TSTP Solution File: GRP211-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP211-1 : 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 : n003.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 10:40:29 EDT 2023
% Result : Unsatisfiable 12.84s 4.37s
% Output : CNFRefutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 37
% Syntax : Number of formulae : 449 ( 366 unt; 11 typ; 0 def)
% Number of atoms : 580 ( 559 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 302 ( 160 ~; 142 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 229 (; 229 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c8 > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(sk_c8,type,
sk_c8: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [X5,X6,X3,X1,X2,X4] :
( ( multiply(X4,X5) != sk_c8 )
| ( inverse(X4) != X5 )
| ( multiply(X5,sk_c7) != sk_c8 )
| ( inverse(X6) != sk_c8 )
| ( multiply(X6,sk_c7) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(sk_c8,X2) != sk_c7 )
| ( multiply(X3,sk_c8) != X2 )
| ( inverse(X3) != sk_c8 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
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_32293,plain,
! [X_443,Y_444,Z_445] : ( multiply(multiply(X_443,Y_444),Z_445) = multiply(X_443,multiply(Y_444,Z_445)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_32326,plain,
! [X_2,Z_445] : ( multiply(inverse(X_2),multiply(X_2,Z_445)) = multiply(identity,Z_445) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_32293]) ).
tff(c_35765,plain,
! [X_488,Z_489] : ( multiply(inverse(X_488),multiply(X_488,Z_489)) = Z_489 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32326]) ).
tff(c_32337,plain,
! [X_2,Z_445] : ( multiply(inverse(X_2),multiply(X_2,Z_445)) = Z_445 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32326]) ).
tff(c_36107,plain,
! [X_494,Z_495] : ( multiply(inverse(inverse(X_494)),Z_495) = multiply(X_494,Z_495) ),
inference(superposition,[status(thm),theory(equality)],[c_35765,c_32337]) ).
tff(c_35813,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_35765]) ).
tff(c_36117,plain,
! [X_494] : ( multiply(X_494,identity) = X_494 ),
inference(superposition,[status(thm),theory(equality)],[c_36107,c_35813]) ).
tff(c_21262,plain,
! [X_302,Y_303,Z_304] : ( multiply(multiply(X_302,Y_303),Z_304) = multiply(X_302,multiply(Y_303,Z_304)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_21295,plain,
! [X_2,Z_304] : ( multiply(inverse(X_2),multiply(X_2,Z_304)) = multiply(identity,Z_304) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_21262]) ).
tff(c_21306,plain,
! [X_2,Z_304] : ( multiply(inverse(X_2),multiply(X_2,Z_304)) = Z_304 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21295]) ).
tff(c_23310,plain,
! [X_342,Z_343] : ( multiply(inverse(X_342),multiply(X_342,Z_343)) = Z_343 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21295]) ).
tff(c_23653,plain,
! [X_348,Z_349] : ( multiply(inverse(inverse(X_348)),Z_349) = multiply(X_348,Z_349) ),
inference(superposition,[status(thm),theory(equality)],[c_21306,c_23310]) ).
tff(c_23358,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_23310]) ).
tff(c_23660,plain,
! [X_348] : ( multiply(X_348,identity) = X_348 ),
inference(superposition,[status(thm),theory(equality)],[c_23653,c_23358]) ).
tff(c_134,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_164,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_134]) ).
tff(c_541,plain,
! [X_26,Z_27] : ( multiply(inverse(X_26),multiply(X_26,Z_27)) = Z_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_174,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_164]) ).
tff(c_1263,plain,
! [X_38,Z_39] : ( multiply(inverse(inverse(X_38)),Z_39) = multiply(X_38,Z_39) ),
inference(superposition,[status(thm),theory(equality)],[c_541,c_174]) ).
tff(c_598,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_541]) ).
tff(c_1270,plain,
! [X_38] : ( multiply(X_38,identity) = X_38 ),
inference(superposition,[status(thm),theory(equality)],[c_1263,c_598]) ).
tff(c_16,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_103,plain,
multiply(sk_c1,sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_18,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_87,plain,
inverse(sk_c1) = sk_c2,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_91,plain,
multiply(sk_c2,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_87,c_4]) ).
tff(c_158,plain,
! [Z_16] : ( multiply(sk_c2,multiply(sk_c1,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_134]) ).
tff(c_482,plain,
! [Z_23] : ( multiply(sk_c2,multiply(sk_c1,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_494,plain,
multiply(sk_c2,sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_103,c_482]) ).
tff(c_565,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_494,c_541]) ).
tff(c_605,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_565]) ).
tff(c_56,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_117,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_38,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_75,plain,
inverse(sk_c3) = sk_c8,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_79,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).
tff(c_161,plain,
! [Z_16] : ( multiply(sk_c8,multiply(sk_c3,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_134]) ).
tff(c_518,plain,
! [Z_25] : ( multiply(sk_c8,multiply(sk_c3,Z_25)) = Z_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_530,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_117,c_518]) ).
tff(c_610,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_605,c_605,c_530]) ).
tff(c_619,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_610]) ).
tff(c_789,plain,
! [X_29,Z_30] : ( multiply(inverse(inverse(X_29)),Z_30) = multiply(X_29,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_541,c_174]) ).
tff(c_796,plain,
! [X_29] : ( multiply(X_29,identity) = X_29 ),
inference(superposition,[status(thm),theory(equality)],[c_789,c_598]) ).
tff(c_200,plain,
! [Z_18] : ( multiply(sk_c8,multiply(sk_c3,Z_18)) = Z_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_212,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_117,c_200]) ).
tff(c_177,plain,
! [Z_17] : ( multiply(sk_c2,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_189,plain,
multiply(sk_c2,sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_103,c_177]) ).
tff(c_216,plain,
! [Z_19] : ( multiply(sk_c1,multiply(sk_c2,Z_19)) = multiply(sk_c8,Z_19) ),
inference(superposition,[status(thm),theory(equality)],[c_103,c_134]) ).
tff(c_231,plain,
multiply(sk_c8,sk_c8) = multiply(sk_c1,sk_c2),
inference(superposition,[status(thm),theory(equality)],[c_189,c_216]) ).
tff(c_244,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_103,c_231]) ).
tff(c_252,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_244]) ).
tff(c_256,plain,
multiply(sk_c2,sk_c7) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_189]) ).
tff(c_28,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_109,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_258,plain,
multiply(sk_c2,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_109]) ).
tff(c_326,plain,
sk_c7 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_256,c_258]) ).
tff(c_328,plain,
multiply(sk_c2,sk_c2) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_326,c_256]) ).
tff(c_364,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_164]) ).
tff(c_385,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_328,c_364]) ).
tff(c_411,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_385]) ).
tff(c_259,plain,
multiply(sk_c1,sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_252,c_103]) ).
tff(c_58,plain,
! [X3_8,X1_9,X6_7,X4_11] :
( ( inverse(X3_8) != sk_c8 )
| ( multiply(sk_c8,multiply(X3_8,sk_c8)) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c8 )
| ( multiply(X6_7,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c8 )
| ( multiply(inverse(X4_11),sk_c7) != sk_c8 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_176,plain,
! [X4_11] :
( ( multiply(inverse(X4_11),sk_c7) != sk_c8 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_291,plain,
! [X4_20] :
( ( multiply(inverse(X4_20),sk_c7) != sk_c7 )
| ( multiply(X4_20,inverse(X4_20)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_252,c_176]) ).
tff(c_295,plain,
( ( multiply(sk_c2,sk_c7) != sk_c7 )
| ( multiply(sk_c1,inverse(sk_c1)) != sk_c7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_87,c_291]) ).
tff(c_302,plain,
multiply(sk_c2,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_259,c_87,c_295]) ).
tff(c_480,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_411,c_302]) ).
tff(c_481,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c8 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c8 )
| ( inverse(X3_8) != sk_c8 )
| ( multiply(sk_c8,multiply(X3_8,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_625,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != identity )
| ( inverse(X6_7) != identity )
| ( multiply(X1_9,sk_c7) != identity )
| ( inverse(X1_9) != identity )
| ( inverse(X3_8) != identity )
| ( multiply(X3_8,identity) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_605,c_2,c_605,c_605,c_605,c_605,c_605,c_605,c_481]) ).
tff(c_626,plain,
! [X3_8] :
( ( inverse(X3_8) != identity )
| ( multiply(X3_8,identity) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_625]) ).
tff(c_1061,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_796,c_619,c_626]) ).
tff(c_618,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_605,c_75]) ).
tff(c_637,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_618,c_4]) ).
tff(c_659,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_637,c_174]) ).
tff(c_671,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_659]) ).
tff(c_675,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_671,c_618]) ).
tff(c_1063,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1061,c_675]) ).
tff(c_1064,plain,
! [X1_9,X6_7] :
( ( multiply(X1_9,sk_c7) != identity )
| ( inverse(X1_9) != identity )
| ( multiply(X6_7,sk_c7) != identity )
| ( inverse(X6_7) != identity ) ),
inference(splitRight,[status(thm)],[c_625]) ).
tff(c_9884,plain,
! [X1_9,X6_7] :
( ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( identity != X6_7 )
| ( inverse(X6_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1270,c_619,c_1270,c_619,c_1064]) ).
tff(c_9886,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_9884]) ).
tff(c_1104,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_618,c_4]) ).
tff(c_1142,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_1104,c_174]) ).
tff(c_1154,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1142]) ).
tff(c_1158,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1154,c_618]) ).
tff(c_9888,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9886,c_1158]) ).
tff(c_9890,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_9884]) ).
tff(c_9892,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9890,c_1158]) ).
tff(c_9894,plain,
multiply(sk_c3,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_52,plain,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_9926,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9894,c_52]) ).
tff(c_54,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_9920,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9894,c_54]) ).
tff(c_9893,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_9898,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9893,c_4]) ).
tff(c_9941,plain,
! [X_133,Y_134,Z_135] : ( multiply(multiply(X_133,Y_134),Z_135) = multiply(X_133,multiply(Y_134,Z_135)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9968,plain,
! [Z_135] : ( multiply(sk_c8,multiply(sk_c5,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_9898,c_9941]) ).
tff(c_10070,plain,
! [Z_140] : ( multiply(sk_c8,multiply(sk_c5,Z_140)) = Z_140 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9968]) ).
tff(c_10082,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_9920,c_10070]) ).
tff(c_10086,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9926,c_10082]) ).
tff(c_9977,plain,
! [Z_135] : ( multiply(sk_c2,multiply(sk_c1,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_9941]) ).
tff(c_10011,plain,
! [Z_137] : ( multiply(sk_c2,multiply(sk_c1,Z_137)) = Z_137 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9977]) ).
tff(c_10023,plain,
multiply(sk_c2,sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_103,c_10011]) ).
tff(c_10091,plain,
multiply(sk_c2,sk_c7) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_10086,c_10023]) ).
tff(c_9983,plain,
! [X_2,Z_135] : ( multiply(inverse(X_2),multiply(X_2,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9941]) ).
tff(c_9995,plain,
! [X_2,Z_135] : ( multiply(inverse(X_2),multiply(X_2,Z_135)) = Z_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9983]) ).
tff(c_10284,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10091,c_9995]) ).
tff(c_10290,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10284]) ).
tff(c_10101,plain,
multiply(sk_c2,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10086,c_109]) ).
tff(c_10280,plain,
sk_c7 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_10091,c_10101]) ).
tff(c_10322,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10290,c_10280]) ).
tff(c_10103,plain,
multiply(sk_c7,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10086,c_79]) ).
tff(c_10308,plain,
multiply(sk_c2,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10280,c_10103]) ).
tff(c_10420,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10322,c_10308]) ).
tff(c_10099,plain,
multiply(sk_c3,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10086,c_9894]) ).
tff(c_10419,plain,
multiply(sk_c3,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_10290,c_10290,c_10099]) ).
tff(c_10421,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_10420,c_10419]) ).
tff(c_10425,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10421]) ).
tff(c_10427,plain,
multiply(sk_c2,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_32,plain,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_10457,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_10427,c_32]) ).
tff(c_34,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_10465,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10427,c_34]) ).
tff(c_36,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_10442,plain,
inverse(sk_c5) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_10427,c_36]) ).
tff(c_10446,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10442,c_4]) ).
tff(c_10482,plain,
! [X_145,Y_146,Z_147] : ( multiply(multiply(X_145,Y_146),Z_147) = multiply(X_145,multiply(Y_146,Z_147)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10509,plain,
! [Z_147] : ( multiply(sk_c8,multiply(sk_c5,Z_147)) = multiply(identity,Z_147) ),
inference(superposition,[status(thm),theory(equality)],[c_10446,c_10482]) ).
tff(c_11465,plain,
! [Z_165] : ( multiply(sk_c8,multiply(sk_c5,Z_165)) = Z_165 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10509]) ).
tff(c_11477,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_10465,c_11465]) ).
tff(c_11481,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10457,c_11477]) ).
tff(c_10518,plain,
! [Z_147] : ( multiply(sk_c2,multiply(sk_c1,Z_147)) = multiply(identity,Z_147) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_10482]) ).
tff(c_10538,plain,
! [Z_148] : ( multiply(sk_c2,multiply(sk_c1,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10518]) ).
tff(c_10550,plain,
multiply(sk_c2,sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_103,c_10538]) ).
tff(c_11486,plain,
multiply(sk_c2,sk_c7) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_11481,c_10550]) ).
tff(c_10524,plain,
! [X_2,Z_147] : ( multiply(inverse(X_2),multiply(X_2,Z_147)) = multiply(identity,Z_147) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10482]) ).
tff(c_14278,plain,
! [X_200,Z_201] : ( multiply(inverse(X_200),multiply(X_200,Z_201)) = Z_201 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10524]) ).
tff(c_14296,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11486,c_14278]) ).
tff(c_14336,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14296]) ).
tff(c_10536,plain,
! [X_2,Z_147] : ( multiply(inverse(X_2),multiply(X_2,Z_147)) = Z_147 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10524]) ).
tff(c_14593,plain,
! [X_204,Z_205] : ( multiply(inverse(inverse(X_204)),Z_205) = multiply(X_204,Z_205) ),
inference(superposition,[status(thm),theory(equality)],[c_14278,c_10536]) ).
tff(c_14329,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14278]) ).
tff(c_14603,plain,
! [X_204] : ( multiply(X_204,identity) = X_204 ),
inference(superposition,[status(thm),theory(equality)],[c_14593,c_14329]) ).
tff(c_11560,plain,
! [X_166,Z_167] : ( multiply(inverse(X_166),multiply(X_166,Z_167)) = Z_167 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10524]) ).
tff(c_11875,plain,
! [X_170,Z_171] : ( multiply(inverse(inverse(X_170)),Z_171) = multiply(X_170,Z_171) ),
inference(superposition,[status(thm),theory(equality)],[c_11560,c_10536]) ).
tff(c_11611,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11560]) ).
tff(c_11885,plain,
! [X_170] : ( multiply(X_170,identity) = X_170 ),
inference(superposition,[status(thm),theory(equality)],[c_11875,c_11611]) ).
tff(c_11578,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11486,c_11560]) ).
tff(c_11618,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11578]) ).
tff(c_10602,plain,
! [Z_151] : ( multiply(sk_c8,multiply(sk_c5,Z_151)) = Z_151 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10509]) ).
tff(c_10614,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_10465,c_10602]) ).
tff(c_10618,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10457,c_10614]) ).
tff(c_10623,plain,
multiply(sk_c2,sk_c7) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_10618,c_10550]) ).
tff(c_10818,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10623,c_10536]) ).
tff(c_10824,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10818]) ).
tff(c_10426,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_10632,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10618,c_10426]) ).
tff(c_10673,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10632,c_4]) ).
tff(c_10886,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10824,c_10673]) ).
tff(c_10834,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10824,c_10632]) ).
tff(c_10887,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10886,c_10834]) ).
tff(c_10561,plain,
! [X4_11] :
( ( multiply(inverse(X4_11),sk_c7) != sk_c8 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_10641,plain,
! [X4_152] :
( ( multiply(inverse(X4_152),sk_c7) != sk_c7 )
| ( multiply(X4_152,inverse(X4_152)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10618,c_10618,c_10561]) ).
tff(c_10646,plain,
( ( sk_c7 != identity )
| ( multiply(sk_c7,inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10641]) ).
tff(c_11423,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10887,c_10824,c_10824,c_2,c_10824,c_10824,c_10646]) ).
tff(c_11424,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c8 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c8 )
| ( inverse(X3_8) != sk_c8 )
| ( multiply(sk_c8,multiply(X3_8,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_11503,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_11481,c_11481,c_11481,c_11481,c_11481,c_11481,c_11481,c_11424]) ).
tff(c_11504,plain,
! [X3_8] :
( ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_11503]) ).
tff(c_14219,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11885,c_11618,c_11618,c_2,c_11618,c_11618,c_11504]) ).
tff(c_11498,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11481,c_75]) ).
tff(c_11515,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11498,c_4]) ).
tff(c_11638,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11618,c_11515]) ).
tff(c_11627,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11618,c_11498]) ).
tff(c_11663,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11638,c_11627]) ).
tff(c_14221,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14219,c_11663]) ).
tff(c_14222,plain,
! [X1_9,X6_7] :
( ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_11503]) ).
tff(c_18813,plain,
! [X1_9,X6_7] :
( ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( identity != X6_7 )
| ( inverse(X6_7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14336,c_14603,c_14336,c_14336,c_14336,c_14603,c_14336,c_14336,c_14222]) ).
tff(c_18815,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_18813]) ).
tff(c_14233,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11498,c_4]) ).
tff(c_14356,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14336,c_14233]) ).
tff(c_14345,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14336,c_11498]) ).
tff(c_14381,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14356,c_14345]) ).
tff(c_18817,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18815,c_14381]) ).
tff(c_18819,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_18813]) ).
tff(c_18821,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18819,c_14381]) ).
tff(c_18823,plain,
multiply(sk_c1,sk_c2) != sk_c8,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_12,plain,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_19410,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_18823,c_12]) ).
tff(c_18865,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_18823,c_12]) ).
tff(c_14,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_18872,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18823,c_14]) ).
tff(c_18822,plain,
inverse(sk_c5) = sk_c8,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_18827,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18822,c_4]) ).
tff(c_18884,plain,
! [X_251,Y_252,Z_253] : ( multiply(multiply(X_251,Y_252),Z_253) = multiply(X_251,multiply(Y_252,Z_253)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18917,plain,
! [Z_253] : ( multiply(sk_c8,multiply(sk_c5,Z_253)) = multiply(identity,Z_253) ),
inference(superposition,[status(thm),theory(equality)],[c_18827,c_18884]) ).
tff(c_18994,plain,
! [Z_257] : ( multiply(sk_c8,multiply(sk_c5,Z_257)) = Z_257 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18917]) ).
tff(c_19006,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_18872,c_18994]) ).
tff(c_19010,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_18865,c_19006]) ).
tff(c_18859,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_18923,plain,
! [Z_253] : ( multiply(sk_c8,multiply(sk_c3,Z_253)) = multiply(identity,Z_253) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_18884]) ).
tff(c_18953,plain,
! [Z_255] : ( multiply(sk_c8,multiply(sk_c3,Z_255)) = Z_255 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18923]) ).
tff(c_18965,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18859,c_18953]) ).
tff(c_19030,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19010,c_19010,c_18965]) ).
tff(c_18926,plain,
! [X_2,Z_253] : ( multiply(inverse(X_2),multiply(X_2,Z_253)) = multiply(identity,Z_253) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18884]) ).
tff(c_18938,plain,
! [X_2,Z_253] : ( multiply(inverse(X_2),multiply(X_2,Z_253)) = Z_253 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18926]) ).
tff(c_19230,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19030,c_18938]) ).
tff(c_19236,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19230]) ).
tff(c_8,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_18842,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_18823,c_8]) ).
tff(c_19037,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19010,c_18842]) ).
tff(c_19051,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19037,c_4]) ).
tff(c_19256,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19236,c_19051]) ).
tff(c_19249,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19236,c_19037]) ).
tff(c_19285,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19256,c_19249]) ).
tff(c_19250,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19236,c_19010]) ).
tff(c_18836,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_18914,plain,
! [Z_253] : ( multiply(sk_c2,multiply(sk_c7,Z_253)) = multiply(sk_c8,Z_253) ),
inference(superposition,[status(thm),theory(equality)],[c_18836,c_18884]) ).
tff(c_19300,plain,
! [Z_262] : ( multiply(sk_c2,Z_262) = Z_262 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19250,c_2,c_19236,c_18914]) ).
tff(c_19315,plain,
sk_c1 = identity,
inference(superposition,[status(thm),theory(equality)],[c_19300,c_91]) ).
tff(c_19330,plain,
inverse(identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_19315,c_87]) ).
tff(c_19333,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19285,c_19330]) ).
tff(c_19040,plain,
multiply(sk_c1,sk_c2) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19010,c_18823]) ).
tff(c_19242,plain,
multiply(sk_c1,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19236,c_19040]) ).
tff(c_19402,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19333,c_2,c_19315,c_19242]) ).
tff(c_19403,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_19428,plain,
! [X_263,Y_264,Z_265] : ( multiply(multiply(X_263,Y_264),Z_265) = multiply(X_263,multiply(Y_264,Z_265)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_19458,plain,
! [Z_265] : ( multiply(sk_c8,multiply(sk_c5,Z_265)) = multiply(identity,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_18827,c_19428]) ).
tff(c_19531,plain,
! [Z_269] : ( multiply(sk_c8,multiply(sk_c5,Z_269)) = Z_269 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19458]) ).
tff(c_19543,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_19403,c_19531]) ).
tff(c_19547,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19410,c_19543]) ).
tff(c_19404,plain,
multiply(sk_c3,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_50,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_19415,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_19404,c_50]) ).
tff(c_18846,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18842,c_4]) ).
tff(c_19452,plain,
! [Z_265] : ( multiply(sk_c8,multiply(sk_c4,Z_265)) = multiply(identity,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_18846,c_19428]) ).
tff(c_19508,plain,
! [Z_268] : ( multiply(sk_c8,multiply(sk_c4,Z_268)) = Z_268 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19452]) ).
tff(c_19520,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19415,c_19508]) ).
tff(c_19563,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19547,c_19547,c_19520]) ).
tff(c_19467,plain,
! [X_2,Z_265] : ( multiply(inverse(X_2),multiply(X_2,Z_265)) = multiply(identity,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19428]) ).
tff(c_19479,plain,
! [X_2,Z_265] : ( multiply(inverse(X_2),multiply(X_2,Z_265)) = Z_265 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19467]) ).
tff(c_19753,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19563,c_19479]) ).
tff(c_19759,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19753]) ).
tff(c_19577,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19547,c_75]) ).
tff(c_19599,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19577,c_4]) ).
tff(c_19779,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19759,c_19599]) ).
tff(c_19568,plain,
multiply(sk_c3,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19547,c_19404]) ).
tff(c_19767,plain,
multiply(sk_c3,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19759,c_19759,c_19568]) ).
tff(c_19877,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19779,c_19767]) ).
tff(c_19879,plain,
multiply(sk_c2,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_20642,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19879,c_32]) ).
tff(c_19905,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19879,c_32]) ).
tff(c_19912,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_19879,c_34]) ).
tff(c_19928,plain,
! [X_274,Y_275,Z_276] : ( multiply(multiply(X_274,Y_275),Z_276) = multiply(X_274,multiply(Y_275,Z_276)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_19958,plain,
! [Z_276] : ( multiply(sk_c8,multiply(sk_c5,Z_276)) = multiply(identity,Z_276) ),
inference(superposition,[status(thm),theory(equality)],[c_18827,c_19928]) ).
tff(c_20035,plain,
! [Z_280] : ( multiply(sk_c8,multiply(sk_c5,Z_280)) = Z_280 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19958]) ).
tff(c_20047,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_19912,c_20035]) ).
tff(c_20051,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19905,c_20047]) ).
tff(c_19900,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_19964,plain,
! [Z_276] : ( multiply(sk_c8,multiply(sk_c3,Z_276)) = multiply(identity,Z_276) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_19928]) ).
tff(c_19995,plain,
! [Z_278] : ( multiply(sk_c8,multiply(sk_c3,Z_278)) = Z_278 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19964]) ).
tff(c_20007,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19900,c_19995]) ).
tff(c_20054,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20051,c_20051,c_20007]) ).
tff(c_19967,plain,
! [X_2,Z_276] : ( multiply(inverse(X_2),multiply(X_2,Z_276)) = multiply(identity,Z_276) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19928]) ).
tff(c_19979,plain,
! [X_2,Z_276] : ( multiply(inverse(X_2),multiply(X_2,Z_276)) = Z_276 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19967]) ).
tff(c_20234,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20054,c_19979]) ).
tff(c_20240,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20234]) ).
tff(c_20064,plain,
multiply(sk_c1,sk_c2) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20051,c_18823]) ).
tff(c_20247,plain,
multiply(sk_c1,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_20240,c_20064]) ).
tff(c_20140,plain,
! [X_282,Z_283] : ( multiply(inverse(X_282),multiply(X_282,Z_283)) = Z_283 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19967]) ).
tff(c_20488,plain,
! [X_287,Z_288] : ( multiply(inverse(inverse(X_287)),Z_288) = multiply(X_287,Z_288) ),
inference(superposition,[status(thm),theory(equality)],[c_20140,c_19979]) ).
tff(c_20191,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20140]) ).
tff(c_20543,plain,
! [X_289] : ( multiply(X_289,identity) = X_289 ),
inference(superposition,[status(thm),theory(equality)],[c_20488,c_20191]) ).
tff(c_20185,plain,
multiply(inverse(sk_c2),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_91,c_20140]) ).
tff(c_20556,plain,
inverse(sk_c2) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_20543,c_20185]) ).
tff(c_20633,plain,
multiply(sk_c1,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20556,c_4]) ).
tff(c_20639,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20247,c_20633]) ).
tff(c_20640,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_20668,plain,
! [X_290,Y_291,Z_292] : ( multiply(multiply(X_290,Y_291),Z_292) = multiply(X_290,multiply(Y_291,Z_292)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_20695,plain,
! [Z_292] : ( multiply(sk_c8,multiply(sk_c5,Z_292)) = multiply(identity,Z_292) ),
inference(superposition,[status(thm),theory(equality)],[c_18827,c_20668]) ).
tff(c_20767,plain,
! [Z_296] : ( multiply(sk_c8,multiply(sk_c5,Z_296)) = Z_296 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20695]) ).
tff(c_20779,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_20640,c_20767]) ).
tff(c_20783,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20642,c_20779]) ).
tff(c_20641,plain,
multiply(sk_c3,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_20655,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_20641,c_50]) ).
tff(c_19878,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_19883,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19878,c_4]) ).
tff(c_20692,plain,
! [Z_292] : ( multiply(sk_c8,multiply(sk_c4,Z_292)) = multiply(identity,Z_292) ),
inference(superposition,[status(thm),theory(equality)],[c_19883,c_20668]) ).
tff(c_20744,plain,
! [Z_295] : ( multiply(sk_c8,multiply(sk_c4,Z_295)) = Z_295 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20692]) ).
tff(c_20756,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20655,c_20744]) ).
tff(c_20786,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20783,c_20783,c_20756]) ).
tff(c_20704,plain,
! [X_2,Z_292] : ( multiply(inverse(X_2),multiply(X_2,Z_292)) = multiply(identity,Z_292) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20668]) ).
tff(c_20901,plain,
! [X_298,Z_299] : ( multiply(inverse(X_298),multiply(X_298,Z_299)) = Z_299 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20704]) ).
tff(c_20934,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20786,c_20901]) ).
tff(c_20971,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20934]) ).
tff(c_20799,plain,
multiply(sk_c7,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20783,c_79]) ).
tff(c_20985,plain,
multiply(identity,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20971,c_20799]) ).
tff(c_20716,plain,
! [X_2,Z_292] : ( multiply(inverse(X_2),multiply(X_2,Z_292)) = Z_292 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20704]) ).
tff(c_21085,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_20985,c_20716]) ).
tff(c_21097,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21085]) ).
tff(c_20790,plain,
multiply(sk_c3,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20783,c_20641]) ).
tff(c_20981,plain,
multiply(sk_c3,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_20971,c_20971,c_20790]) ).
tff(c_21202,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21097,c_20981]) ).
tff(c_21204,plain,
inverse(sk_c1) != sk_c2,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_22,plain,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_21233,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_21204,c_22]) ).
tff(c_24,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_21238,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_21204,c_24]) ).
tff(c_26,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_21217,plain,
inverse(sk_c5) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_21204,c_26]) ).
tff(c_21221,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21217,c_4]) ).
tff(c_21286,plain,
! [Z_304] : ( multiply(sk_c8,multiply(sk_c5,Z_304)) = multiply(identity,Z_304) ),
inference(superposition,[status(thm),theory(equality)],[c_21221,c_21262]) ).
tff(c_21308,plain,
! [Z_305] : ( multiply(sk_c8,multiply(sk_c5,Z_305)) = Z_305 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21286]) ).
tff(c_21320,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_21238,c_21308]) ).
tff(c_21324,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21233,c_21320]) ).
tff(c_21203,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_21332,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21324,c_21203]) ).
tff(c_20,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_21244,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_21204,c_20]) ).
tff(c_21326,plain,
multiply(sk_c4,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21324,c_21244]) ).
tff(c_23340,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_21326,c_23310]) ).
tff(c_23366,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21332,c_23340]) ).
tff(c_23378,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23366,c_21306]) ).
tff(c_23384,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23378]) ).
tff(c_21409,plain,
! [X_306,Z_307] : ( multiply(inverse(X_306),multiply(X_306,Z_307)) = Z_307 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21295]) ).
tff(c_21752,plain,
! [X_312,Z_313] : ( multiply(inverse(inverse(X_312)),Z_313) = multiply(X_312,Z_313) ),
inference(superposition,[status(thm),theory(equality)],[c_21306,c_21409]) ).
tff(c_21773,plain,
! [X_312] : ( multiply(X_312,inverse(X_312)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_21752,c_4]) ).
tff(c_21439,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_21326,c_21409]) ).
tff(c_21465,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21332,c_21439]) ).
tff(c_21477,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_21465,c_21306]) ).
tff(c_21483,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21477]) ).
tff(c_21457,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_21409]) ).
tff(c_21759,plain,
! [X_312] : ( multiply(X_312,identity) = X_312 ),
inference(superposition,[status(thm),theory(equality)],[c_21752,c_21457]) ).
tff(c_21353,plain,
! [X3_8,X1_9,X6_7,X4_11] :
( ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(inverse(X4_11),sk_c7) != sk_c7 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_21324,c_21324,c_21324,c_21324,c_21324,c_21324,c_21324,c_21324,c_21324,c_58]) ).
tff(c_21354,plain,
! [X4_11] :
( ( multiply(inverse(X4_11),sk_c7) != sk_c7 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_21353]) ).
tff(c_23252,plain,
! [X4_11] : ( inverse(X4_11) != identity ),
inference(demodulation,[status(thm),theory(equality)],[c_21773,c_21483,c_21759,c_21483,c_21483,c_21354]) ).
tff(c_21330,plain,
inverse(sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21324,c_21217]) ).
tff(c_21528,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21483,c_21330]) ).
tff(c_21565,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21528,c_4]) ).
tff(c_21604,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_21565,c_21306]) ).
tff(c_21616,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21604]) ).
tff(c_21621,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21616,c_21528]) ).
tff(c_23254,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23252,c_21621]) ).
tff(c_23255,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_21353]) ).
tff(c_31881,plain,
! [X6_7,X1_9,X3_8] :
( ( identity != X6_7 )
| ( inverse(X6_7) != identity )
| ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( inverse(X3_8) != identity )
| ( identity != X3_8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_23660,c_23384,c_23384,c_2,c_23384,c_23384,c_23384,c_23660,c_23384,c_23384,c_23384,c_23660,c_23384,c_23384,c_23255]) ).
tff(c_31883,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_31881]) ).
tff(c_23429,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23384,c_21330]) ).
tff(c_23466,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_23429,c_4]) ).
tff(c_23505,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_23466,c_21306]) ).
tff(c_23517,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23505]) ).
tff(c_23522,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23517,c_23429]) ).
tff(c_31885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31883,c_23522]) ).
tff(c_31886,plain,
! [X1_9,X6_7] :
( ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( identity != X6_7 )
| ( inverse(X6_7) != identity ) ),
inference(splitRight,[status(thm)],[c_31881]) ).
tff(c_31888,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_31886]) ).
tff(c_31890,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31888,c_23522]) ).
tff(c_32219,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_31886]) ).
tff(c_32221,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32219,c_23522]) ).
tff(c_32223,plain,
inverse(sk_c3) != sk_c8,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_42,plain,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_32250,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_32223,c_42]) ).
tff(c_44,plain,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_32267,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_32223,c_44]) ).
tff(c_46,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_32236,plain,
inverse(sk_c5) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_32223,c_46]) ).
tff(c_32240,plain,
multiply(sk_c8,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32236,c_4]) ).
tff(c_32320,plain,
! [Z_445] : ( multiply(sk_c8,multiply(sk_c5,Z_445)) = multiply(identity,Z_445) ),
inference(superposition,[status(thm),theory(equality)],[c_32240,c_32293]) ).
tff(c_32339,plain,
! [Z_446] : ( multiply(sk_c8,multiply(sk_c5,Z_446)) = Z_446 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32320]) ).
tff(c_32351,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_32267,c_32339]) ).
tff(c_32355,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32250,c_32351]) ).
tff(c_32222,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_32364,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32355,c_32222]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_32276,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_32223,c_40]) ).
tff(c_32357,plain,
multiply(sk_c4,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32355,c_32276]) ).
tff(c_35795,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32357,c_35765]) ).
tff(c_35822,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32364,c_35795]) ).
tff(c_35832,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_35822,c_32337]) ).
tff(c_35838,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_35832]) ).
tff(c_32424,plain,
! [X_447,Z_448] : ( multiply(inverse(X_447),multiply(X_447,Z_448)) = Z_448 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32326]) ).
tff(c_32766,plain,
! [X_453,Z_454] : ( multiply(inverse(inverse(X_453)),Z_454) = multiply(X_453,Z_454) ),
inference(superposition,[status(thm),theory(equality)],[c_32424,c_32337]) ).
tff(c_32813,plain,
! [X_453] : ( multiply(X_453,inverse(X_453)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_32766]) ).
tff(c_32454,plain,
multiply(inverse(sk_c4),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32357,c_32424]) ).
tff(c_32481,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32364,c_32454]) ).
tff(c_32491,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32481,c_32337]) ).
tff(c_32497,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32491]) ).
tff(c_32472,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_32424]) ).
tff(c_32776,plain,
! [X_453] : ( multiply(X_453,identity) = X_453 ),
inference(superposition,[status(thm),theory(equality)],[c_32766,c_32472]) ).
tff(c_32376,plain,
! [X3_8,X1_9,X6_7,X4_11] :
( ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(inverse(X4_11),sk_c7) != sk_c7 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32355,c_32355,c_32355,c_32355,c_32355,c_32355,c_32355,c_32355,c_32355,c_58]) ).
tff(c_32377,plain,
! [X4_11] :
( ( multiply(inverse(X4_11),sk_c7) != sk_c7 )
| ( multiply(X4_11,inverse(X4_11)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_32376]) ).
tff(c_35715,plain,
! [X4_11] : ( inverse(X4_11) != identity ),
inference(demodulation,[status(thm),theory(equality)],[c_32813,c_32497,c_32776,c_32497,c_32497,c_32377]) ).
tff(c_32361,plain,
inverse(sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_32355,c_32236]) ).
tff(c_32372,plain,
multiply(sk_c7,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32361,c_4]) ).
tff(c_32501,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32497,c_32372]) ).
tff(c_32608,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_32501,c_32337]) ).
tff(c_32620,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32608]) ).
tff(c_32505,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32497,c_32361]) ).
tff(c_32625,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32620,c_32505]) ).
tff(c_35717,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_35715,c_32625]) ).
tff(c_35718,plain,
! [X6_7,X1_9,X3_8] :
( ( multiply(X6_7,sk_c7) != sk_c7 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c7 )
| ( inverse(X1_9) != sk_c7 )
| ( inverse(X3_8) != sk_c7 )
| ( multiply(sk_c7,multiply(X3_8,sk_c7)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_32376]) ).
tff(c_42816,plain,
! [X6_7,X1_9,X3_8] :
( ( identity != X6_7 )
| ( inverse(X6_7) != identity )
| ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( inverse(X3_8) != identity )
| ( identity != X3_8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_36117,c_35838,c_35838,c_2,c_35838,c_35838,c_35838,c_36117,c_35838,c_35838,c_35838,c_36117,c_35838,c_35838,c_35718]) ).
tff(c_42818,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_42816]) ).
tff(c_35842,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_35838,c_32372]) ).
tff(c_35949,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_35842,c_32337]) ).
tff(c_35961,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_35949]) ).
tff(c_35846,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_35838,c_32361]) ).
tff(c_35966,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_35961,c_35846]) ).
tff(c_42820,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42818,c_35966]) ).
tff(c_42821,plain,
! [X1_9,X6_7] :
( ( identity != X1_9 )
| ( inverse(X1_9) != identity )
| ( identity != X6_7 )
| ( inverse(X6_7) != identity ) ),
inference(splitRight,[status(thm)],[c_42816]) ).
tff(c_42823,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_42821]) ).
tff(c_42825,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42823,c_35966]) ).
tff(c_42828,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_42821]) ).
tff(c_42830,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42828,c_35966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP211-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.14 % 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
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 22:22:09 EDT 2023
% 0.15/0.35 % CPUTime :
% 12.84/4.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.92/4.40
% 12.92/4.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.23/4.46
% 13.23/4.46 Inference rules
% 13.23/4.46 ----------------------
% 13.23/4.46 #Ref : 0
% 13.23/4.46 #Sup : 10611
% 13.23/4.46 #Fact : 0
% 13.23/4.46 #Define : 0
% 13.23/4.46 #Split : 27
% 13.23/4.46 #Chain : 0
% 13.23/4.46 #Close : 0
% 13.23/4.46
% 13.23/4.46 Ordering : KBO
% 13.23/4.46
% 13.23/4.46 Simplification rules
% 13.23/4.46 ----------------------
% 13.23/4.46 #Subsume : 3
% 13.23/4.46 #Demod : 20441
% 13.23/4.46 #Tautology : 8459
% 13.23/4.46 #SimpNegUnit : 56
% 13.23/4.46 #BackRed : 492
% 13.23/4.46
% 13.23/4.46 #Partial instantiations: 0
% 13.23/4.46 #Strategies tried : 1
% 13.23/4.46
% 13.23/4.46 Timing (in seconds)
% 13.23/4.46 ----------------------
% 13.23/4.47 Preprocessing : 0.51
% 13.23/4.47 Parsing : 0.22
% 13.23/4.47 CNF conversion : 0.02
% 13.23/4.47 Main loop : 2.80
% 13.23/4.47 Inferencing : 0.85
% 13.23/4.47 Reduction : 1.35
% 13.23/4.47 Demodulation : 1.18
% 13.23/4.47 BG Simplification : 0.09
% 13.23/4.47 Subsumption : 0.32
% 13.23/4.47 Abstraction : 0.15
% 13.23/4.47 MUC search : 0.00
% 13.23/4.47 Cooper : 0.00
% 13.23/4.47 Total : 3.41
% 13.23/4.47 Index Insertion : 0.00
% 13.23/4.47 Index Deletion : 0.00
% 13.23/4.47 Index Matching : 0.00
% 13.23/4.47 BG Taut test : 0.00
%------------------------------------------------------------------------------