TSTP Solution File: GRP305-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP305-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 10:40:51 EDT 2023
% Result : Unsatisfiable 9.83s 3.30s
% Output : CNFRefutation 9.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 33
% Syntax : Number of formulae : 485 ( 418 unt; 9 typ; 0 def)
% Number of atoms : 584 ( 567 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 226 ( 118 ~; 108 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 190 (; 190 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > 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_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_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_98,axiom,
( ( inverse(sk_c6) = sk_c4 )
| ( inverse(sk_c2) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
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_119,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( inverse(sk_c3) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c4 )
| ( inverse(sk_c2) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c5,sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [X2,X1,X3] :
( ( multiply(sk_c6,sk_c5) != sk_c4 )
| ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( inverse(sk_c6) != sk_c4 )
| ( multiply(X2,sk_c6) != sk_c4 )
| ( inverse(X2) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( inverse(X1) != sk_c6 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( inverse(X3) != sk_c5 )
| ( multiply(X3,sk_c4) != sk_c5 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c5,sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c5,sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c5,sk_c4) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c4 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c6) = sk_c4 )
| ( inverse(sk_c3) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
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_30,plain,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_87,plain,
inverse(sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_91,plain,
multiply(sk_c4,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_87,c_4]) ).
tff(c_50,plain,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_75,plain,
inverse(sk_c1) = sk_c6,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_79,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).
tff(c_3268,plain,
! [X_76,Y_77,Z_78] : ( multiply(multiply(X_76,Y_77),Z_78) = multiply(X_76,multiply(Y_77,Z_78)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3298,plain,
! [Z_78] : ( multiply(sk_c4,multiply(sk_c6,Z_78)) = multiply(identity,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_3268]) ).
tff(c_3318,plain,
! [Z_79] : ( multiply(sk_c4,multiply(sk_c6,Z_79)) = Z_79 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3298]) ).
tff(c_3333,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_3318]) ).
tff(c_2256,plain,
! [X_54,Y_55,Z_56] : ( multiply(multiply(X_54,Y_55),Z_56) = multiply(X_54,multiply(Y_55,Z_56)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2289,plain,
! [Z_56] : ( multiply(sk_c4,multiply(sk_c6,Z_56)) = multiply(identity,Z_56) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_2256]) ).
tff(c_2309,plain,
! [Z_57] : ( multiply(sk_c4,multiply(sk_c6,Z_57)) = Z_57 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2289]) ).
tff(c_2327,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_2309]) ).
tff(c_1357,plain,
! [X_38,Y_39,Z_40] : ( multiply(multiply(X_38,Y_39),Z_40) = multiply(X_38,multiply(Y_39,Z_40)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1393,plain,
! [Z_40] : ( multiply(sk_c4,multiply(sk_c6,Z_40)) = multiply(identity,Z_40) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_1357]) ).
tff(c_1413,plain,
! [Z_41] : ( multiply(sk_c4,multiply(sk_c6,Z_41)) = Z_41 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1393]) ).
tff(c_1431,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_1413]) ).
tff(c_44,plain,
( ( inverse(sk_c3) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_107,plain,
multiply(sk_c1,sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_898,plain,
! [X_29,Y_30,Z_31] : ( multiply(multiply(X_29,Y_30),Z_31) = multiply(X_29,multiply(Y_30,Z_31)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_937,plain,
! [Z_31] : ( multiply(sk_c6,multiply(sk_c1,Z_31)) = multiply(identity,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_898]) ).
tff(c_1010,plain,
! [Z_33] : ( multiply(sk_c6,multiply(sk_c1,Z_33)) = Z_33 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_937]) ).
tff(c_1028,plain,
multiply(sk_c6,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_107,c_1010]) ).
tff(c_934,plain,
! [Z_31] : ( multiply(sk_c4,multiply(sk_c6,Z_31)) = multiply(identity,Z_31) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_898]) ).
tff(c_950,plain,
! [Z_31] : ( multiply(sk_c4,multiply(sk_c6,Z_31)) = Z_31 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_934]) ).
tff(c_1035,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_1028,c_950]) ).
tff(c_1041,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_1035]) ).
tff(c_10,plain,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_102,plain,
multiply(sk_c6,sk_c5) = sk_c4,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_954,plain,
! [Z_32] : ( multiply(sk_c4,multiply(sk_c6,Z_32)) = Z_32 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_934]) ).
tff(c_969,plain,
multiply(sk_c4,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_102,c_954]) ).
tff(c_1130,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1041,c_1041,c_969]) ).
tff(c_1140,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1130]) ).
tff(c_972,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_954]) ).
tff(c_1129,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1041,c_972]) ).
tff(c_1139,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1129]) ).
tff(c_134,plain,
! [X_11,Y_12,Z_13] : ( multiply(multiply(X_11,Y_12),Z_13) = multiply(X_11,multiply(Y_12,Z_13)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_161,plain,
! [Z_13] : ( multiply(sk_c6,multiply(sk_c1,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_134]) ).
tff(c_621,plain,
! [Z_24] : ( multiply(sk_c6,multiply(sk_c1,Z_24)) = Z_24 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_636,plain,
multiply(sk_c6,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_107,c_621]) ).
tff(c_158,plain,
! [Z_13] : ( multiply(sk_c4,multiply(sk_c6,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_134]) ).
tff(c_172,plain,
! [Z_13] : ( multiply(sk_c4,multiply(sk_c6,Z_13)) = Z_13 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_747,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_636,c_172]) ).
tff(c_753,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_747]) ).
tff(c_587,plain,
! [Z_23] : ( multiply(sk_c4,multiply(sk_c6,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_602,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_587]) ).
tff(c_756,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_753,c_602]) ).
tff(c_765,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_756]) ).
tff(c_761,plain,
multiply(sk_c1,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_753,c_107]) ).
tff(c_813,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_765,c_761]) ).
tff(c_764,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_753,c_87]) ).
tff(c_814,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_813,c_764]) ).
tff(c_599,plain,
multiply(sk_c4,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_102,c_587]) ).
tff(c_757,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_753,c_753,c_599]) ).
tff(c_766,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_757]) ).
tff(c_644,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_636,c_172]) ).
tff(c_650,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_644]) ).
tff(c_653,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_650,c_602]) ).
tff(c_662,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_653]) ).
tff(c_658,plain,
multiply(sk_c1,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_650,c_107]) ).
tff(c_710,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_662,c_658]) ).
tff(c_661,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_650,c_87]) ).
tff(c_711,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_710,c_661]) ).
tff(c_470,plain,
! [Z_21] : ( multiply(sk_c6,multiply(sk_c1,Z_21)) = Z_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_491,plain,
multiply(sk_c6,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_107,c_470]) ).
tff(c_501,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_491,c_172]) ).
tff(c_508,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_501]) ).
tff(c_520,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_508,c_87]) ).
tff(c_417,plain,
! [Z_19] : ( multiply(sk_c4,multiply(sk_c6,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_432,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_417]) ).
tff(c_512,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_508,c_432]) ).
tff(c_522,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_512]) ).
tff(c_529,plain,
multiply(sk_c6,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_522,c_79]) ).
tff(c_429,plain,
multiply(sk_c4,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_102,c_417]) ).
tff(c_152,plain,
! [Z_13] : ( multiply(sk_c1,multiply(sk_c6,Z_13)) = multiply(sk_c4,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_107,c_134]) ).
tff(c_498,plain,
multiply(sk_c4,sk_c4) = multiply(sk_c1,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_491,c_152]) ).
tff(c_507,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_429,c_107,c_498]) ).
tff(c_536,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_508,c_507]) ).
tff(c_179,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c1,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_191,plain,
multiply(sk_c6,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_107,c_179]) ).
tff(c_238,plain,
! [Z_16] : ( multiply(sk_c4,multiply(sk_c6,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_250,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_191,c_238]) ).
tff(c_263,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_250]) ).
tff(c_274,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_263,c_87]) ).
tff(c_289,plain,
multiply(identity,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_274,c_4]) ).
tff(c_164,plain,
! [X_2,Z_13] : ( multiply(inverse(X_2),multiply(X_2,Z_13)) = multiply(identity,Z_13) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_134]) ).
tff(c_174,plain,
! [X_2,Z_13] : ( multiply(inverse(X_2),multiply(X_2,Z_13)) = Z_13 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_359,plain,
multiply(inverse(identity),identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_289,c_174]) ).
tff(c_371,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_359]) ).
tff(c_202,plain,
! [Z_15] : ( multiply(sk_c1,multiply(sk_c6,Z_15)) = multiply(sk_c4,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_107,c_134]) ).
tff(c_217,plain,
multiply(sk_c4,sk_c4) = multiply(sk_c1,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_191,c_202]) ).
tff(c_230,plain,
multiply(sk_c4,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_107,c_217]) ).
tff(c_256,plain,
multiply(sk_c4,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_102,c_238]) ).
tff(c_264,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_230,c_256]) ).
tff(c_281,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_263,c_264]) ).
tff(c_20,plain,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_113,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_58,plain,
! [X3_8,X1_7,X2_6] :
( ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 )
| ( inverse(sk_c6) != sk_c4 )
| ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_177,plain,
! [X3_8,X1_7,X2_6] :
( ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_113,c_87,c_58]) ).
tff(c_178,plain,
multiply(sk_c5,sk_c6) != sk_c4,
inference(splitLeft,[status(thm)],[c_177]) ).
tff(c_269,plain,
multiply(sk_c5,sk_c6) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_263,c_178]) ).
tff(c_406,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_371,c_2,c_281,c_269]) ).
tff(c_407,plain,
! [X2_6,X1_7,X3_8] :
( ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_416,plain,
! [X3_8] :
( ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_407]) ).
tff(c_541,plain,
! [X3_8] :
( ( multiply(X3_8,identity) != identity )
| ( inverse(X3_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_536,c_536,c_508,c_416]) ).
tff(c_576,plain,
inverse(sk_c6) != identity,
inference(superposition,[status(thm),theory(equality)],[c_529,c_541]) ).
tff(c_585,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_520,c_576]) ).
tff(c_586,plain,
! [X1_7,X2_6] :
( ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 ) ),
inference(splitRight,[status(thm)],[c_407]) ).
tff(c_640,plain,
! [X2_6] :
( ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 ) ),
inference(splitLeft,[status(thm)],[c_586]) ).
tff(c_726,plain,
! [X2_26] :
( ( inverse(X2_26) != identity )
| ( multiply(X2_26,identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_710,c_650,c_710,c_640]) ).
tff(c_734,plain,
inverse(inverse(identity)) != identity,
inference(superposition,[status(thm),theory(equality)],[c_4,c_726]) ).
tff(c_742,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_711,c_711,c_734]) ).
tff(c_743,plain,
! [X1_7] :
( ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_586]) ).
tff(c_829,plain,
! [X1_28] :
( ( multiply(X1_28,identity) != identity )
| ( inverse(X1_28) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_813,c_813,c_766,c_743]) ).
tff(c_837,plain,
inverse(inverse(identity)) != identity,
inference(superposition,[status(thm),theory(equality)],[c_4,c_829]) ).
tff(c_845,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_814,c_814,c_837]) ).
tff(c_846,plain,
inverse(sk_c2) = sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_851,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_846,c_4]) ).
tff(c_966,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_851,c_954]) ).
tff(c_993,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_972,c_966]) ).
tff(c_847,plain,
multiply(sk_c5,sk_c4) != sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_22,plain,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_880,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_847,c_22]) ).
tff(c_994,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_993,c_880]) ).
tff(c_1147,plain,
multiply(identity,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_1139,c_994]) ).
tff(c_1152,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1147]) ).
tff(c_1203,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1140,c_1152]) ).
tff(c_1134,plain,
multiply(sk_c5,identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_1041,c_847]) ).
tff(c_1298,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1203,c_2,c_1140,c_1134]) ).
tff(c_1300,plain,
multiply(sk_c1,sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_38,plain,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( multiply(sk_c1,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_1341,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_1300,c_38]) ).
tff(c_1885,plain,
! [Z_50] : ( multiply(sk_c6,multiply(sk_c5,Z_50)) = multiply(sk_c4,Z_50) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_1357]) ).
tff(c_1900,plain,
multiply(sk_c6,sk_c4) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_1341,c_1885]) ).
tff(c_1910,plain,
multiply(sk_c6,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_1900]) ).
tff(c_1409,plain,
! [Z_40] : ( multiply(sk_c4,multiply(sk_c6,Z_40)) = Z_40 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1393]) ).
tff(c_1915,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_1910,c_1409]) ).
tff(c_1921,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1431,c_1915]) ).
tff(c_1934,plain,
multiply(sk_c1,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_91]) ).
tff(c_1932,plain,
multiply(sk_c1,sk_c6) != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1300]) ).
tff(c_1974,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_1934,c_1932]) ).
tff(c_1299,plain,
inverse(sk_c3) = sk_c5,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_1352,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_1300,c_46]) ).
tff(c_1929,plain,
multiply(sk_c3,sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1352]) ).
tff(c_1399,plain,
! [X_2,Z_40] : ( multiply(inverse(X_2),multiply(X_2,Z_40)) = multiply(identity,Z_40) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1357]) ).
tff(c_2021,plain,
! [X_51,Z_52] : ( multiply(inverse(X_51),multiply(X_51,Z_52)) = Z_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1399]) ).
tff(c_2057,plain,
multiply(inverse(sk_c3),sk_c5) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_1929,c_2021]) ).
tff(c_2101,plain,
multiply(sk_c5,sk_c5) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1299,c_2057]) ).
tff(c_1411,plain,
! [X_2,Z_40] : ( multiply(inverse(X_2),multiply(X_2,Z_40)) = Z_40 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1399]) ).
tff(c_2112,plain,
multiply(inverse(sk_c5),sk_c1) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2101,c_1411]) ).
tff(c_1930,plain,
multiply(sk_c5,sk_c6) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1341]) ).
tff(c_2054,plain,
multiply(inverse(sk_c5),sk_c1) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_1930,c_2021]) ).
tff(c_2187,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2112,c_2054]) ).
tff(c_1315,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_1931,plain,
multiply(sk_c5,sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1315]) ).
tff(c_2042,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_1931,c_2021]) ).
tff(c_2198,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2187,c_2042]) ).
tff(c_2210,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2198]) ).
tff(c_2212,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1974,c_2210]) ).
tff(c_2214,plain,
multiply(sk_c5,sk_c4) != sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2246,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_2214,c_18]) ).
tff(c_2365,plain,
! [Z_58] : ( multiply(sk_c6,multiply(sk_c5,Z_58)) = multiply(sk_c4,Z_58) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_2256]) ).
tff(c_2380,plain,
multiply(sk_c6,sk_c4) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_2246,c_2365]) ).
tff(c_2387,plain,
multiply(sk_c6,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_2380]) ).
tff(c_2305,plain,
! [Z_56] : ( multiply(sk_c4,multiply(sk_c6,Z_56)) = Z_56 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2289]) ).
tff(c_2391,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_2387,c_2305]) ).
tff(c_2397,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2327,c_2391]) ).
tff(c_2411,plain,
inverse(sk_c6) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2397,c_87]) ).
tff(c_2420,plain,
multiply(sk_c1,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2411,c_4]) ).
tff(c_2408,plain,
multiply(sk_c1,sk_c6) != sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2397,c_1300]) ).
tff(c_2529,plain,
sk_c1 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2420,c_2408]) ).
tff(c_2409,plain,
multiply(sk_c6,sk_c5) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2397,c_102]) ).
tff(c_2324,plain,
multiply(sk_c4,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_102,c_2309]) ).
tff(c_2403,plain,
multiply(sk_c1,sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2397,c_2397,c_2324]) ).
tff(c_26,plain,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_2238,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_2214,c_26]) ).
tff(c_2406,plain,
multiply(sk_c3,sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2397,c_2238]) ).
tff(c_2295,plain,
! [X_2,Z_56] : ( multiply(inverse(X_2),multiply(X_2,Z_56)) = multiply(identity,Z_56) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_2256]) ).
tff(c_2307,plain,
! [X_2,Z_56] : ( multiply(inverse(X_2),multiply(X_2,Z_56)) = Z_56 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2295]) ).
tff(c_2496,plain,
multiply(inverse(sk_c3),sk_c5) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_2406,c_2307]) ).
tff(c_2502,plain,
multiply(sk_c5,sk_c5) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_1299,c_2496]) ).
tff(c_2213,plain,
inverse(sk_c2) = sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_2218,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2213,c_4]) ).
tff(c_2321,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_2218,c_2309]) ).
tff(c_2348,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2327,c_2321]) ).
tff(c_42,plain,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_2232,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_1300,c_42]) ).
tff(c_2277,plain,
! [Z_56] : ( multiply(sk_c2,multiply(sk_c5,Z_56)) = multiply(sk_c6,Z_56) ),
inference(superposition,[status(thm),theory(equality)],[c_2232,c_2256]) ).
tff(c_2553,plain,
! [Z_56] : ( multiply(sk_c1,multiply(sk_c5,Z_56)) = multiply(sk_c6,Z_56) ),
inference(demodulation,[status(thm),theory(equality)],[c_2348,c_2277]) ).
tff(c_2582,plain,
multiply(sk_c6,sk_c5) = multiply(sk_c1,sk_c1),
inference(superposition,[status(thm),theory(equality)],[c_2502,c_2553]) ).
tff(c_2591,plain,
sk_c5 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2409,c_2403,c_2582]) ).
tff(c_2596,plain,
multiply(sk_c6,sk_c1) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2591,c_2409]) ).
tff(c_2604,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_79,c_2596]) ).
tff(c_2606,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2529,c_2604]) ).
tff(c_2607,plain,
inverse(sk_c2) = sk_c6,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_2612,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2607,c_4]) ).
tff(c_3330,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_2612,c_3318]) ).
tff(c_3347,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_3333,c_3330]) ).
tff(c_2608,plain,
multiply(sk_c6,sk_c5) != sk_c4,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_2616,plain,
multiply(sk_c1,sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_2670,plain,
! [X_62,Y_63,Z_64] : ( multiply(multiply(X_62,Y_63),Z_64) = multiply(X_62,multiply(Y_63,Z_64)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2709,plain,
! [Z_64] : ( multiply(sk_c6,multiply(sk_c1,Z_64)) = multiply(identity,Z_64) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_2670]) ).
tff(c_2796,plain,
! [Z_67] : ( multiply(sk_c6,multiply(sk_c1,Z_67)) = Z_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2709]) ).
tff(c_2820,plain,
multiply(sk_c6,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2616,c_2796]) ).
tff(c_2706,plain,
! [Z_64] : ( multiply(sk_c4,multiply(sk_c6,Z_64)) = multiply(identity,Z_64) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_2670]) ).
tff(c_2722,plain,
! [Z_64] : ( multiply(sk_c4,multiply(sk_c6,Z_64)) = Z_64 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2706]) ).
tff(c_2830,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_2820,c_2722]) ).
tff(c_2837,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_2830]) ).
tff(c_2726,plain,
! [Z_65] : ( multiply(sk_c4,multiply(sk_c6,Z_65)) = Z_65 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2706]) ).
tff(c_2741,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_2726]) ).
tff(c_2841,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2837,c_2741]) ).
tff(c_2851,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2841]) ).
tff(c_2738,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_2612,c_2726]) ).
tff(c_2755,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_2741,c_2738]) ).
tff(c_12,plain,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_2650,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2608,c_12]) ).
tff(c_2764,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2755,c_2650]) ).
tff(c_2857,plain,
multiply(identity,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2851,c_2764]) ).
tff(c_2862,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2857]) ).
tff(c_2849,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2837,c_87]) ).
tff(c_2909,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2862,c_2849]) ).
tff(c_2916,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2909,c_4]) ).
tff(c_2712,plain,
! [X_2,Z_64] : ( multiply(inverse(X_2),multiply(X_2,Z_64)) = multiply(identity,Z_64) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_2670]) ).
tff(c_2724,plain,
! [X_2,Z_64] : ( multiply(inverse(X_2),multiply(X_2,Z_64)) = Z_64 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2712]) ).
tff(c_2923,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2916,c_2724]) ).
tff(c_2935,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2923]) ).
tff(c_2940,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2935,c_2862]) ).
tff(c_2846,plain,
multiply(sk_c6,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2837,c_2608]) ).
tff(c_3013,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2940,c_2935,c_2846]) ).
tff(c_3015,plain,
multiply(sk_c1,sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_3054,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_3015,c_38]) ).
tff(c_3070,plain,
! [X_70,Y_71,Z_72] : ( multiply(multiply(X_70,Y_71),Z_72) = multiply(X_70,multiply(Y_71,Z_72)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3103,plain,
! [Z_72] : ( multiply(sk_c4,multiply(sk_c6,Z_72)) = multiply(identity,Z_72) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_3070]) ).
tff(c_3123,plain,
! [Z_73] : ( multiply(sk_c4,multiply(sk_c6,Z_73)) = Z_73 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3103]) ).
tff(c_3138,plain,
multiply(sk_c4,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_79,c_3123]) ).
tff(c_3135,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_2612,c_3123]) ).
tff(c_3152,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_3138,c_3135]) ).
tff(c_3049,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_3015,c_42]) ).
tff(c_3161,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3152,c_3049]) ).
tff(c_3106,plain,
! [Z_72] : ( multiply(sk_c6,multiply(sk_c1,Z_72)) = multiply(identity,Z_72) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_3070]) ).
tff(c_3199,plain,
! [Z_75] : ( multiply(sk_c6,multiply(sk_c1,Z_75)) = Z_75 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3106]) ).
tff(c_3214,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3161,c_3199]) ).
tff(c_3119,plain,
! [Z_72] : ( multiply(sk_c4,multiply(sk_c6,Z_72)) = Z_72 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3103]) ).
tff(c_3221,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3214,c_3119]) ).
tff(c_3042,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_3094,plain,
! [Z_72] : ( multiply(sk_c5,multiply(sk_c4,Z_72)) = multiply(sk_c6,Z_72) ),
inference(superposition,[status(thm),theory(equality)],[c_3042,c_3070]) ).
tff(c_3231,plain,
multiply(sk_c6,sk_c5) = multiply(sk_c5,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_3221,c_3094]) ).
tff(c_3237,plain,
multiply(sk_c6,sk_c5) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3054,c_3231]) ).
tff(c_3239,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2608,c_3237]) ).
tff(c_3240,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_3356,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3347,c_3240]) ).
tff(c_3301,plain,
! [Z_78] : ( multiply(sk_c6,multiply(sk_c1,Z_78)) = multiply(identity,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_3268]) ).
tff(c_3388,plain,
! [Z_81] : ( multiply(sk_c6,multiply(sk_c1,Z_81)) = Z_81 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3301]) ).
tff(c_3406,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3356,c_3388]) ).
tff(c_3253,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_3015,c_38]) ).
tff(c_3283,plain,
! [Z_78] : ( multiply(sk_c5,multiply(sk_c6,Z_78)) = multiply(sk_c4,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_3253,c_3268]) ).
tff(c_3413,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_3406,c_3283]) ).
tff(c_3422,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_3413]) ).
tff(c_3014,plain,
inverse(sk_c3) = sk_c5,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_3241,plain,
multiply(sk_c5,sk_c4) != sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_3246,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3241,c_26]) ).
tff(c_3304,plain,
! [X_2,Z_78] : ( multiply(inverse(X_2),multiply(X_2,Z_78)) = multiply(identity,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3268]) ).
tff(c_3439,plain,
! [X_82,Z_83] : ( multiply(inverse(X_82),multiply(X_82,Z_83)) = Z_83 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3304]) ).
tff(c_3487,plain,
multiply(inverse(sk_c3),sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_3246,c_3439]) ).
tff(c_3518,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3422,c_3014,c_3487]) ).
tff(c_3314,plain,
! [Z_78] : ( multiply(sk_c4,multiply(sk_c6,Z_78)) = Z_78 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3298]) ).
tff(c_3416,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3406,c_3314]) ).
tff(c_3522,plain,
multiply(identity,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3518,c_3416]) ).
tff(c_3533,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3522]) ).
tff(c_3540,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3533,c_3533,c_3406]) ).
tff(c_3545,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3422,c_3540]) ).
tff(c_3595,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3545,c_3533]) ).
tff(c_3524,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_3518,c_3333]) ).
tff(c_3535,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3524]) ).
tff(c_3529,plain,
multiply(sk_c1,sk_c6) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3518,c_3015]) ).
tff(c_3686,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3595,c_2,c_3535,c_3529]) ).
tff(c_3688,plain,
inverse(sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_36,plain,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_3726,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3688,c_36]) ).
tff(c_34,plain,
( ( inverse(sk_c3) = sk_c5 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_3701,plain,
inverse(sk_c3) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3688,c_34]) ).
tff(c_3705,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3701,c_4]) ).
tff(c_3746,plain,
! [X_86,Y_87,Z_88] : ( multiply(multiply(X_86,Y_87),Z_88) = multiply(X_86,multiply(Y_87,Z_88)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3770,plain,
! [Z_88] : ( multiply(sk_c5,multiply(sk_c3,Z_88)) = multiply(identity,Z_88) ),
inference(superposition,[status(thm),theory(equality)],[c_3705,c_3746]) ).
tff(c_3792,plain,
! [Z_89] : ( multiply(sk_c5,multiply(sk_c3,Z_89)) = Z_89 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3770]) ).
tff(c_3804,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_3726,c_3792]) ).
tff(c_32,plain,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_3731,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_3688,c_32]) ).
tff(c_3687,plain,
inverse(sk_c2) = sk_c6,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_3692,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3687,c_4]) ).
tff(c_3773,plain,
! [Z_88] : ( multiply(sk_c6,multiply(sk_c2,Z_88)) = multiply(identity,Z_88) ),
inference(superposition,[status(thm),theory(equality)],[c_3692,c_3746]) ).
tff(c_3817,plain,
! [Z_90] : ( multiply(sk_c6,multiply(sk_c2,Z_90)) = Z_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3773]) ).
tff(c_3829,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3731,c_3817]) ).
tff(c_28,plain,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_3714,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_3688,c_28]) ).
tff(c_3853,plain,
! [Z_92] : ( multiply(sk_c5,multiply(sk_c6,Z_92)) = multiply(sk_c4,Z_92) ),
inference(superposition,[status(thm),theory(equality)],[c_3714,c_3746]) ).
tff(c_3868,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_3829,c_3853]) ).
tff(c_3881,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3804,c_3868]) ).
tff(c_3779,plain,
! [X_2,Z_88] : ( multiply(inverse(X_2),multiply(X_2,Z_88)) = multiply(identity,Z_88) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3746]) ).
tff(c_3914,plain,
! [X_93,Z_94] : ( multiply(inverse(X_93),multiply(X_93,Z_94)) = Z_94 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3779]) ).
tff(c_3938,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3881,c_3914]) ).
tff(c_3997,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3938]) ).
tff(c_4046,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3997,c_3997,c_3829]) ).
tff(c_4052,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4046]) ).
tff(c_4003,plain,
! [Z_95] : ( multiply(sk_c3,multiply(sk_c4,Z_95)) = multiply(sk_c5,Z_95) ),
inference(superposition,[status(thm),theory(equality)],[c_3726,c_3746]) ).
tff(c_4024,plain,
multiply(sk_c5,sk_c6) = multiply(sk_c3,sk_c4),
inference(superposition,[status(thm),theory(equality)],[c_3881,c_4003]) ).
tff(c_4030,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3726,c_3714,c_4024]) ).
tff(c_4104,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4052,c_4030]) ).
tff(c_4048,plain,
inverse(identity) != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_3997,c_3688]) ).
tff(c_4113,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_4104,c_4048]) ).
tff(c_4049,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3997,c_79]) ).
tff(c_4164,plain,
sk_c1 = identity,
inference(superposition,[status(thm),theory(equality)],[c_4049,c_2]) ).
tff(c_4050,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3997,c_75]) ).
tff(c_4175,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4164,c_4050]) ).
tff(c_4180,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4113,c_4175]) ).
tff(c_4182,plain,
inverse(sk_c1) != sk_c6,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_56,plain,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_14765,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_4182,c_56]) ).
tff(c_4194,plain,
inverse(sk_c6) = sk_c4,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_4198,plain,
multiply(sk_c4,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4194,c_4]) ).
tff(c_4238,plain,
multiply(sk_c3,sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_4182,c_56]) ).
tff(c_54,plain,
( ( inverse(sk_c3) = sk_c5 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_4202,plain,
inverse(sk_c3) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_4182,c_54]) ).
tff(c_4206,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4202,c_4]) ).
tff(c_4252,plain,
! [X_98,Y_99,Z_100] : ( multiply(multiply(X_98,Y_99),Z_100) = multiply(X_98,multiply(Y_99,Z_100)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4279,plain,
! [Z_100] : ( multiply(sk_c5,multiply(sk_c3,Z_100)) = multiply(identity,Z_100) ),
inference(superposition,[status(thm),theory(equality)],[c_4206,c_4252]) ).
tff(c_4298,plain,
! [Z_101] : ( multiply(sk_c5,multiply(sk_c3,Z_101)) = Z_101 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4279]) ).
tff(c_4310,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_4238,c_4298]) ).
tff(c_52,plain,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_4222,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_4182,c_52]) ).
tff(c_4181,plain,
inverse(sk_c2) = sk_c6,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_4186,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4181,c_4]) ).
tff(c_4282,plain,
! [Z_100] : ( multiply(sk_c6,multiply(sk_c2,Z_100)) = multiply(identity,Z_100) ),
inference(superposition,[status(thm),theory(equality)],[c_4186,c_4252]) ).
tff(c_4321,plain,
! [Z_102] : ( multiply(sk_c6,multiply(sk_c2,Z_102)) = Z_102 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4282]) ).
tff(c_4333,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4222,c_4321]) ).
tff(c_48,plain,
( ( multiply(sk_c5,sk_c6) = sk_c4 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_4233,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_4182,c_48]) ).
tff(c_4377,plain,
! [Z_104] : ( multiply(sk_c5,multiply(sk_c6,Z_104)) = multiply(sk_c4,Z_104) ),
inference(superposition,[status(thm),theory(equality)],[c_4233,c_4252]) ).
tff(c_4389,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_4333,c_4377]) ).
tff(c_4399,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4310,c_4198,c_4389]) ).
tff(c_4404,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4399,c_4310]) ).
tff(c_4276,plain,
! [Z_100] : ( multiply(sk_c4,multiply(sk_c6,Z_100)) = multiply(identity,Z_100) ),
inference(superposition,[status(thm),theory(equality)],[c_4198,c_4252]) ).
tff(c_4347,plain,
! [Z_103] : ( multiply(sk_c4,multiply(sk_c6,Z_103)) = Z_103 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4276]) ).
tff(c_4365,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_4186,c_4347]) ).
tff(c_4401,plain,
multiply(identity,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_4399,c_4365]) ).
tff(c_4410,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4401]) ).
tff(c_4416,plain,
multiply(identity,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4410,c_4222]) ).
tff(c_4420,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4416]) ).
tff(c_4418,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4410,c_4181]) ).
tff(c_4439,plain,
inverse(identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4420,c_4418]) ).
tff(c_4285,plain,
! [X_2,Z_100] : ( multiply(inverse(X_2),multiply(X_2,Z_100)) = multiply(identity,Z_100) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4252]) ).
tff(c_4447,plain,
! [X_105,Z_106] : ( multiply(inverse(X_105),multiply(X_105,Z_106)) = Z_106 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4285]) ).
tff(c_4486,plain,
! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_4447]) ).
tff(c_4494,plain,
! [X_1] : ( multiply(sk_c5,X_1) = X_1 ),
inference(demodulation,[status(thm),theory(equality)],[c_4439,c_4486]) ).
tff(c_4539,plain,
sk_c5 = identity,
inference(superposition,[status(thm),theory(equality)],[c_4404,c_4494]) ).
tff(c_4559,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4539,c_4420]) ).
tff(c_4345,plain,
! [X3_8,X1_7,X2_6] :
( ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 )
| ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c4 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4194,c_4233,c_58]) ).
tff(c_4346,plain,
multiply(sk_c6,sk_c5) != sk_c4,
inference(splitLeft,[status(thm)],[c_4345]) ).
tff(c_4403,plain,
multiply(sk_c6,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_4399,c_4346]) ).
tff(c_4617,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4559,c_4539,c_4403]) ).
tff(c_4619,plain,
multiply(sk_c6,sk_c5) = sk_c4,
inference(splitRight,[status(thm)],[c_4345]) ).
tff(c_4771,plain,
! [Z_111] : ( multiply(sk_c2,multiply(sk_c5,Z_111)) = multiply(sk_c6,Z_111) ),
inference(superposition,[status(thm),theory(equality)],[c_4222,c_4252]) ).
tff(c_4789,plain,
multiply(sk_c6,sk_c5) = multiply(sk_c2,sk_c4),
inference(superposition,[status(thm),theory(equality)],[c_4310,c_4771]) ).
tff(c_4802,plain,
multiply(sk_c2,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4619,c_4789]) ).
tff(c_4795,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c2,sk_c4),
inference(superposition,[status(thm),theory(equality)],[c_4233,c_4771]) ).
tff(c_4803,plain,
multiply(sk_c2,sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4333,c_4795]) ).
tff(c_4815,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4802,c_4803]) ).
tff(c_4835,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4815,c_4233]) ).
tff(c_4839,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_4835]) ).
tff(c_4845,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4839,c_4815]) ).
tff(c_5081,plain,
! [X_118,Z_119] : ( multiply(inverse(X_118),multiply(X_118,Z_119)) = Z_119 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4285]) ).
tff(c_4296,plain,
! [X_2,Z_100] : ( multiply(inverse(X_2),multiply(X_2,Z_100)) = Z_100 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4285]) ).
tff(c_5236,plain,
! [X_122,Z_123] : ( multiply(inverse(inverse(X_122)),Z_123) = multiply(X_122,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_5081,c_4296]) ).
tff(c_5102,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5081]) ).
tff(c_5247,plain,
! [X_122] : ( multiply(X_122,identity) = X_122 ),
inference(superposition,[status(thm),theory(equality)],[c_5236,c_5102]) ).
tff(c_4627,plain,
! [Z_109] : ( multiply(sk_c4,multiply(sk_c6,Z_109)) = Z_109 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4276]) ).
tff(c_4648,plain,
multiply(sk_c4,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_4186,c_4627]) ).
tff(c_4847,plain,
multiply(identity,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_4839,c_4648]) ).
tff(c_4851,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4847]) ).
tff(c_4836,plain,
multiply(sk_c2,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4815,c_4222]) ).
tff(c_4840,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4802,c_4836]) ).
tff(c_4856,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4839,c_4840]) ).
tff(c_4860,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4856,c_4181]) ).
tff(c_4875,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4851,c_4860]) ).
tff(c_4909,plain,
! [X_113,Z_114] : ( multiply(inverse(X_113),multiply(X_113,Z_114)) = Z_114 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4285]) ).
tff(c_4989,plain,
! [X_115] : ( multiply(inverse(inverse(X_115)),identity) = X_115 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4909]) ).
tff(c_4995,plain,
! [X_115] : ( multiply(inverse(inverse(inverse(X_115))),X_115) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_4989,c_4296]) ).
tff(c_4668,plain,
! [Z_110] : ( multiply(sk_c3,multiply(sk_c4,Z_110)) = multiply(sk_c5,Z_110) ),
inference(superposition,[status(thm),theory(equality)],[c_4238,c_4252]) ).
tff(c_4692,plain,
multiply(sk_c5,sk_c6) = multiply(sk_c3,identity),
inference(superposition,[status(thm),theory(equality)],[c_4198,c_4668]) ).
tff(c_4696,plain,
multiply(sk_c3,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4233,c_4692]) ).
tff(c_4294,plain,
! [Z_100] : ( multiply(sk_c5,multiply(sk_c3,Z_100)) = Z_100 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4279]) ).
tff(c_4700,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4696,c_4294]) ).
tff(c_4618,plain,
! [X2_6,X1_7,X3_8] :
( ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_4345]) ).
tff(c_4652,plain,
multiply(sk_c5,sk_c4) != sk_c6,
inference(splitLeft,[status(thm)],[c_4618]) ).
tff(c_4708,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_4700,c_4652]) ).
tff(c_4642,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4333,c_4627]) ).
tff(c_4267,plain,
! [Z_100] : ( multiply(sk_c3,multiply(sk_c4,Z_100)) = multiply(sk_c5,Z_100) ),
inference(superposition,[status(thm),theory(equality)],[c_4238,c_4252]) ).
tff(c_4720,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c3,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_4642,c_4267]) ).
tff(c_4726,plain,
multiply(sk_c3,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_4310,c_4720]) ).
tff(c_4731,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4726,c_4294]) ).
tff(c_4737,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4700,c_4731]) ).
tff(c_4739,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4708,c_4737]) ).
tff(c_4740,plain,
! [X3_8,X1_7,X2_6] :
( ( multiply(X3_8,sk_c4) != sk_c5 )
| ( inverse(X3_8) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X1_7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c4 ) ),
inference(splitRight,[status(thm)],[c_4618]) ).
tff(c_4865,plain,
! [X3_8,X1_7,X2_6] :
( ( multiply(X3_8,identity) != sk_c5 )
| ( inverse(X3_8) != sk_c5 )
| ( multiply(X1_7,sk_c5) != identity )
| ( inverse(X1_7) != identity )
| ( inverse(X2_6) != identity )
| ( multiply(X2_6,identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4856,c_4839,c_4856,c_4856,c_4856,c_4839,c_4740]) ).
tff(c_5048,plain,
! [X2_117] :
( ( inverse(X2_117) != identity )
| ( multiply(X2_117,identity) != identity ) ),
inference(splitLeft,[status(thm)],[c_4865]) ).
tff(c_5052,plain,
inverse(inverse(inverse(inverse(identity)))) != identity,
inference(superposition,[status(thm),theory(equality)],[c_4995,c_5048]) ).
tff(c_5071,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4875,c_4875,c_4875,c_4875,c_5052]) ).
tff(c_5072,plain,
! [X1_7,X3_8] :
( ( multiply(X1_7,sk_c5) != identity )
| ( inverse(X1_7) != identity )
| ( multiply(X3_8,identity) != sk_c5 )
| ( inverse(X3_8) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_4865]) ).
tff(c_14739,plain,
! [X1_7,X3_8] :
( ( identity != X1_7 )
| ( inverse(X1_7) != identity )
| ( identity != X3_8 )
| ( inverse(X3_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4845,c_5247,c_4845,c_5247,c_4845,c_5072]) ).
tff(c_14741,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_14739]) ).
tff(c_4850,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4839,c_4194]) ).
tff(c_5120,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4856,c_4850]) ).
tff(c_14743,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14741,c_5120]) ).
tff(c_14745,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_14739]) ).
tff(c_14747,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14745,c_5120]) ).
tff(c_14748,plain,
inverse(sk_c3) = sk_c5,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_14753,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14748,c_4]) ).
tff(c_14801,plain,
! [X_223,Y_224,Z_225] : ( multiply(multiply(X_223,Y_224),Z_225) = multiply(X_223,multiply(Y_224,Z_225)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14825,plain,
! [Z_225] : ( multiply(sk_c5,multiply(sk_c3,Z_225)) = multiply(identity,Z_225) ),
inference(superposition,[status(thm),theory(equality)],[c_14753,c_14801]) ).
tff(c_14845,plain,
! [Z_226] : ( multiply(sk_c5,multiply(sk_c3,Z_226)) = Z_226 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14825]) ).
tff(c_14857,plain,
multiply(sk_c5,sk_c5) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_14765,c_14845]) ).
tff(c_14778,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_4182,c_52]) ).
tff(c_14828,plain,
! [Z_225] : ( multiply(sk_c6,multiply(sk_c2,Z_225)) = multiply(identity,Z_225) ),
inference(superposition,[status(thm),theory(equality)],[c_4186,c_14801]) ).
tff(c_14868,plain,
! [Z_227] : ( multiply(sk_c6,multiply(sk_c2,Z_227)) = Z_227 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14828]) ).
tff(c_14880,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_14778,c_14868]) ).
tff(c_14749,plain,
inverse(sk_c6) != sk_c4,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_14772,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_14749,c_28]) ).
tff(c_14819,plain,
! [Z_225] : ( multiply(sk_c5,multiply(sk_c6,Z_225)) = multiply(sk_c4,Z_225) ),
inference(superposition,[status(thm),theory(equality)],[c_14772,c_14801]) ).
tff(c_14906,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_14880,c_14819]) ).
tff(c_14912,plain,
multiply(sk_c4,sk_c6) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_14857,c_14906]) ).
tff(c_14831,plain,
! [X_2,Z_225] : ( multiply(inverse(X_2),multiply(X_2,Z_225)) = multiply(identity,Z_225) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14801]) ).
tff(c_14929,plain,
! [X_229,Z_230] : ( multiply(inverse(X_229),multiply(X_229,Z_230)) = Z_230 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14831]) ).
tff(c_14950,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14912,c_14929]) ).
tff(c_14999,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14950]) ).
tff(c_15005,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14999,c_14999,c_14880]) ).
tff(c_15014,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15005]) ).
tff(c_15051,plain,
multiply(identity,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_15014,c_15014,c_14857]) ).
tff(c_15058,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15051]) ).
tff(c_15010,plain,
inverse(identity) != sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_14999,c_14749]) ).
tff(c_15104,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15058,c_15010]) ).
tff(c_15013,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14999,c_4181]) ).
tff(c_15073,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15013,c_4]) ).
tff(c_14841,plain,
! [X_2,Z_225] : ( multiply(inverse(X_2),multiply(X_2,Z_225)) = Z_225 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14831]) ).
tff(c_15080,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_15073,c_14841]) ).
tff(c_15092,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15080]) ).
tff(c_15096,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15092,c_15013]) ).
tff(c_15133,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15104,c_15096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP305-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 22:06:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 9.83/3.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.83/3.36
% 9.83/3.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.83/3.43
% 9.83/3.43 Inference rules
% 9.83/3.43 ----------------------
% 9.83/3.43 #Ref : 0
% 9.83/3.43 #Sup : 3816
% 9.83/3.43 #Fact : 0
% 9.83/3.43 #Define : 0
% 9.83/3.43 #Split : 20
% 9.83/3.43 #Chain : 0
% 9.83/3.43 #Close : 0
% 9.83/3.43
% 9.83/3.43 Ordering : KBO
% 9.83/3.43
% 9.83/3.43 Simplification rules
% 9.83/3.43 ----------------------
% 9.83/3.43 #Subsume : 9
% 9.83/3.43 #Demod : 7742
% 9.83/3.43 #Tautology : 3066
% 9.83/3.43 #SimpNegUnit : 60
% 9.83/3.43 #BackRed : 322
% 9.83/3.43
% 9.83/3.43 #Partial instantiations: 0
% 9.83/3.43 #Strategies tried : 1
% 9.83/3.43
% 9.83/3.43 Timing (in seconds)
% 9.83/3.43 ----------------------
% 9.83/3.43 Preprocessing : 0.48
% 9.83/3.43 Parsing : 0.21
% 9.83/3.43 CNF conversion : 0.02
% 9.83/3.43 Main loop : 1.92
% 9.83/3.43 Inferencing : 0.64
% 9.83/3.43 Reduction : 0.84
% 9.83/3.43 Demodulation : 0.71
% 9.83/3.43 BG Simplification : 0.07
% 9.83/3.43 Subsumption : 0.23
% 9.83/3.43 Abstraction : 0.11
% 9.83/3.43 MUC search : 0.00
% 9.83/3.43 Cooper : 0.00
% 9.83/3.43 Total : 2.54
% 9.83/3.43 Index Insertion : 0.00
% 9.83/3.43 Index Deletion : 0.00
% 9.83/3.43 Index Matching : 0.00
% 9.83/3.43 BG Taut test : 0.00
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