%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP339-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 06:25:59 PM UTC 2025
% Result : Unsatisfiable 35.57s 22.10s
% Output : CNFRefutation 36.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 33
% Syntax : Number of formulae : 539 ( 435 unt; 0 typ; 0 def)
% Number of atoms : 792 ( 766 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 537 ( 284 ~; 253 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 222 ( 222 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c9 > 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_c9,type,
sk_c9: $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_165,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_63,axiom,
multiply(sk_c8,sk_c9) = sk_c7,
file(unknown,unknown) ).
tff(f_138,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( inverse(sk_c6) = sk_c5 ) ),
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_69,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_111,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( inverse(sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_213,axiom,
! [X5,X6,X3,X1,X2,X4] :
( ( multiply(sk_c8,sk_c9) != sk_c7 )
| ( inverse(X3) != sk_c9 )
| ( multiply(X3,sk_c8) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c9 )
| ( inverse(X4) != sk_c8 )
| ( multiply(X1,sk_c9) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( inverse(sk_c8) != sk_c7 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( inverse(X5) != X6 )
| ( inverse(X6) != sk_c9 )
| ( multiply(X5,sk_c9) != X6 ) ),
file(unknown,unknown) ).
tff(f_126,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( inverse(sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_120,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_123,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_99,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( inverse(sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_105,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_135,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_144,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_108,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_96,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_114,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( inverse(sk_c5) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_102,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_81,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_78,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_72,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_66,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_75,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_84,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c5) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_90,axiom,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_162,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_159,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_147,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_150,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_153,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
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_76,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_105,plain,
inverse(sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_76]) ).
tff(c_109,plain,
multiply(sk_c8,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_105,c_4]) ).
tff(c_8,plain,
multiply(sk_c8,sk_c9) = sk_c7,
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_58,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_144,plain,
multiply(sk_c2,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_171,plain,
! [X_14,Y_15,Z_16] : ( multiply(multiply(X_14,Y_15),Z_16) = multiply(X_14,multiply(Y_15,Z_16)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_195,plain,
! [Z_16] : ( multiply(sk_c8,multiply(sk_c2,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_171]) ).
tff(c_236,plain,
! [Z_18] : ( multiply(sk_c8,multiply(sk_c2,Z_18)) = Z_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_195]) ).
tff(c_248,plain,
multiply(sk_c8,sk_c9) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_144,c_236]) ).
tff(c_252,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_248]) ).
tff(c_282,plain,
multiply(sk_c7,sk_c9) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_8]) ).
tff(c_198,plain,
! [X_2,Z_16] : ( multiply(inverse(X_2),multiply(X_2,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_171]) ).
tff(c_541,plain,
! [X_24,Z_25] : ( multiply(inverse(X_24),multiply(X_24,Z_25)) = Z_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_198]) ).
tff(c_565,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_282,c_541]) ).
tff(c_591,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_565]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_119,plain,
inverse(sk_c1) = sk_c9,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_597,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_591,c_119]) ).
tff(c_40,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_137,plain,
multiply(sk_c1,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_279,plain,
multiply(sk_c1,sk_c7) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_137]) ).
tff(c_623,plain,
multiply(sk_c1,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_591,c_279]) ).
tff(c_211,plain,
! [X_2,Z_16] : ( multiply(inverse(X_2),multiply(X_2,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_198]) ).
tff(c_627,plain,
multiply(inverse(sk_c1),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_623,c_211]) ).
tff(c_633,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_597,c_627]) ).
tff(c_124,plain,
multiply(sk_c9,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_119,c_4]) ).
tff(c_253,plain,
! [Z_19] : ( multiply(sk_c8,multiply(sk_c9,Z_19)) = multiply(sk_c7,Z_19) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_171]) ).
tff(c_271,plain,
multiply(sk_c8,identity) = multiply(sk_c7,sk_c1),
inference(superposition,[status(thm),theory(equality)],[c_124,c_253]) ).
tff(c_337,plain,
multiply(sk_c7,sk_c1) = multiply(sk_c7,identity),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_271]) ).
tff(c_372,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_198]) ).
tff(c_396,plain,
multiply(inverse(sk_c7),multiply(sk_c7,identity)) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_337,c_372]) ).
tff(c_437,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_211,c_396]) ).
tff(c_411,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_282,c_372]) ).
tff(c_440,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_411]) ).
tff(c_449,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_440,c_119]) ).
tff(c_512,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_437,c_449]) ).
tff(c_192,plain,
! [Z_16] : ( multiply(sk_c9,multiply(sk_c1,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_124,c_171]) ).
tff(c_213,plain,
! [Z_17] : ( multiply(sk_c9,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_192]) ).
tff(c_225,plain,
multiply(sk_c9,sk_c9) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_137,c_213]) ).
tff(c_277,plain,
multiply(sk_c9,sk_c9) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_225]) ).
tff(c_443,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_440,c_440,c_277]) ).
tff(c_450,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_443]) ).
tff(c_82,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( inverse(sk_c8) != sk_c7 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( multiply(X3_8,sk_c8) != sk_c9 )
| ( inverse(X3_8) != sk_c9 )
| ( multiply(sk_c8,sk_c9) != sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_213]) ).
tff(c_84,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( inverse(sk_c8) != sk_c7 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( multiply(X3_8,sk_c8) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_82]) ).
tff(c_316,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(sk_c9,sk_c7) != sk_c7 )
| ( inverse(sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c7 )
| ( inverse(X4_11) != sk_c7 )
| ( multiply(X4_11,sk_c7) != sk_c9 )
| ( multiply(X3_8,sk_c7) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_252,c_252,c_252,c_252,c_252,c_252,c_252,c_84]) ).
tff(c_317,plain,
inverse(sk_c7) != sk_c7,
inference(splitLeft,[status(thm)],[c_316]) ).
tff(c_462,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_450,c_450,c_317]) ).
tff(c_538,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_512,c_462]) ).
tff(c_540,plain,
inverse(sk_c7) = sk_c7,
inference(splitRight,[status(thm)],[c_316]) ).
tff(c_637,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_633,c_633,c_540]) ).
tff(c_819,plain,
! [X_29,Z_30] : ( multiply(inverse(inverse(X_29)),Z_30) = multiply(X_29,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_211,c_541]) ).
tff(c_583,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_541]) ).
tff(c_826,plain,
! [X_29] : ( multiply(X_29,identity) = X_29 ),
inference(superposition,[status(thm),theory(equality)],[c_819,c_583]) ).
tff(c_539,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( multiply(sk_c9,sk_c7) != sk_c7 )
| ( multiply(X3_8,sk_c7) != sk_c9 )
| ( inverse(X3_8) != sk_c9 )
| ( inverse(X4_11) != sk_c7 )
| ( multiply(X4_11,sk_c7) != sk_c9 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) ) ),
inference(splitRight,[status(thm)],[c_316]) ).
tff(c_9261,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( identity != X3_8 )
| ( inverse(X3_8) != identity )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( identity != X2_10 )
| ( inverse(X2_10) != identity )
| ( inverse(X5_6) != identity )
| ( inverse(X5_6) != X5_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_826,c_591,c_826,c_591,c_591,c_633,c_826,c_633,c_633,c_826,c_633,c_591,c_591,c_826,c_633,c_591,c_633,c_591,c_826,c_633,c_591,c_2,c_591,c_539]) ).
tff(c_9263,plain,
! [X5_122] :
( ( inverse(X5_122) != identity )
| ( inverse(X5_122) != X5_122 ) ),
inference(splitLeft,[status(thm)],[c_9261]) ).
tff(c_9271,plain,
inverse(identity) != identity,
inference(superposition,[status(thm),theory(equality)],[c_637,c_9263]) ).
tff(c_9278,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_637,c_9271]) ).
tff(c_9279,plain,
! [X2_10,X1_9,X4_11,X3_8] :
( ( identity != X2_10 )
| ( inverse(X2_10) != identity )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( identity != X3_8 )
| ( inverse(X3_8) != identity ) ),
inference(splitRight,[status(thm)],[c_9261]) ).
tff(c_70994,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_9279]) ).
tff(c_70996,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70994,c_637]) ).
tff(c_70997,plain,
! [X4_11,X1_9,X2_10] :
( ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( identity != X2_10 )
| ( inverse(X2_10) != identity ) ),
inference(splitRight,[status(thm)],[c_9279]) ).
tff(c_70999,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_70997]) ).
tff(c_71001,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70999,c_637]) ).
tff(c_71002,plain,
! [X1_9,X4_11] :
( ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 ) ),
inference(splitRight,[status(thm)],[c_70997]) ).
tff(c_72473,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_71002]) ).
tff(c_72475,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72473,c_637]) ).
tff(c_72477,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_71002]) ).
tff(c_72479,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72477,c_637]) ).
tff(c_72481,plain,
multiply(sk_c2,sk_c8) != sk_c9,
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_50,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_72525,plain,
inverse(sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_72481,c_50]) ).
tff(c_72529,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_72525,c_4]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_72552,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_72481,c_46]) ).
tff(c_48,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_72538,plain,
inverse(sk_c3) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_72481,c_48]) ).
tff(c_72542,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_72538,c_4]) ).
tff(c_72575,plain,
! [X_349,Y_350,Z_351] : ( multiply(multiply(X_349,Y_350),Z_351) = multiply(X_349,multiply(Y_350,Z_351)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_72602,plain,
! [Z_351] : ( multiply(sk_c9,multiply(sk_c3,Z_351)) = multiply(identity,Z_351) ),
inference(superposition,[status(thm),theory(equality)],[c_72542,c_72575]) ).
tff(c_72835,plain,
! [Z_358] : ( multiply(sk_c9,multiply(sk_c3,Z_358)) = Z_358 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_72602]) ).
tff(c_72847,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_72552,c_72835]) ).
tff(c_72858,plain,
! [Z_359] : ( multiply(sk_c8,multiply(sk_c9,Z_359)) = multiply(sk_c7,Z_359) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_72575]) ).
tff(c_72870,plain,
multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_72847,c_72858]) ).
tff(c_72895,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_72529,c_72870]) ).
tff(c_72899,plain,
multiply(identity,sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_72895,c_72529]) ).
tff(c_72936,plain,
sk_c8 = identity,
inference(superposition,[status(thm),theory(equality)],[c_72899,c_2]) ).
tff(c_72959,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_72936,c_105]) ).
tff(c_72990,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_72959,c_4]) ).
tff(c_72626,plain,
! [X_2,Z_351] : ( multiply(inverse(X_2),multiply(X_2,Z_351)) = multiply(identity,Z_351) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_72575]) ).
tff(c_72644,plain,
! [X_2,Z_351] : ( multiply(inverse(X_2),multiply(X_2,Z_351)) = Z_351 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_72626]) ).
tff(c_73129,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_72990,c_72644]) ).
tff(c_73141,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_73129]) ).
tff(c_72901,plain,
multiply(sk_c8,sk_c9) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_72895,c_8]) ).
tff(c_72973,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_72936,c_72901]) ).
tff(c_72956,plain,
multiply(sk_c2,identity) != sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_72936,c_72481]) ).
tff(c_73155,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73141,c_72973,c_72956]) ).
tff(c_73157,plain,
multiply(sk_c1,sk_c8) != sk_c9,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_32,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_73170,plain,
inverse(sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_73157,c_32]) ).
tff(c_73174,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73170,c_4]) ).
tff(c_73890,plain,
! [X_372,Y_373,Z_374] : ( multiply(multiply(X_372,Y_373),Z_374) = multiply(X_372,multiply(Y_373,Z_374)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_73926,plain,
! [Z_374] : ( multiply(sk_c7,multiply(sk_c8,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_73174,c_73890]) ).
tff(c_74977,plain,
! [Z_393] : ( multiply(sk_c7,multiply(sk_c8,Z_393)) = Z_393 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73926]) ).
tff(c_74995,plain,
multiply(sk_c7,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_109,c_74977]) ).
tff(c_36,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_73214,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_73157,c_36]) ).
tff(c_73218,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73214,c_4]) ).
tff(c_74992,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_73218,c_74977]) ).
tff(c_75010,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_74995,c_74992]) ).
tff(c_56,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_73851,plain,
multiply(sk_c2,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_62,plain,
( ( multiply(sk_c6,sk_c9) = sk_c5 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_73230,plain,
multiply(sk_c2,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_62]) ).
tff(c_73259,plain,
! [X_362,Y_363,Z_364] : ( multiply(multiply(X_362,Y_363),Z_364) = multiply(X_362,multiply(Y_363,Z_364)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_73307,plain,
! [Z_364] : ( multiply(sk_c8,multiply(sk_c2,Z_364)) = multiply(identity,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_73259]) ).
tff(c_73379,plain,
! [Z_367] : ( multiply(sk_c8,multiply(sk_c2,Z_367)) = Z_367 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73307]) ).
tff(c_73391,plain,
multiply(sk_c8,sk_c9) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_73230,c_73379]) ).
tff(c_73395,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_73391]) ).
tff(c_73410,plain,
multiply(sk_c7,sk_c9) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_73395,c_8]) ).
tff(c_73310,plain,
! [X_2,Z_364] : ( multiply(inverse(X_2),multiply(X_2,Z_364)) = multiply(identity,Z_364) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_73259]) ).
tff(c_73471,plain,
! [X_368,Z_369] : ( multiply(inverse(X_368),multiply(X_368,Z_369)) = Z_369 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73310]) ).
tff(c_73501,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_73410,c_73471]) ).
tff(c_73549,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_73501]) ).
tff(c_73561,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_73549,c_124]) ).
tff(c_73328,plain,
! [X_2,Z_364] : ( multiply(inverse(X_2),multiply(X_2,Z_364)) = Z_364 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73310]) ).
tff(c_73827,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_73561,c_73328]) ).
tff(c_73839,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_73827]) ).
tff(c_73405,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_73395,c_73174]) ).
tff(c_73404,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_73395,c_73214]) ).
tff(c_38,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_73243,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_73157,c_38]) ).
tff(c_73400,plain,
multiply(sk_c4,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_73395,c_73243]) ).
tff(c_73688,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_73400,c_73328]) ).
tff(c_73694,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_73405,c_73404,c_73688]) ).
tff(c_73407,plain,
multiply(sk_c1,sk_c7) != sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_73395,c_73157]) ).
tff(c_73767,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_73694,c_73549,c_73407]) ).
tff(c_73843,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_73839,c_73767]) ).
tff(c_73848,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73843]) ).
tff(c_73850,plain,
multiply(sk_c2,sk_c8) != sk_c9,
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_73861,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_73851,c_73850]) ).
tff(c_73862,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_75019,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75010,c_73862]) ).
tff(c_73935,plain,
! [Z_374] : ( multiply(sk_c8,multiply(sk_c2,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_73890]) ).
tff(c_73955,plain,
! [Z_374] : ( multiply(sk_c8,multiply(sk_c2,Z_374)) = Z_374 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73935]) ).
tff(c_75355,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_75019,c_73955]) ).
tff(c_73952,plain,
! [Z_374] : ( multiply(sk_c7,multiply(sk_c8,Z_374)) = Z_374 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73926]) ).
tff(c_75365,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_75355,c_73952]) ).
tff(c_74998,plain,
multiply(sk_c7,sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_8,c_74977]) ).
tff(c_75372,plain,
sk_c9 = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75365,c_74998]) ).
tff(c_73877,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_73850,c_46]) ).
tff(c_30,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_73199,plain,
inverse(sk_c3) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_73157,c_30]) ).
tff(c_73203,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73199,c_4]) ).
tff(c_73920,plain,
! [Z_374] : ( multiply(sk_c9,multiply(sk_c3,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_73203,c_73890]) ).
tff(c_74230,plain,
! [Z_381] : ( multiply(sk_c9,multiply(sk_c3,Z_381)) = Z_381 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73920]) ).
tff(c_74242,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_73877,c_74230]) ).
tff(c_75384,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75372,c_75372,c_74242]) ).
tff(c_75399,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75355,c_75384]) ).
tff(c_42,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_73187,plain,
inverse(sk_c5) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_73157,c_42]) ).
tff(c_75394,plain,
inverse(sk_c5) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75372,c_73187]) ).
tff(c_75478,plain,
inverse(sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_75394]) ).
tff(c_73156,plain,
inverse(sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_73161,plain,
multiply(sk_c5,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73156,c_4]) ).
tff(c_73938,plain,
! [X_2,Z_374] : ( multiply(inverse(X_2),multiply(X_2,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_73890]) ).
tff(c_75497,plain,
! [X_399,Z_400] : ( multiply(inverse(X_399),multiply(X_399,Z_400)) = Z_400 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73938]) ).
tff(c_75542,plain,
multiply(inverse(sk_c5),identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_73161,c_75497]) ).
tff(c_75558,plain,
sk_c6 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_74995,c_75478,c_75542]) ).
tff(c_75563,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75558,c_73156]) ).
tff(c_75438,plain,
inverse(sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_105]) ).
tff(c_75568,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75563,c_75438]) ).
tff(c_75436,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_73170]) ).
tff(c_75474,plain,
multiply(sk_c7,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75436,c_4]) ).
tff(c_75673,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75568,c_75568,c_75474]) ).
tff(c_75430,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_75365]) ).
tff(c_75690,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75673,c_75568,c_75568,c_75568,c_75430]) ).
tff(c_75056,plain,
! [Z_394] : ( multiply(sk_c8,multiply(sk_c9,Z_394)) = multiply(sk_c7,Z_394) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_73890]) ).
tff(c_75080,plain,
multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_74242,c_75056]) ).
tff(c_75103,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_73174,c_75080]) ).
tff(c_75039,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_75019,c_73955]) ).
tff(c_34,plain,
( ( multiply(sk_c9,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_73872,plain,
multiply(sk_c9,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_73157,c_34]) ).
tff(c_75089,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c7,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_73872,c_75056]) ).
tff(c_75104,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75039,c_74998,c_75089]) ).
tff(c_75123,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75103,c_75104]) ).
tff(c_73849,plain,
multiply(sk_c6,sk_c9) = sk_c5,
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_73929,plain,
! [Z_374] : ( multiply(sk_c5,multiply(sk_c6,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_73161,c_73890]) ).
tff(c_74460,plain,
! [Z_387] : ( multiply(sk_c5,multiply(sk_c6,Z_387)) = Z_387 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73929]) ).
tff(c_74475,plain,
multiply(sk_c5,sk_c5) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_73849,c_74460]) ).
tff(c_73191,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73187,c_4]) ).
tff(c_73923,plain,
! [Z_374] : ( multiply(sk_c9,multiply(sk_c5,Z_374)) = multiply(identity,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_73191,c_73890]) ).
tff(c_73951,plain,
! [Z_374] : ( multiply(sk_c9,multiply(sk_c5,Z_374)) = Z_374 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73923]) ).
tff(c_74482,plain,
multiply(sk_c9,sk_c9) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_74475,c_73951]) ).
tff(c_75124,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75123,c_75123,c_74482]) ).
tff(c_75141,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75124]) ).
tff(c_74436,plain,
! [Z_386] : ( multiply(sk_c9,multiply(sk_c5,Z_386)) = Z_386 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73923]) ).
tff(c_74448,plain,
multiply(sk_c9,identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_73161,c_74436]) ).
tff(c_75126,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_75123,c_74448]) ).
tff(c_75142,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75126]) ).
tff(c_75183,plain,
inverse(identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75142,c_73156]) ).
tff(c_75215,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75141,c_75183]) ).
tff(c_75111,plain,
multiply(sk_c9,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75103,c_73872]) ).
tff(c_75118,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_74448,c_75111]) ).
tff(c_74497,plain,
! [Z_388] : ( multiply(sk_c7,multiply(sk_c8,Z_388)) = Z_388 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73926]) ).
tff(c_74515,plain,
multiply(sk_c7,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_109,c_74497]) ).
tff(c_74512,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_73218,c_74497]) ).
tff(c_74530,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_74515,c_74512]) ).
tff(c_74546,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74530,c_73862]) ).
tff(c_74558,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_74546,c_73955]) ).
tff(c_74568,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_74558,c_73952]) ).
tff(c_74518,plain,
multiply(sk_c7,sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_8,c_74497]) ).
tff(c_74575,plain,
sk_c9 = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74568,c_74518]) ).
tff(c_74587,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74575,c_74575,c_74242]) ).
tff(c_74602,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74558,c_74587]) ).
tff(c_74597,plain,
inverse(sk_c5) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74575,c_73187]) ).
tff(c_74681,plain,
inverse(sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74602,c_74597]) ).
tff(c_74700,plain,
! [X_390,Z_391] : ( multiply(inverse(X_390),multiply(X_390,Z_391)) = Z_391 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73938]) ).
tff(c_74745,plain,
multiply(inverse(sk_c5),identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_73161,c_74700]) ).
tff(c_74761,plain,
sk_c6 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_74515,c_74681,c_74745]) ).
tff(c_74766,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_74761,c_73156]) ).
tff(c_74641,plain,
inverse(sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74602,c_105]) ).
tff(c_74771,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_74766,c_74641]) ).
tff(c_74639,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74602,c_73170]) ).
tff(c_74677,plain,
multiply(sk_c7,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_74639,c_4]) ).
tff(c_74876,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74771,c_74771,c_74677]) ).
tff(c_74633,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74602,c_74568]) ).
tff(c_74893,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74876,c_74771,c_74771,c_74771,c_74633]) ).
tff(c_74783,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_74771,c_74771,c_74639]) ).
tff(c_74900,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74893,c_74893,c_74783]) ).
tff(c_74254,plain,
! [Z_382] : ( multiply(sk_c9,multiply(sk_c5,Z_382)) = Z_382 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73923]) ).
tff(c_74266,plain,
multiply(sk_c9,identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_73161,c_74254]) ).
tff(c_74297,plain,
! [Z_384] : ( multiply(sk_c8,multiply(sk_c9,Z_384)) = multiply(sk_c7,Z_384) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_73890]) ).
tff(c_74315,plain,
multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_74242,c_74297]) ).
tff(c_74337,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_73174,c_74315]) ).
tff(c_74339,plain,
multiply(sk_c9,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74337,c_73872]) ).
tff(c_74345,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_74266,c_74339]) ).
tff(c_74343,plain,
multiply(sk_c8,sk_c9) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74337,c_8]) ).
tff(c_74422,plain,
multiply(sk_c6,sk_c9) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74345,c_74343]) ).
tff(c_74342,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74337,c_73170]) ).
tff(c_74363,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_73156,c_74345,c_74342]) ).
tff(c_74370,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74363,c_73156]) ).
tff(c_74368,plain,
inverse(identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_74363,c_73187]) ).
tff(c_73987,plain,
! [Z_377] : ( multiply(sk_c9,multiply(sk_c3,Z_377)) = Z_377 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_73920]) ).
tff(c_73999,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_73877,c_73987]) ).
tff(c_74010,plain,
! [Z_378] : ( multiply(sk_c8,multiply(sk_c9,Z_378)) = multiply(sk_c7,Z_378) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_73890]) ).
tff(c_74022,plain,
multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_73999,c_74010]) ).
tff(c_74044,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_73174,c_74022]) ).
tff(c_74048,plain,
multiply(identity,sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74044,c_73174]) ).
tff(c_74114,plain,
sk_c8 = identity,
inference(superposition,[status(thm),theory(equality)],[c_74048,c_2]) ).
tff(c_74049,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74044,c_73170]) ).
tff(c_74127,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74114,c_74049]) ).
tff(c_73972,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( multiply(X3_8,sk_c8) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_73170,c_73872,c_84]) ).
tff(c_74087,plain,
! [X3_379] :
( ( multiply(X3_379,sk_c8) != sk_c9 )
| ( inverse(X3_379) != sk_c9 ) ),
inference(splitLeft,[status(thm)],[c_73972]) ).
tff(c_74102,plain,
( ( sk_c9 != sk_c8 )
| ( inverse(identity) != sk_c9 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_74087]) ).
tff(c_74187,plain,
( ( sk_c9 != identity )
| ( sk_c9 != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_74127,c_74114,c_74102]) ).
tff(c_74188,plain,
sk_c9 != identity,
inference(splitLeft,[status(thm)],[c_74187]) ).
tff(c_74046,plain,
multiply(sk_c9,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_74044,c_73872]) ).
tff(c_74125,plain,
multiply(sk_c9,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74114,c_74046]) ).
tff(c_74128,plain,
multiply(sk_c9,identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_74114,c_73999]) ).
tff(c_74199,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_74125,c_74128]) ).
tff(c_74200,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_74188,c_74199]) ).
tff(c_74202,plain,
sk_c9 = identity,
inference(splitRight,[status(thm)],[c_74187]) ).
tff(c_74103,plain,
inverse(sk_c9) != sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_73999,c_74087]) ).
tff(c_74203,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_74202,c_74202,c_74103]) ).
tff(c_74215,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_74127,c_74203]) ).
tff(c_74216,plain,
! [X4_11,X1_9,X2_10,X5_6] :
( ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) ) ),
inference(splitRight,[status(thm)],[c_73972]) ).
tff(c_74253,plain,
! [X5_6] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) ) ),
inference(splitLeft,[status(thm)],[c_74216]) ).
tff(c_74426,plain,
( ( inverse(identity) != sk_c9 )
| ( multiply(sk_c6,sk_c9) != inverse(sk_c6) ) ),
inference(superposition,[status(thm),theory(equality)],[c_74422,c_74253]) ).
tff(c_74434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_74422,c_74370,c_74368,c_74426]) ).
tff(c_74435,plain,
! [X2_10,X1_9,X4_11] :
( ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 ) ),
inference(splitRight,[status(thm)],[c_74216]) ).
tff(c_74496,plain,
! [X4_11] :
( ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 ) ),
inference(splitLeft,[status(thm)],[c_74435]) ).
tff(c_74609,plain,
! [X4_389] :
( ( inverse(X4_389) != sk_c8 )
| ( multiply(X4_389,sk_c8) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_74575,c_74496]) ).
tff(c_74630,plain,
inverse(identity) != sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_2,c_74609]) ).
tff(c_74658,plain,
inverse(identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_74602,c_74630]) ).
tff(c_74785,plain,
inverse(identity) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_74771,c_74658]) ).
tff(c_74896,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_74893,c_74785]) ).
tff(c_74975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_74900,c_74896]) ).
tff(c_74976,plain,
! [X1_9,X2_10] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_74435]) ).
tff(c_75028,plain,
! [X2_10] :
( ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_74976]) ).
tff(c_75162,plain,
! [X2_395] :
( ( multiply(X2_395,identity) != sk_c6 )
| ( inverse(X2_395) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_75118,c_75118,c_75103,c_75028]) ).
tff(c_75174,plain,
( ( sk_c6 != identity )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_75162]) ).
tff(c_75343,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_75215,c_75142,c_75142,c_75174]) ).
tff(c_75344,plain,
! [X1_9] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_74976]) ).
tff(c_75406,plain,
! [X1_398] :
( ( inverse(X1_398) != sk_c8 )
| ( multiply(X1_398,sk_c8) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_75372,c_75372,c_75344]) ).
tff(c_75427,plain,
inverse(identity) != sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_2,c_75406]) ).
tff(c_75455,plain,
inverse(identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_75427]) ).
tff(c_75582,plain,
inverse(identity) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75568,c_75455]) ).
tff(c_75693,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_75690,c_75582]) ).
tff(c_75701,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75690,c_75568]) ).
tff(c_75392,plain,
inverse(sk_c3) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_75372,c_73199]) ).
tff(c_75456,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75399,c_75392]) ).
tff(c_75460,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75456,c_4]) ).
tff(c_75769,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75701,c_75460]) ).
tff(c_75581,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_75568,c_75456]) ).
tff(c_75695,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75690,c_75581]) ).
tff(c_75770,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75769,c_75695]) ).
tff(c_75772,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_75693,c_75770]) ).
tff(c_75774,plain,
inverse(sk_c1) != sk_c9,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_20,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_75862,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_75774,c_20]) ).
tff(c_18,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_75787,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_75774,c_18]) ).
tff(c_75791,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75787,c_4]) ).
tff(c_75878,plain,
! [X_403,Y_404,Z_405] : ( multiply(multiply(X_403,Y_404),Z_405) = multiply(X_403,multiply(Y_404,Z_405)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_75914,plain,
! [Z_405] : ( multiply(sk_c8,multiply(sk_c4,Z_405)) = multiply(identity,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_75791,c_75878]) ).
tff(c_75965,plain,
! [Z_407] : ( multiply(sk_c8,multiply(sk_c4,Z_407)) = Z_407 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75914]) ).
tff(c_75977,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_75862,c_75965]) ).
tff(c_14,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_75795,plain,
inverse(sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_75774,c_14]) ).
tff(c_75799,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75795,c_4]) ).
tff(c_75911,plain,
! [Z_405] : ( multiply(sk_c7,multiply(sk_c8,Z_405)) = multiply(identity,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_75799,c_75878]) ).
tff(c_76697,plain,
! [Z_420] : ( multiply(sk_c7,multiply(sk_c8,Z_420)) = Z_420 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75911]) ).
tff(c_76712,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_75977,c_76697]) ).
tff(c_76724,plain,
multiply(sk_c7,sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_8,c_76697]) ).
tff(c_77121,plain,
sk_c9 = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76712,c_76724]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_75846,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_75774,c_10]) ).
tff(c_75773,plain,
inverse(sk_c3) = sk_c9,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_75778,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75773,c_4]) ).
tff(c_75917,plain,
! [Z_405] : ( multiply(sk_c9,multiply(sk_c3,Z_405)) = multiply(identity,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_75778,c_75878]) ).
tff(c_76332,plain,
! [Z_414] : ( multiply(sk_c9,multiply(sk_c3,Z_414)) = Z_414 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75917]) ).
tff(c_76344,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_75846,c_76332]) ).
tff(c_77281,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_77121,c_77121,c_76344]) ).
tff(c_77296,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75977,c_77281]) ).
tff(c_77309,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77296,c_75795]) ).
tff(c_16,plain,
( ( multiply(sk_c9,sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_75855,plain,
multiply(sk_c9,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_75774,c_16]) ).
tff(c_77287,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_77121,c_75855]) ).
tff(c_77366,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77296,c_77296,c_77287]) ).
tff(c_77302,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77296,c_77121]) ).
tff(c_77130,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_77121,c_77121,c_76344]) ).
tff(c_77145,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75977,c_77130]) ).
tff(c_76764,plain,
! [Z_421] : ( multiply(sk_c8,multiply(sk_c9,Z_421)) = multiply(sk_c7,Z_421) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_75878]) ).
tff(c_76794,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c7,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_75855,c_76764]) ).
tff(c_76806,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76724,c_75977,c_76794]) ).
tff(c_76809,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76806,c_76806,c_76344]) ).
tff(c_76824,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75799,c_76809]) ).
tff(c_76721,plain,
multiply(sk_c7,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_109,c_76697]) ).
tff(c_76831,plain,
multiply(identity,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_76824,c_76721]) ).
tff(c_76836,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76831]) ).
tff(c_76856,plain,
inverse(identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76836,c_105]) ).
tff(c_22,plain,
( ( inverse(sk_c6) = sk_c5 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_75824,plain,
inverse(sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_75774,c_22]) ).
tff(c_75828,plain,
multiply(sk_c5,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75824,c_4]) ).
tff(c_24,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_75812,plain,
inverse(sk_c5) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_75774,c_24]) ).
tff(c_75816,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75812,c_4]) ).
tff(c_75908,plain,
! [Z_405] : ( multiply(sk_c9,multiply(sk_c5,Z_405)) = multiply(identity,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_75816,c_75878]) ).
tff(c_75988,plain,
! [Z_408] : ( multiply(sk_c9,multiply(sk_c5,Z_408)) = Z_408 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75908]) ).
tff(c_76006,plain,
multiply(sk_c9,identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_75828,c_75988]) ).
tff(c_76812,plain,
multiply(sk_c7,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_76806,c_76006]) ).
tff(c_76825,plain,
sk_c6 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_76721,c_76812]) ).
tff(c_76843,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_76825,c_75824]) ).
tff(c_76973,plain,
sk_c8 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_76856,c_76836,c_76843]) ).
tff(c_76835,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76824,c_75795]) ).
tff(c_76923,plain,
multiply(identity,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_76835,c_4]) ).
tff(c_77007,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76973,c_76923]) ).
tff(c_76819,plain,
inverse(sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76806,c_75812]) ).
tff(c_76911,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76824,c_76819]) ).
tff(c_77011,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77007,c_76911]) ).
tff(c_77010,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77007,c_76973]) ).
tff(c_76830,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76824,c_76806]) ).
tff(c_76369,plain,
! [Z_416] : ( multiply(sk_c7,multiply(sk_c8,Z_416)) = Z_416 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75911]) ).
tff(c_76384,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_75977,c_76369]) ).
tff(c_76396,plain,
multiply(sk_c7,sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_8,c_76369]) ).
tff(c_76446,plain,
sk_c9 = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76384,c_76396]) ).
tff(c_76454,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76446,c_76446,c_76344]) ).
tff(c_76469,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_75977,c_76454]) ).
tff(c_76481,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76469,c_75799]) ).
tff(c_76460,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76446,c_75855]) ).
tff(c_76557,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76469,c_76469,c_76460]) ).
tff(c_76580,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76481,c_76557]) ).
tff(c_76393,plain,
multiply(sk_c7,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_109,c_76369]) ).
tff(c_76602,plain,
multiply(identity,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_76580,c_76393]) ).
tff(c_76604,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76602]) ).
tff(c_76484,plain,
inverse(sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76469,c_105]) ).
tff(c_76598,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76580,c_76484]) ).
tff(c_76664,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76604,c_76598]) ).
tff(c_76475,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76469,c_76446]) ).
tff(c_76482,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76469,c_75795]) ).
tff(c_76028,plain,
! [Z_409] : ( multiply(sk_c9,multiply(sk_c3,Z_409)) = Z_409 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75917]) ).
tff(c_76040,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_75846,c_76028]) ).
tff(c_75929,plain,
! [Z_405] : ( multiply(sk_c8,multiply(sk_c9,Z_405)) = multiply(sk_c7,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_75878]) ).
tff(c_76082,plain,
multiply(sk_c8,sk_c9) = multiply(sk_c7,sk_c8),
inference(superposition,[status(thm),theory(equality)],[c_76040,c_75929]) ).
tff(c_76088,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75799,c_8,c_76082]) ).
tff(c_76093,plain,
multiply(sk_c9,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_76088,c_75855]) ).
tff(c_76098,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_76006,c_76093]) ).
tff(c_76095,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76088,c_75795]) ).
tff(c_76114,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_75824,c_76098,c_76095]) ).
tff(c_26,plain,
( ( multiply(sk_c6,sk_c9) = sk_c5 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_75837,plain,
multiply(sk_c6,sk_c9) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_75774,c_26]) ).
tff(c_75905,plain,
! [Z_405] : ( multiply(sk_c5,multiply(sk_c6,Z_405)) = multiply(identity,Z_405) ),
inference(superposition,[status(thm),theory(equality)],[c_75828,c_75878]) ).
tff(c_75942,plain,
! [Z_406] : ( multiply(sk_c5,multiply(sk_c6,Z_406)) = Z_406 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_75905]) ).
tff(c_75954,plain,
multiply(sk_c5,sk_c5) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_75837,c_75942]) ).
tff(c_76117,plain,
multiply(identity,identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_76114,c_76114,c_75954]) ).
tff(c_76125,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76117]) ).
tff(c_76123,plain,
inverse(identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_76114,c_75812]) ).
tff(c_76166,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_76125,c_76123]) ).
tff(c_76131,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_76125,c_76006]) ).
tff(c_76135,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76131]) ).
tff(c_76011,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( multiply(X3_8,sk_c8) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_75795,c_75855,c_84]) ).
tff(c_76012,plain,
! [X3_8] :
( ( multiply(X3_8,sk_c8) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(splitLeft,[status(thm)],[c_76011]) ).
tff(c_76141,plain,
! [X3_411] :
( ( multiply(X3_411,sk_c6) != identity )
| ( inverse(X3_411) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76125,c_76125,c_76098,c_76012]) ).
tff(c_76154,plain,
inverse(inverse(sk_c6)) != identity,
inference(superposition,[status(thm),theory(equality)],[c_4,c_76141]) ).
tff(c_76315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_76166,c_76166,c_76135,c_76154]) ).
tff(c_76316,plain,
! [X4_11,X1_9,X2_10,X5_6] :
( ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) ) ),
inference(splitRight,[status(thm)],[c_76011]) ).
tff(c_76489,plain,
! [X5_417] :
( ( inverse(multiply(X5_417,sk_c9)) != sk_c9 )
| ( multiply(X5_417,sk_c9) != inverse(X5_417) ) ),
inference(splitLeft,[status(thm)],[c_76316]) ).
tff(c_76501,plain,
( ( inverse(sk_c9) != sk_c9 )
| ( multiply(identity,sk_c9) != inverse(identity) ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_76489]) ).
tff(c_76504,plain,
( ( inverse(sk_c9) != sk_c9 )
| ( inverse(identity) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76501]) ).
tff(c_76566,plain,
inverse(identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_76475,c_76482,c_76475,c_76475,c_76504]) ).
tff(c_76592,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_76580,c_76566]) ).
tff(c_76695,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_76664,c_76592]) ).
tff(c_76696,plain,
! [X2_10,X1_9,X4_11] :
( ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 ) ),
inference(splitRight,[status(thm)],[c_76316]) ).
tff(c_76736,plain,
! [X4_11] :
( ( inverse(X4_11) != sk_c8 )
| ( multiply(X4_11,sk_c8) != sk_c9 ) ),
inference(splitLeft,[status(thm)],[c_76696]) ).
tff(c_76863,plain,
! [X4_422] :
( ( inverse(X4_422) != sk_c8 )
| ( multiply(X4_422,sk_c8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76830,c_76736]) ).
tff(c_76876,plain,
inverse(inverse(sk_c8)) != sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_4,c_76863]) ).
tff(c_77081,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_77011,c_77011,c_77010,c_77010,c_76876]) ).
tff(c_77082,plain,
! [X1_9,X2_10] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_76696]) ).
tff(c_77129,plain,
! [X2_10] :
( ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_77082]) ).
tff(c_77227,plain,
! [X2_426] :
( ( multiply(X2_426,sk_c7) != sk_c7 )
| ( inverse(X2_426) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_77145,c_77145,c_77129]) ).
tff(c_77242,plain,
inverse(identity) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_2,c_77227]) ).
tff(c_77158,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77145,c_75795]) ).
tff(c_77213,plain,
multiply(sk_c7,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77158,c_4]) ).
tff(c_77151,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77145,c_77121]) ).
tff(c_77169,plain,
! [Z_405] : ( multiply(sk_c7,multiply(sk_c7,Z_405)) = multiply(sk_c7,Z_405) ),
inference(demodulation,[status(thm),theory(equality)],[c_77151,c_77145,c_75929]) ).
tff(c_77264,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c7,identity),
inference(superposition,[status(thm),theory(equality)],[c_77213,c_77169]) ).
tff(c_77272,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77213,c_76721,c_77264]) ).
tff(c_77160,plain,
inverse(sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77145,c_105]) ).
tff(c_77275,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77272,c_77160]) ).
tff(c_77279,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_77242,c_77275]) ).
tff(c_77280,plain,
! [X1_9] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_77082]) ).
tff(c_77321,plain,
! [X1_9] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_77302,c_77296,c_77302,c_77280]) ).
tff(c_77370,plain,
inverse(sk_c7) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_77366,c_77321]) ).
tff(c_77379,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_77309,c_77370]) ).
tff(c_77381,plain,
inverse(sk_c2) != sk_c8,
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_74,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_77476,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_77381,c_74]) ).
tff(c_72,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_77439,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_77381,c_72]) ).
tff(c_77443,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77439,c_4]) ).
tff(c_77499,plain,
! [X_428,Y_429,Z_430] : ( multiply(multiply(X_428,Y_429),Z_430) = multiply(X_428,multiply(Y_429,Z_430)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_77529,plain,
! [Z_430] : ( multiply(sk_c8,multiply(sk_c4,Z_430)) = multiply(identity,Z_430) ),
inference(superposition,[status(thm),theory(equality)],[c_77443,c_77499]) ).
tff(c_77563,plain,
! [Z_431] : ( multiply(sk_c8,multiply(sk_c4,Z_431)) = Z_431 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_77529]) ).
tff(c_77575,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_77476,c_77563]) ).
tff(c_64,plain,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_77471,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_77381,c_64]) ).
tff(c_66,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_77418,plain,
inverse(sk_c3) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_77381,c_66]) ).
tff(c_77422,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77418,c_4]) ).
tff(c_77532,plain,
! [Z_430] : ( multiply(sk_c9,multiply(sk_c3,Z_430)) = multiply(identity,Z_430) ),
inference(superposition,[status(thm),theory(equality)],[c_77422,c_77499]) ).
tff(c_77611,plain,
! [Z_433] : ( multiply(sk_c9,multiply(sk_c3,Z_433)) = Z_433 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_77532]) ).
tff(c_77629,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_77471,c_77611]) ).
tff(c_77520,plain,
! [Z_430] : ( multiply(sk_c3,multiply(sk_c9,Z_430)) = multiply(sk_c8,Z_430) ),
inference(superposition,[status(thm),theory(equality)],[c_77471,c_77499]) ).
tff(c_77636,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c3,sk_c9),
inference(superposition,[status(thm),theory(equality)],[c_77629,c_77520]) ).
tff(c_77642,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77575,c_77471,c_77636]) ).
tff(c_77644,plain,
multiply(sk_c9,sk_c7) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77629]) ).
tff(c_77544,plain,
! [X_2,Z_430] : ( multiply(inverse(X_2),multiply(X_2,Z_430)) = multiply(identity,Z_430) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_77499]) ).
tff(c_77974,plain,
! [X_436,Z_437] : ( multiply(inverse(X_436),multiply(X_436,Z_437)) = Z_437 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_77544]) ).
tff(c_77998,plain,
multiply(inverse(sk_c9),sk_c9) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_77644,c_77974]) ).
tff(c_78055,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_77998]) ).
tff(c_77652,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77439]) ).
tff(c_77664,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77652,c_4]) ).
tff(c_78092,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_78055,c_77664]) ).
tff(c_78068,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_78055,c_77652]) ).
tff(c_78117,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_78092,c_78068]) ).
tff(c_77561,plain,
! [X_2,Z_430] : ( multiply(inverse(X_2),multiply(X_2,Z_430)) = Z_430 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_77544]) ).
tff(c_78302,plain,
! [X_440,Z_441] : ( multiply(inverse(inverse(X_440)),Z_441) = multiply(X_440,Z_441) ),
inference(superposition,[status(thm),theory(equality)],[c_77974,c_77561]) ).
tff(c_78046,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_77974]) ).
tff(c_78309,plain,
! [X_440] : ( multiply(X_440,identity) = X_440 ),
inference(superposition,[status(thm),theory(equality)],[c_78302,c_78046]) ).
tff(c_77646,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77642,c_77575]) ).
tff(c_68,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_77393,plain,
inverse(sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_77381,c_68]) ).
tff(c_77654,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77393]) ).
tff(c_77656,plain,
multiply(sk_c7,sk_c9) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_8]) ).
tff(c_78004,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_77656,c_77974]) ).
tff(c_78057,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_77646,c_77654,c_78004]) ).
tff(c_78075,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_78055,c_78057]) ).
tff(c_77397,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77393,c_4]) ).
tff(c_77653,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77397]) ).
tff(c_77700,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77653,c_77646]) ).
tff(c_77701,plain,
multiply(identity,sk_c9) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_77700,c_77700,c_77656]) ).
tff(c_77844,plain,
multiply(inverse(identity),identity) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_77701,c_77561]) ).
tff(c_77856,plain,
sk_c9 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_77844]) ).
tff(c_77676,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) )
| ( multiply(X2_10,sk_c7) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(sk_c9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c7 )
| ( inverse(X4_11) != sk_c7 )
| ( multiply(X4_11,sk_c7) != sk_c9 )
| ( multiply(X3_8,sk_c7) != sk_c9 )
| ( inverse(X3_8) != sk_c9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_77642,c_77642,c_77642,c_77642,c_77654,c_77642,c_77642,c_77642,c_77642,c_84]) ).
tff(c_77677,plain,
multiply(sk_c9,sk_c7) != sk_c7,
inference(splitLeft,[status(thm)],[c_77676]) ).
tff(c_77932,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_77856,c_77700,c_77700,c_77677]) ).
tff(c_77933,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( multiply(X3_8,sk_c7) != sk_c9 )
| ( inverse(X3_8) != sk_c9 )
| ( inverse(X4_11) != sk_c7 )
| ( multiply(X4_11,sk_c7) != sk_c9 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( inverse(multiply(X5_6,sk_c9)) != sk_c9 )
| ( multiply(X5_6,sk_c9) != inverse(X5_6) ) ),
inference(splitRight,[status(thm)],[c_77676]) ).
tff(c_103839,plain,
! [X5_6,X2_10,X3_8,X1_9,X4_11] :
( ( identity != X3_8 )
| ( inverse(X3_8) != identity )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( identity != X2_10 )
| ( inverse(X2_10) != identity )
| ( inverse(X5_6) != identity )
| ( inverse(X5_6) != X5_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_78309,c_78075,c_78309,c_78075,c_78075,c_78055,c_78309,c_78055,c_78055,c_78309,c_78075,c_78055,c_78075,c_78309,c_78075,c_78055,c_78055,c_78075,c_78309,c_78075,c_78055,c_77933]) ).
tff(c_103841,plain,
! [X5_616] :
( ( inverse(X5_616) != identity )
| ( inverse(X5_616) != X5_616 ) ),
inference(splitLeft,[status(thm)],[c_103839]) ).
tff(c_103853,plain,
inverse(identity) != identity,
inference(superposition,[status(thm),theory(equality)],[c_78117,c_103841]) ).
tff(c_103862,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_78117,c_103853]) ).
tff(c_103863,plain,
! [X2_10,X1_9,X4_11,X3_8] :
( ( identity != X2_10 )
| ( inverse(X2_10) != identity )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( identity != X3_8 )
| ( inverse(X3_8) != identity ) ),
inference(splitRight,[status(thm)],[c_103839]) ).
tff(c_149752,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_103863]) ).
tff(c_149754,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_149752,c_78117]) ).
tff(c_149755,plain,
! [X4_11,X1_9,X2_10] :
( ( inverse(X4_11) != identity )
| ( identity != X4_11 )
| ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( identity != X2_10 )
| ( inverse(X2_10) != identity ) ),
inference(splitRight,[status(thm)],[c_103863]) ).
tff(c_149757,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_149755]) ).
tff(c_149759,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_149757,c_78117]) ).
tff(c_149760,plain,
! [X1_9,X4_11] :
( ( inverse(X1_9) != identity )
| ( identity != X1_9 )
| ( inverse(X4_11) != identity )
| ( identity != X4_11 ) ),
inference(splitRight,[status(thm)],[c_149755]) ).
tff(c_150906,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_149760]) ).
tff(c_150908,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_150906,c_78117]) ).
tff(c_150910,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_149760]) ).
tff(c_150912,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_150910,c_78117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP339-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 21:42:53 EDT 2025
% 0.14/0.34 % CPUTime :
% 35.57/22.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.99/22.22
% 35.99/22.22 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------