_13084,c_13067]) ).
tff(c_13249,plain,
multiply(sk_c6,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13248,c_13248,c_13086]) ).
tff(c_13455,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13363,c_13249]) ).
tff(c_13457,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(splitRight,[status(thm)],[c_13066]) ).
tff(c_13483,plain,
multiply(sk_c7,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_13457]) ).
tff(c_15090,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14987,c_14974,c_14974,c_13483]) ).
tff(c_15097,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15090,c_13063]) ).
tff(c_15104,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15097]) ).
tff(c_15115,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15104,c_14987]) ).
tff(c_15116,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15104,c_14974]) ).
tff(c_13601,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_13052]) ).
tff(c_13899,plain,
! [X_214,Z_215] : ( multiply(inverse(inverse(X_214)),Z_215) = multiply(X_214,Z_215) ),
inference(superposition,[status(thm),theory(equality)],[c_13063,c_13601]) ).
tff(c_13658,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_13601]) ).
tff(c_13906,plain,
! [X_214] : ( multiply(X_214,identity) = X_214 ),
inference(superposition,[status(thm),theory(equality)],[c_13899,c_13658]) ).
tff(c_13631,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_13486,c_13601]) ).
tff(c_13668,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_13631]) ).
tff(c_13634,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_13485,c_13601]) ).
tff(c_13669,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13489,c_13494,c_13634]) ).
tff(c_13683,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13668,c_13669]) ).
tff(c_13456,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c8 )
| ( multiply(sk_c8,multiply(X4_10,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_13066]) ).
tff(c_13543,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(sk_c6,multiply(X4_10,sk_c6)) != sk_c7 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_13481,c_13481,c_13481,c_13481,c_13481,c_13481,c_13481,c_13481,c_13456]) ).
tff(c_13544,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_13543]) ).
tff(c_14894,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_13906,c_13683,c_2,c_13683,c_13668,c_13683,c_13544]) ).
tff(c_13688,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13683,c_13683,c_13488]) ).
tff(c_14896,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14894,c_13688]) ).
tff(c_14897,plain,
! [X1_8,X4_10] :
( ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(sk_c6,multiply(X4_10,sk_c6)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_13543]) ).
tff(c_23833,plain,
! [X1_8,X4_10] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_15256,c_15115,c_15116,c_2,c_15116,c_15116,c_15256,c_15115,c_15116,c_15116,c_14897]) ).
tff(c_23835,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_23833]) ).
tff(c_14990,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14974,c_14974,c_13488]) ).
tff(c_15109,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15104,c_15104,c_14990]) ).
tff(c_23837,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23835,c_15109]) ).
tff(c_23839,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_23833]) ).
tff(c_23841,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23839,c_15109]) ).
tff(c_23842,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_23853,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12937,c_58]) ).
tff(c_23881,plain,
! [X_333,Y_334,Z_335] : ( multiply(multiply(X_333,Y_334),Z_335) = multiply(X_333,multiply(Y_334,Z_335)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_23908,plain,
! [Z_335] : ( multiply(sk_c8,multiply(sk_c3,Z_335)) = multiply(identity,Z_335) ),
inference(superposition,[status(thm),theory(equality)],[c_12949,c_23881]) ).
tff(c_23926,plain,
! [Z_336] : ( multiply(sk_c8,multiply(sk_c3,Z_336)) = Z_336 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23908]) ).
tff(c_23938,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_23853,c_23926]) ).
tff(c_23942,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23842,c_23938]) ).
tff(c_23946,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23942,c_23842]) ).
tff(c_23914,plain,
! [X_2,Z_335] : ( multiply(inverse(X_2),multiply(X_2,Z_335)) = multiply(identity,Z_335) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_23881]) ).
tff(c_24011,plain,
! [X_337,Z_338] : ( multiply(inverse(X_337),multiply(X_337,Z_338)) = Z_338 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23914]) ).
tff(c_24032,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23946,c_24011]) ).
tff(c_24061,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_24032]) ).
tff(c_23948,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_23942,c_12966]) ).
tff(c_24069,plain,
multiply(sk_c6,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24061,c_23948]) ).
tff(c_23953,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23942,c_12936]) ).
tff(c_23843,plain,
inverse(sk_c8) != sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_23858,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_23843,c_28]) ).
tff(c_23944,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_23942,c_23858]) ).
tff(c_24029,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_23944,c_24011]) ).
tff(c_24060,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23953,c_24029]) ).
tff(c_24081,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24069,c_24060]) ).
tff(c_23969,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_23953,c_4]) ).
tff(c_24095,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24081,c_23969]) ).
tff(c_24086,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24081,c_23953]) ).
tff(c_24114,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24095,c_24086]) ).
tff(c_23947,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23942,c_23843]) ).
tff(c_24089,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_24081,c_24081,c_23947]) ).
tff(c_24128,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24114,c_24089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP359-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.12 % 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
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Aug 3 22:05:21 EDT 2023
% 0.12/0.32 % CPUTime :
% 10.85/3.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.85/3.63
% 10.85/3.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.85/3.69
% 10.85/3.69 Inference rules
% 10.85/3.69 ----------------------
% 10.85/3.69 #Ref : 0
% 10.85/3.69 #Sup : 6002
% 10.85/3.69 #Fact : 0
% 10.85/3.69 #Define : 0
% 10.85/3.69 #Split : 21
% 10.85/3.69 #Chain : 0
% 10.85/3.69 #Close : 0
% 10.85/3.69
% 10.85/3.69 Ordering : KBO
% 10.85/3.69
% 10.85/3.69 Simplification rules
% 10.85/3.69 ----------------------
% 10.85/3.69 #Subsume : 8
% 10.85/3.69 #Demod : 13093
% 10.85/3.69 #Tautology : 4890
% 10.85/3.69 #SimpNegUnit : 59
% 10.85/3.69 #BackRed : 386
% 10.85/3.69
% 10.85/3.69 #Partial instantiations: 0
% 10.85/3.69 #Strategies tried : 1
% 10.85/3.69
% 10.85/3.69 Timing (in seconds)
% 10.85/3.69 ----------------------
% 10.85/3.69 Preprocessing : 0.52
% 10.85/3.69 Parsing : 0.21
% 10.85/3.69 CNF conversion : 0.03
% 10.85/3.69 Main loop : 2.15
% 10.85/3.69 Inferencing : 0.69
% 10.85/3.69 Reduction : 0.99
% 10.85/3.69 Demodulation : 0.85
% 10.85/3.69 BG Simplification : 0.08
% 10.85/3.69 Subsumption : 0.24
% 10.85/3.69 Abstraction : 0.12
% 10.85/3.69 MUC search : 0.00
% 10.85/3.69 Cooper : 0.00
% 10.85/3.69 Total : 2.78
% 10.85/3.69 Index Insertion : 0.00
% 10.85/3.69 Index Deletion : 0.00
% 10.85/3.69 Index Matching : 0.00
% 10.85/3.69 BG Taut test : 0.00
%------------------------------------------------------------------------------