TSTP Solution File: GRP262-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP262-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n011.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 10:40:41 EDT 2023
% Result : Unsatisfiable 15.80s 6.62s
% Output : CNFRefutation 15.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 38
% Syntax : Number of formulae : 577 ( 483 unt; 10 typ; 0 def)
% Number of atoms : 767 ( 739 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 436 ( 236 ~; 200 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 288 (; 288 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [X3,X4,X1,X2] :
( ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c5 )
| ( inverse(X4) != sk_c6 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_30481,plain,
! [X_360,Y_361,Z_362] : ( multiply(multiply(X_360,Y_361),Z_362) = multiply(X_360,multiply(Y_361,Z_362)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_30514,plain,
! [X_2,Z_362] : ( multiply(inverse(X_2),multiply(X_2,Z_362)) = multiply(identity,Z_362) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_30481]) ).
tff(c_31131,plain,
! [X_377,Z_378] : ( multiply(inverse(X_377),multiply(X_377,Z_378)) = Z_378 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30514]) ).
tff(c_30525,plain,
! [X_2,Z_362] : ( multiply(inverse(X_2),multiply(X_2,Z_362)) = Z_362 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30514]) ).
tff(c_32300,plain,
! [X_393,Z_394] : ( multiply(inverse(inverse(X_393)),Z_394) = multiply(X_393,Z_394) ),
inference(superposition,[status(thm),theory(equality)],[c_31131,c_30525]) ).
tff(c_31206,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31131]) ).
tff(c_32307,plain,
! [X_393] : ( multiply(X_393,identity) = X_393 ),
inference(superposition,[status(thm),theory(equality)],[c_32300,c_31206]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_101,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_87,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_91,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_87,c_4]) ).
tff(c_3052,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_3085,plain,
! [Z_78] : ( multiply(sk_c7,multiply(sk_c1,Z_78)) = multiply(identity,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_3052]) ).
tff(c_3120,plain,
! [Z_80] : ( multiply(sk_c7,multiply(sk_c1,Z_80)) = Z_80 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3085]) ).
tff(c_3132,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_101,c_3120]) ).
tff(c_3091,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_3052]) ).
tff(c_3227,plain,
! [X_83,Z_84] : ( multiply(inverse(X_83),multiply(X_83,Z_84)) = Z_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3091]) ).
tff(c_3263,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3132,c_3227]) ).
tff(c_3321,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3263]) ).
tff(c_3143,plain,
! [Z_81] : ( multiply(sk_c1,multiply(sk_c7,Z_81)) = multiply(sk_c6,Z_81) ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_3052]) ).
tff(c_3158,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_3132,c_3143]) ).
tff(c_3171,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_101,c_3158]) ).
tff(c_134,plain,
! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_164,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_134]) ).
tff(c_846,plain,
! [X_31,Z_32] : ( multiply(inverse(X_31),multiply(X_31,Z_32)) = Z_32 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_174,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_1663,plain,
! [X_46,Z_47] : ( multiply(inverse(inverse(X_46)),Z_47) = multiply(X_46,Z_47) ),
inference(superposition,[status(thm),theory(equality)],[c_846,c_174]) ).
tff(c_912,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_846]) ).
tff(c_1670,plain,
! [X_46] : ( multiply(X_46,identity) = X_46 ),
inference(superposition,[status(thm),theory(equality)],[c_1663,c_912]) ).
tff(c_158,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_134]) ).
tff(c_524,plain,
! [Z_23] : ( multiply(sk_c7,multiply(sk_c1,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_536,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_101,c_524]) ).
tff(c_876,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_536,c_846]) ).
tff(c_921,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_876]) ).
tff(c_30,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_119,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_40,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_75,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_79,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).
tff(c_161,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_134]) ).
tff(c_580,plain,
! [Z_25] : ( multiply(sk_c6,multiply(sk_c2,Z_25)) = Z_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_592,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_119,c_580]) ).
tff(c_867,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_592,c_846]) ).
tff(c_919,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_867]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_110,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_152,plain,
! [Z_14] : ( multiply(sk_c5,multiply(sk_c7,Z_14)) = multiply(sk_c6,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_110,c_134]) ).
tff(c_1100,plain,
! [Z_14] : ( multiply(sk_c7,Z_14) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_921,c_2,c_919,c_152]) ).
tff(c_974,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_921,c_536]) ).
tff(c_1101,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1100,c_974]) ).
tff(c_1192,plain,
! [X_36,Z_37] : ( multiply(inverse(inverse(X_36)),Z_37) = multiply(X_36,Z_37) ),
inference(superposition,[status(thm),theory(equality)],[c_846,c_174]) ).
tff(c_1199,plain,
! [X_36] : ( multiply(X_36,identity) = X_36 ),
inference(superposition,[status(thm),theory(equality)],[c_1192,c_912]) ).
tff(c_631,plain,
! [X_27,Z_28] : ( multiply(inverse(X_27),multiply(X_27,Z_28)) = Z_28 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_661,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_536,c_631]) ).
tff(c_706,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_661]) ).
tff(c_179,plain,
! [Z_15] : ( multiply(sk_c6,multiply(sk_c2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_191,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_119,c_179]) ).
tff(c_263,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_296,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_191,c_263]) ).
tff(c_335,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_296]) ).
tff(c_218,plain,
! [Z_17] : ( multiply(sk_c7,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_233,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_101,c_218]) ).
tff(c_287,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_233,c_263]) ).
tff(c_334,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_287]) ).
tff(c_58,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_177,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_58]) ).
tff(c_178,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitLeft,[status(thm)],[c_177]) ).
tff(c_384,plain,
multiply(identity,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_334,c_178]) ).
tff(c_394,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_384]) ).
tff(c_403,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_335,c_394]) ).
tff(c_386,plain,
multiply(sk_c5,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_334,c_110]) ).
tff(c_513,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_335,c_386]) ).
tff(c_514,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_403,c_513]) ).
tff(c_515,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_612,plain,
! [X2_26] :
( ( multiply(X2_26,sk_c5) != sk_c6 )
| ( inverse(X2_26) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_515]) ).
tff(c_627,plain,
( ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_612]) ).
tff(c_629,plain,
inverse(identity) != sk_c6,
inference(splitLeft,[status(thm)],[c_627]) ).
tff(c_722,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_706,c_629]) ).
tff(c_731,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_706,c_75]) ).
tff(c_763,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_731,c_4]) ).
tff(c_771,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_763,c_174]) ).
tff(c_783,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_771]) ).
tff(c_787,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_783,c_731]) ).
tff(c_791,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_722,c_787]) ).
tff(c_792,plain,
sk_c6 != sk_c5,
inference(splitRight,[status(thm)],[c_627]) ).
tff(c_793,plain,
inverse(identity) = sk_c6,
inference(splitRight,[status(thm)],[c_627]) ).
tff(c_797,plain,
multiply(sk_c6,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_793,c_4]) ).
tff(c_6,plain,
! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_804,plain,
! [Z_5] : ( multiply(sk_c6,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_797,c_6]) ).
tff(c_807,plain,
! [Z_5] : ( multiply(sk_c6,Z_5) = Z_5 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_804]) ).
tff(c_811,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_807,c_592]) ).
tff(c_815,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_792,c_811]) ).
tff(c_816,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_515]) ).
tff(c_818,plain,
! [X3_30] :
( ( inverse(X3_30) != sk_c7 )
| ( multiply(X3_30,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_816]) ).
tff(c_831,plain,
inverse(sk_c1) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_101,c_818]) ).
tff(c_844,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_87,c_831]) ).
tff(c_845,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_816]) ).
tff(c_1025,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_921,c_921,c_919,c_921,c_845]) ).
tff(c_1026,plain,
! [X1_8] :
( ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_1025]) ).
tff(c_1455,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_1101,c_1199,c_1101,c_1026]) ).
tff(c_978,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_921,c_75]) ).
tff(c_993,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_978,c_4]) ).
tff(c_1059,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_993,c_174]) ).
tff(c_1071,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1059]) ).
tff(c_1076,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1071,c_978]) ).
tff(c_1457,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1455,c_1076]) ).
tff(c_1458,plain,
! [X4_7] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_1025]) ).
tff(c_1929,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_1670,c_1458]) ).
tff(c_915,plain,
! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_846]) ).
tff(c_1510,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_993,c_174]) ).
tff(c_1522,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_915,c_1510]) ).
tff(c_1527,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1522,c_978]) ).
tff(c_1931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1929,c_1527]) ).
tff(c_1933,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_36,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_1981,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_1933,c_36]) ).
tff(c_34,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_1941,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_1947,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1941,c_1933]) ).
tff(c_1948,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_1953,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_1948,c_4]) ).
tff(c_1986,plain,
! [X_53,Y_54,Z_55] : ( multiply(multiply(X_53,Y_54),Z_55) = multiply(X_53,multiply(Y_54,Z_55)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2010,plain,
! [Z_55] : ( multiply(sk_c6,multiply(sk_c4,Z_55)) = multiply(identity,Z_55) ),
inference(superposition,[status(thm),theory(equality)],[c_1953,c_1986]) ).
tff(c_2172,plain,
! [Z_62] : ( multiply(sk_c6,multiply(sk_c4,Z_62)) = Z_62 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2010]) ).
tff(c_2184,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_1981,c_2172]) ).
tff(c_2022,plain,
! [Z_55] : ( multiply(sk_c7,multiply(sk_c1,Z_55)) = multiply(identity,Z_55) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_1986]) ).
tff(c_2042,plain,
! [Z_56] : ( multiply(sk_c7,multiply(sk_c1,Z_56)) = Z_56 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2022]) ).
tff(c_2054,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_101,c_2042]) ).
tff(c_2195,plain,
! [Z_63] : ( multiply(sk_c1,multiply(sk_c7,Z_63)) = multiply(sk_c6,Z_63) ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_1986]) ).
tff(c_2210,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_2054,c_2195]) ).
tff(c_2223,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2184,c_101,c_2210]) ).
tff(c_2225,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2223,c_2223,c_2184]) ).
tff(c_2028,plain,
! [X_2,Z_55] : ( multiply(inverse(X_2),multiply(X_2,Z_55)) = multiply(identity,Z_55) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1986]) ).
tff(c_2323,plain,
! [X_64,Z_65] : ( multiply(inverse(X_64),multiply(X_64,Z_65)) = Z_65 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2028]) ).
tff(c_2353,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_2225,c_2323]) ).
tff(c_2398,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2353]) ).
tff(c_2238,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2223,c_75]) ).
tff(c_2253,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2238,c_4]) ).
tff(c_2430,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2398,c_2253]) ).
tff(c_2233,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2223,c_1933]) ).
tff(c_2403,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2398,c_2398,c_2233]) ).
tff(c_2485,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2430,c_2403]) ).
tff(c_2486,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_2487,plain,
multiply(sk_c5,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_56,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_3041,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2487,c_56]) ).
tff(c_3275,plain,
multiply(inverse(sk_c4),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3041,c_3227]) ).
tff(c_3322,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3171,c_2486,c_3275]) ).
tff(c_3352,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3321,c_3322]) ).
tff(c_3340,plain,
multiply(sk_c5,sk_c7) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3321,c_2487]) ).
tff(c_3516,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3352,c_3340]) ).
tff(c_48,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_3034,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_2487,c_48]) ).
tff(c_3070,plain,
! [Z_78] : ( multiply(sk_c6,multiply(sk_c7,Z_78)) = multiply(sk_c5,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_3034,c_3052]) ).
tff(c_3546,plain,
! [Z_78] : ( multiply(sk_c7,Z_78) = Z_78 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3352,c_2,c_3321,c_3070]) ).
tff(c_3333,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_3321,c_3132]) ).
tff(c_3547,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3546,c_3333]) ).
tff(c_3549,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3516,c_3547]) ).
tff(c_3551,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_3601,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3551,c_8]) ).
tff(c_50,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_3566,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_32,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_3589,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_3614,plain,
! [X_87,Y_88,Z_89] : ( multiply(multiply(X_87,Y_88),Z_89) = multiply(X_87,multiply(Y_88,Z_89)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4694,plain,
! [Z_107] : ( multiply(sk_c2,multiply(sk_c6,Z_107)) = multiply(sk_c5,Z_107) ),
inference(superposition,[status(thm),theory(equality)],[c_3589,c_3614]) ).
tff(c_4712,plain,
multiply(sk_c5,sk_c7) = multiply(sk_c2,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_3601,c_4694]) ).
tff(c_4722,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3566,c_4712]) ).
tff(c_3653,plain,
! [Z_89] : ( multiply(sk_c6,multiply(sk_c2,Z_89)) = multiply(identity,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_3614]) ).
tff(c_3667,plain,
! [Z_89] : ( multiply(sk_c6,multiply(sk_c2,Z_89)) = Z_89 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3653]) ).
tff(c_4726,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4722,c_3667]) ).
tff(c_3638,plain,
! [Z_89] : ( multiply(sk_c2,multiply(sk_c6,Z_89)) = multiply(sk_c5,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_3589,c_3614]) ).
tff(c_4747,plain,
multiply(sk_c5,sk_c6) = multiply(sk_c2,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_4726,c_3638]) ).
tff(c_4753,plain,
multiply(sk_c5,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4722,c_4747]) ).
tff(c_12,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_3595,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_3551,c_12]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_3575,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_3551,c_10]) ).
tff(c_3579,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3575,c_4]) ).
tff(c_3641,plain,
! [Z_89] : ( multiply(sk_c7,multiply(sk_c3,Z_89)) = multiply(identity,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_3579,c_3614]) ).
tff(c_4975,plain,
! [Z_114] : ( multiply(sk_c7,multiply(sk_c3,Z_114)) = Z_114 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3641]) ).
tff(c_4990,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3595,c_4975]) ).
tff(c_3644,plain,
! [Z_89] : ( multiply(sk_c5,multiply(sk_c7,Z_89)) = multiply(sk_c6,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_3566,c_3614]) ).
tff(c_4997,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_4990,c_3644]) ).
tff(c_5003,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3601,c_4753,c_4997]) ).
tff(c_5016,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5003,c_3601]) ).
tff(c_3656,plain,
! [X_2,Z_89] : ( multiply(inverse(X_2),multiply(X_2,Z_89)) = multiply(identity,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3614]) ).
tff(c_5093,plain,
! [X_115,Z_116] : ( multiply(inverse(X_115),multiply(X_115,Z_116)) = Z_116 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3656]) ).
tff(c_5114,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5016,c_5093]) ).
tff(c_5166,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5114]) ).
tff(c_5191,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5166,c_91]) ).
tff(c_3668,plain,
! [X_2,Z_89] : ( multiply(inverse(X_2),multiply(X_2,Z_89)) = Z_89 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3656]) ).
tff(c_5368,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_5191,c_3668]) ).
tff(c_5380,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5368]) ).
tff(c_3683,plain,
! [Z_91] : ( multiply(sk_c6,multiply(sk_c2,Z_91)) = Z_91 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3653]) ).
tff(c_3695,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3589,c_3683]) ).
tff(c_4736,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_3695,c_3638]) ).
tff(c_4742,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3589,c_4736]) ).
tff(c_5138,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4742,c_5093]) ).
tff(c_5169,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5138]) ).
tff(c_5021,plain,
multiply(sk_c1,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5003,c_3551]) ).
tff(c_5281,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_5166,c_5169,c_5021]) ).
tff(c_5384,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_5380,c_5281]) ).
tff(c_5389,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5384]) ).
tff(c_5391,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_5407,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_5391,c_36]) ).
tff(c_3550,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_3555,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3550,c_4]) ).
tff(c_5415,plain,
! [X_119,Y_120,Z_121] : ( multiply(multiply(X_119,Y_120),Z_121) = multiply(X_119,multiply(Y_120,Z_121)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_5445,plain,
! [Z_121] : ( multiply(sk_c6,multiply(sk_c4,Z_121)) = multiply(identity,Z_121) ),
inference(superposition,[status(thm),theory(equality)],[c_3555,c_5415]) ).
tff(c_5908,plain,
! [Z_134] : ( multiply(sk_c6,multiply(sk_c4,Z_134)) = Z_134 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5445]) ).
tff(c_5920,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_5407,c_5908]) ).
tff(c_28,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_5397,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_5391,c_28]) ).
tff(c_5390,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_5439,plain,
! [Z_121] : ( multiply(sk_c7,multiply(sk_c3,Z_121)) = multiply(identity,Z_121) ),
inference(superposition,[status(thm),theory(equality)],[c_3579,c_5415]) ).
tff(c_5863,plain,
! [Z_133] : ( multiply(sk_c7,multiply(sk_c3,Z_133)) = Z_133 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5439]) ).
tff(c_5878,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_5390,c_5863]) ).
tff(c_5442,plain,
! [Z_121] : ( multiply(sk_c5,multiply(sk_c7,Z_121)) = multiply(sk_c6,Z_121) ),
inference(superposition,[status(thm),theory(equality)],[c_3566,c_5415]) ).
tff(c_5885,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_5878,c_5442]) ).
tff(c_5891,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5397,c_5885]) ).
tff(c_5961,plain,
! [Z_136] : ( multiply(sk_c4,multiply(sk_c5,Z_136)) = multiply(sk_c6,Z_136) ),
inference(superposition,[status(thm),theory(equality)],[c_5407,c_5415]) ).
tff(c_5976,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_5891,c_5961]) ).
tff(c_5986,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_5407,c_5976]) ).
tff(c_6012,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5920,c_5986]) ).
tff(c_6014,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6012,c_6012,c_5920]) ).
tff(c_5454,plain,
! [X_2,Z_121] : ( multiply(inverse(X_2),multiply(X_2,Z_121)) = multiply(identity,Z_121) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5415]) ).
tff(c_6102,plain,
! [X_137,Z_138] : ( multiply(inverse(X_137),multiply(X_137,Z_138)) = Z_138 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5454]) ).
tff(c_6135,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_6014,c_6102]) ).
tff(c_6175,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6135]) ).
tff(c_6032,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6012,c_75]) ).
tff(c_6194,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_6175,c_6032]) ).
tff(c_6240,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_6194,c_4]) ).
tff(c_5466,plain,
! [X_2,Z_121] : ( multiply(inverse(X_2),multiply(X_2,Z_121)) = Z_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5454]) ).
tff(c_6262,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_6240,c_5466]) ).
tff(c_6274,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6262]) ).
tff(c_6025,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6012,c_5391]) ).
tff(c_6288,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6274,c_6175,c_6175,c_6025]) ).
tff(c_6290,plain,
multiply(sk_c5,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_6835,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_6290,c_56]) ).
tff(c_6844,plain,
! [X_151,Y_152,Z_153] : ( multiply(multiply(X_151,Y_152),Z_153) = multiply(X_151,multiply(Y_152,Z_153)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_6871,plain,
! [Z_153] : ( multiply(sk_c6,multiply(sk_c4,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_3555,c_6844]) ).
tff(c_6943,plain,
! [Z_157] : ( multiply(sk_c6,multiply(sk_c4,Z_157)) = Z_157 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6871]) ).
tff(c_6955,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_6835,c_6943]) ).
tff(c_6310,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_6338,plain,
! [X_139,Y_140,Z_141] : ( multiply(multiply(X_139,Y_140),Z_141) = multiply(X_139,multiply(Y_140,Z_141)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_6374,plain,
! [Z_141] : ( multiply(sk_c6,multiply(sk_c2,Z_141)) = multiply(identity,Z_141) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_6338]) ).
tff(c_6393,plain,
! [Z_142] : ( multiply(sk_c6,multiply(sk_c2,Z_142)) = Z_142 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6374]) ).
tff(c_6405,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_6310,c_6393]) ).
tff(c_6377,plain,
! [X_2,Z_141] : ( multiply(inverse(X_2),multiply(X_2,Z_141)) = multiply(identity,Z_141) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_6338]) ).
tff(c_6520,plain,
! [X_147,Z_148] : ( multiply(inverse(X_147),multiply(X_147,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6377]) ).
tff(c_6559,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_6405,c_6520]) ).
tff(c_6613,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6559]) ).
tff(c_6628,plain,
multiply(identity,sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_6613,c_6290]) ).
tff(c_6631,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6628]) ).
tff(c_6624,plain,
multiply(sk_c6,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_6613,c_6405]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_6331,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_3551,c_16]) ).
tff(c_6353,plain,
! [Z_141] : ( multiply(sk_c4,multiply(sk_c5,Z_141)) = multiply(sk_c6,Z_141) ),
inference(superposition,[status(thm),theory(equality)],[c_6331,c_6338]) ).
tff(c_6739,plain,
! [Z_150] : ( multiply(sk_c6,Z_150) = multiply(sk_c4,Z_150) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6613,c_6353]) ).
tff(c_6320,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_6290,c_48]) ).
tff(c_6626,plain,
multiply(sk_c6,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_6613,c_6320]) ).
tff(c_6745,plain,
multiply(sk_c4,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_6739,c_6626]) ).
tff(c_6389,plain,
! [X_2,Z_141] : ( multiply(inverse(X_2),multiply(X_2,Z_141)) = Z_141 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6377]) ).
tff(c_6804,plain,
multiply(inverse(sk_c4),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_6745,c_6389]) ).
tff(c_6813,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_6624,c_3550,c_6804]) ).
tff(c_6815,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6631,c_6813]) ).
tff(c_6816,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_6289,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_6294,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_6289,c_4]) ).
tff(c_6868,plain,
! [Z_153] : ( multiply(sk_c7,multiply(sk_c3,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_6294,c_6844]) ).
tff(c_6920,plain,
! [Z_156] : ( multiply(sk_c7,multiply(sk_c3,Z_156)) = Z_156 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6868]) ).
tff(c_6932,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_6816,c_6920]) ).
tff(c_6818,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_6290,c_48]) ).
tff(c_7286,plain,
! [Z_164] : ( multiply(sk_c6,multiply(sk_c7,Z_164)) = multiply(sk_c5,Z_164) ),
inference(superposition,[status(thm),theory(equality)],[c_6818,c_6844]) ).
tff(c_7307,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_6932,c_7286]) ).
tff(c_7317,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6955,c_7307]) ).
tff(c_7318,plain,
sk_c6 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7317,c_6290]) ).
tff(c_6880,plain,
! [X_2,Z_153] : ( multiply(inverse(X_2),multiply(X_2,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_6844]) ).
tff(c_6968,plain,
! [X_158,Z_159] : ( multiply(inverse(X_158),multiply(X_158,Z_159)) = Z_159 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6880]) ).
tff(c_7034,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_79,c_6968]) ).
tff(c_7022,plain,
multiply(inverse(sk_c6),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_3555,c_6968]) ).
tff(c_7139,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_7034,c_7022]) ).
tff(c_7141,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_7139,c_6835]) ).
tff(c_6859,plain,
! [Z_153] : ( multiply(sk_c4,multiply(sk_c5,Z_153)) = multiply(sk_c6,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_6835,c_6844]) ).
tff(c_7176,plain,
! [Z_153] : ( multiply(sk_c2,multiply(sk_c5,Z_153)) = multiply(sk_c6,Z_153) ),
inference(demodulation,[status(thm),theory(equality)],[c_7139,c_6859]) ).
tff(c_7322,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c2,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_7317,c_7176]) ).
tff(c_7331,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7141,c_6818,c_7322]) ).
tff(c_7334,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7318,c_7331]) ).
tff(c_7336,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_7368,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_7336,c_18]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_7376,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_7336,c_22]) ).
tff(c_7335,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_7341,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7335,c_4]) ).
tff(c_7394,plain,
! [X_165,Y_166,Z_167] : ( multiply(multiply(X_165,Y_166),Z_167) = multiply(X_165,multiply(Y_166,Z_167)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_7421,plain,
! [Z_167] : ( multiply(sk_c7,multiply(sk_c3,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_7341,c_7394]) ).
tff(c_7921,plain,
! [Z_177] : ( multiply(sk_c7,multiply(sk_c3,Z_177)) = Z_177 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7421]) ).
tff(c_7933,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7376,c_7921]) ).
tff(c_26,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_7363,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_7336,c_26]) ).
tff(c_24,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_7349,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_7336,c_24]) ).
tff(c_7353,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7349,c_4]) ).
tff(c_7418,plain,
! [Z_167] : ( multiply(sk_c6,multiply(sk_c4,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_7353,c_7394]) ).
tff(c_7440,plain,
! [Z_168] : ( multiply(sk_c6,multiply(sk_c4,Z_168)) = Z_168 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7418]) ).
tff(c_7452,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_7363,c_7440]) ).
tff(c_7427,plain,
! [X_2,Z_167] : ( multiply(inverse(X_2),multiply(X_2,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_7394]) ).
tff(c_7502,plain,
! [X_171,Z_172] : ( multiply(inverse(X_171),multiply(X_171,Z_172)) = Z_172 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7427]) ).
tff(c_7529,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7452,c_7502]) ).
tff(c_7541,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_7368,c_7502]) ).
tff(c_7779,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_7529,c_7541]) ).
tff(c_7466,plain,
! [Z_169] : ( multiply(sk_c7,multiply(sk_c3,Z_169)) = Z_169 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7421]) ).
tff(c_7478,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7376,c_7466]) ).
tff(c_7523,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_7478,c_7502]) ).
tff(c_7814,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_7779,c_7779,c_7523]) ).
tff(c_7826,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7814]) ).
tff(c_7818,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_7779,c_7779,c_7478]) ).
tff(c_7829,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7452,c_7818]) ).
tff(c_7856,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_7826,c_7829]) ).
tff(c_7464,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_7368,c_58]) ).
tff(c_7465,plain,
multiply(sk_c5,sk_c7) != sk_c6,
inference(splitLeft,[status(thm)],[c_7464]) ).
tff(c_7820,plain,
multiply(sk_c5,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_7779,c_7465]) ).
tff(c_7911,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7856,c_7826,c_7826,c_7820]) ).
tff(c_7913,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_7464]) ).
tff(c_7992,plain,
! [Z_181] : ( multiply(sk_c5,multiply(sk_c7,Z_181)) = multiply(sk_c6,Z_181) ),
inference(superposition,[status(thm),theory(equality)],[c_7913,c_6]) ).
tff(c_8004,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_7933,c_7992]) ).
tff(c_8014,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7368,c_8004]) ).
tff(c_8030,plain,
! [X_182,Z_183] : ( multiply(inverse(X_182),multiply(X_182,Z_183)) = Z_183 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7427]) ).
tff(c_8051,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8014,c_8030]) ).
tff(c_8112,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8051]) ).
tff(c_8129,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_7353]) ).
tff(c_8713,plain,
sk_c4 = identity,
inference(superposition,[status(thm),theory(equality)],[c_8129,c_2]) ).
tff(c_8130,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_7349]) ).
tff(c_8724,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8713,c_8130]) ).
tff(c_8124,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_8112,c_7452]) ).
tff(c_8135,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8124]) ).
tff(c_8010,plain,
multiply(sk_c6,sk_c3) = multiply(sk_c5,identity),
inference(superposition,[status(thm),theory(equality)],[c_7341,c_7992]) ).
tff(c_8118,plain,
multiply(sk_c5,identity) = multiply(identity,sk_c3),
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_8010]) ).
tff(c_8133,plain,
multiply(sk_c5,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8118]) ).
tff(c_8808,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8135,c_8133]) ).
tff(c_8812,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8808,c_7335]) ).
tff(c_8815,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8724,c_8812]) ).
tff(c_7438,plain,
! [X_2,Z_167] : ( multiply(inverse(X_2),multiply(X_2,Z_167)) = Z_167 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7427]) ).
tff(c_8870,plain,
! [X_197,Z_198] : ( multiply(inverse(inverse(X_197)),Z_198) = multiply(X_197,Z_198) ),
inference(superposition,[status(thm),theory(equality)],[c_7438,c_8030]) ).
tff(c_8105,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8030]) ).
tff(c_8877,plain,
! [X_197] : ( multiply(X_197,identity) = X_197 ),
inference(superposition,[status(thm),theory(equality)],[c_8870,c_8105]) ).
tff(c_8379,plain,
! [X_187,Z_188] : ( multiply(inverse(inverse(X_187)),Z_188) = multiply(X_187,Z_188) ),
inference(superposition,[status(thm),theory(equality)],[c_8030,c_7438]) ).
tff(c_8386,plain,
! [X_187] : ( multiply(X_187,identity) = X_187 ),
inference(superposition,[status(thm),theory(equality)],[c_8379,c_8105]) ).
tff(c_7412,plain,
! [Z_167] : ( multiply(sk_c6,multiply(sk_c7,Z_167)) = multiply(sk_c5,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_7368,c_7394]) ).
tff(c_8218,plain,
! [Z_184] : ( multiply(sk_c7,Z_184) = Z_184 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8135,c_2,c_8112,c_7412]) ).
tff(c_8122,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_7933]) ).
tff(c_8224,plain,
sk_c7 = identity,
inference(superposition,[status(thm),theory(equality)],[c_8218,c_8122]) ).
tff(c_7912,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_7464]) ).
tff(c_7958,plain,
! [X2_179] :
( ( multiply(X2_179,sk_c5) != sk_c6 )
| ( inverse(X2_179) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_7912]) ).
tff(c_7965,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7363,c_7958]) ).
tff(c_7977,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7349,c_7965]) ).
tff(c_7978,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_7912]) ).
tff(c_8144,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_8135,c_8112,c_8112,c_8112,c_7978]) ).
tff(c_8145,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != identity ) ),
inference(splitLeft,[status(thm)],[c_8144]) ).
tff(c_8650,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_8386,c_8224,c_8224,c_8145]) ).
tff(c_8131,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_79]) ).
tff(c_8175,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_8131,c_2]) ).
tff(c_8132,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8112,c_75]) ).
tff(c_8185,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8175,c_8132]) ).
tff(c_8652,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8650,c_8185]) ).
tff(c_8653,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_8144]) ).
tff(c_30400,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8815,c_8877,c_8815,c_8877,c_8653]) ).
tff(c_30402,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_30400]) ).
tff(c_30404,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30402,c_8724]) ).
tff(c_30407,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_30400]) ).
tff(c_30409,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30407,c_8724]) ).
tff(c_30411,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_38,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_30449,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_30411,c_38]) ).
tff(c_46,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_30464,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_30411,c_46]) ).
tff(c_44,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_30436,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_30411,c_44]) ).
tff(c_30440,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_30436,c_4]) ).
tff(c_30505,plain,
! [Z_362] : ( multiply(sk_c6,multiply(sk_c4,Z_362)) = multiply(identity,Z_362) ),
inference(superposition,[status(thm),theory(equality)],[c_30440,c_30481]) ).
tff(c_30527,plain,
! [Z_363] : ( multiply(sk_c6,multiply(sk_c4,Z_363)) = Z_363 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30505]) ).
tff(c_30539,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_30464,c_30527]) ).
tff(c_30589,plain,
! [X_366,Z_367] : ( multiply(inverse(X_366),multiply(X_366,Z_367)) = Z_367 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30514]) ).
tff(c_30616,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_30539,c_30589]) ).
tff(c_30631,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_30449,c_30589]) ).
tff(c_30887,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30616,c_30631]) ).
tff(c_42,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_30459,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_30411,c_42]) ).
tff(c_30410,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_30415,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_30410,c_4]) ).
tff(c_30511,plain,
! [Z_362] : ( multiply(sk_c7,multiply(sk_c3,Z_362)) = multiply(identity,Z_362) ),
inference(superposition,[status(thm),theory(equality)],[c_30415,c_30481]) ).
tff(c_30553,plain,
! [Z_364] : ( multiply(sk_c7,multiply(sk_c3,Z_364)) = Z_364 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30511]) ).
tff(c_30565,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_30459,c_30553]) ).
tff(c_30610,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_30565,c_30589]) ).
tff(c_30898,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30887,c_30887,c_30610]) ).
tff(c_30909,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30898]) ).
tff(c_30904,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30887,c_30887,c_30565]) ).
tff(c_30911,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_30539,c_30904]) ).
tff(c_30952,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_30909,c_30911]) ).
tff(c_30544,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_30449,c_58]) ).
tff(c_30545,plain,
multiply(sk_c5,sk_c7) != sk_c6,
inference(splitLeft,[status(thm)],[c_30544]) ).
tff(c_30905,plain,
multiply(sk_c5,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_30887,c_30545]) ).
tff(c_31041,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30952,c_30909,c_30909,c_30905]) ).
tff(c_31043,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_30544]) ).
tff(c_31081,plain,
! [Z_375] : ( multiply(sk_c4,multiply(sk_c5,Z_375)) = multiply(sk_c6,Z_375) ),
inference(superposition,[status(thm),theory(equality)],[c_30464,c_30481]) ).
tff(c_31096,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_31043,c_31081]) ).
tff(c_31100,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_30449,c_31096]) ).
tff(c_30522,plain,
! [Z_362] : ( multiply(sk_c6,multiply(sk_c4,Z_362)) = Z_362 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30505]) ).
tff(c_31104,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31100,c_30522]) ).
tff(c_31152,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_31104,c_31131]) ).
tff(c_31213,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_31152]) ).
tff(c_31225,plain,
multiply(identity,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31213,c_31043]) ).
tff(c_31981,plain,
sk_c7 = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31225,c_2]) ).
tff(c_31227,plain,
multiply(sk_c6,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31213,c_30449]) ).
tff(c_32050,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31981,c_31227]) ).
tff(c_31058,plain,
! [Z_374] : ( multiply(sk_c7,multiply(sk_c3,Z_374)) = Z_374 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_30511]) ).
tff(c_31070,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_30459,c_31058]) ).
tff(c_31990,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31981,c_31981,c_31070]) ).
tff(c_32119,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32050,c_31990]) ).
tff(c_32127,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32119,c_31981]) ).
tff(c_31224,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31213,c_30539]) ).
tff(c_31256,plain,
sk_c7 = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31225,c_2]) ).
tff(c_31271,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31256,c_30410]) ).
tff(c_31267,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31256,c_30459]) ).
tff(c_31395,plain,
multiply(inverse(sk_c3),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31267,c_30525]) ).
tff(c_31401,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31224,c_31271,c_31395]) ).
tff(c_31572,plain,
! [X_381,Z_382] : ( multiply(inverse(inverse(X_381)),Z_382) = multiply(X_381,Z_382) ),
inference(superposition,[status(thm),theory(equality)],[c_30525,c_31131]) ).
tff(c_31579,plain,
! [X_381] : ( multiply(X_381,identity) = X_381 ),
inference(superposition,[status(thm),theory(equality)],[c_31572,c_31206]) ).
tff(c_31042,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_30544]) ).
tff(c_31233,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != identity )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_31213,c_31213,c_31042]) ).
tff(c_31234,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_31233]) ).
tff(c_31956,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_31401,c_31579,c_31401,c_31234]) ).
tff(c_30424,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_31269,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31256,c_30424]) ).
tff(c_31294,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31269,c_4]) ).
tff(c_31461,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31401,c_31294]) ).
tff(c_31410,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31401,c_31269]) ).
tff(c_31462,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31461,c_31410]) ).
tff(c_31958,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31956,c_31462]) ).
tff(c_31959,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != identity )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_31233]) ).
tff(c_52869,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32307,c_32127,c_32119,c_32127,c_32307,c_32119,c_32119,c_32127,c_32307,c_32127,c_32119,c_31959]) ).
tff(c_52871,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_52869]) ).
tff(c_31996,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31981,c_30410]) ).
tff(c_32126,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32119,c_31996]) ).
tff(c_32150,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32126,c_4]) ).
tff(c_32157,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_32150,c_30525]) ).
tff(c_32169,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_32157]) ).
tff(c_32173,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_32169,c_32126]) ).
tff(c_52873,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52871,c_32173]) ).
tff(c_52874,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_52869]) ).
tff(c_52876,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_52874]) ).
tff(c_52878,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52876,c_32173]) ).
tff(c_52881,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_52874]) ).
tff(c_52883,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52881,c_32173]) ).
tff(c_52885,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_52913,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_52885,c_26]) ).
tff(c_52884,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_52889,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_52884,c_4]) ).
tff(c_52935,plain,
! [X_551,Y_552,Z_553] : ( multiply(multiply(X_551,Y_552),Z_553) = multiply(X_551,multiply(Y_552,Z_553)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_52959,plain,
! [Z_553] : ( multiply(sk_c6,multiply(sk_c4,Z_553)) = multiply(identity,Z_553) ),
inference(superposition,[status(thm),theory(equality)],[c_52889,c_52935]) ).
tff(c_52977,plain,
! [Z_554] : ( multiply(sk_c6,multiply(sk_c4,Z_554)) = Z_554 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52959]) ).
tff(c_52989,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_52913,c_52977]) ).
tff(c_52906,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_30411,c_42]) ).
tff(c_52962,plain,
! [Z_553] : ( multiply(sk_c7,multiply(sk_c3,Z_553)) = multiply(identity,Z_553) ),
inference(superposition,[status(thm),theory(equality)],[c_30415,c_52935]) ).
tff(c_53003,plain,
! [Z_555] : ( multiply(sk_c7,multiply(sk_c3,Z_555)) = Z_555 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52962]) ).
tff(c_53015,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_52906,c_53003]) ).
tff(c_52899,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_30411,c_38]) ).
tff(c_53101,plain,
! [Z_558] : ( multiply(sk_c6,multiply(sk_c7,Z_558)) = multiply(sk_c5,Z_558) ),
inference(superposition,[status(thm),theory(equality)],[c_52899,c_52935]) ).
tff(c_53116,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_53015,c_53101]) ).
tff(c_53126,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_52989,c_53116]) ).
tff(c_52965,plain,
! [X_2,Z_553] : ( multiply(inverse(X_2),multiply(X_2,Z_553)) = multiply(identity,Z_553) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_52935]) ).
tff(c_52975,plain,
! [X_2,Z_553] : ( multiply(inverse(X_2),multiply(X_2,Z_553)) = Z_553 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52965]) ).
tff(c_53131,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_53126,c_52975]) ).
tff(c_53137,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_53131]) ).
tff(c_53142,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_53137,c_53137,c_53015]) ).
tff(c_53150,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_53142]) ).
tff(c_53192,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_53150,c_53150,c_52989]) ).
tff(c_53198,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_53192]) ).
tff(c_53001,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_52899,c_58]) ).
tff(c_53002,plain,
multiply(sk_c5,sk_c7) != sk_c6,
inference(splitLeft,[status(thm)],[c_53001]) ).
tff(c_53127,plain,
sk_c6 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_53126,c_53002]) ).
tff(c_53191,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_53150,c_53127]) ).
tff(c_53208,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53198,c_53191]) ).
tff(c_53210,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_53001]) ).
tff(c_53218,plain,
! [Z_560] : ( multiply(sk_c7,multiply(sk_c3,Z_560)) = Z_560 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52962]) ).
tff(c_53230,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_52906,c_53218]) ).
tff(c_53270,plain,
! [Z_562] : ( multiply(sk_c6,multiply(sk_c7,Z_562)) = multiply(sk_c5,Z_562) ),
inference(superposition,[status(thm),theory(equality)],[c_52899,c_52935]) ).
tff(c_53282,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_53230,c_53270]) ).
tff(c_53292,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_52989,c_53210,c_53282]) ).
tff(c_53300,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_53292,c_52899]) ).
tff(c_53695,plain,
! [X_570,Z_571] : ( multiply(inverse(X_570),multiply(X_570,Z_571)) = Z_571 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52965]) ).
tff(c_53719,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_53300,c_53695]) ).
tff(c_53749,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_53719]) ).
tff(c_53916,plain,
! [X_574,Z_575] : ( multiply(inverse(inverse(X_574)),Z_575) = multiply(X_574,Z_575) ),
inference(superposition,[status(thm),theory(equality)],[c_52975,c_53695]) ).
tff(c_53740,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_53695]) ).
tff(c_53927,plain,
! [X_574] : ( multiply(X_574,identity) = X_574 ),
inference(superposition,[status(thm),theory(equality)],[c_53916,c_53740]) ).
tff(c_53296,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_53292,c_53292,c_52989]) ).
tff(c_53713,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_53296,c_53695]) ).
tff(c_53747,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_53713]) ).
tff(c_53392,plain,
! [X_564,Z_565] : ( multiply(inverse(X_564),multiply(X_564,Z_565)) = Z_565 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_52965]) ).
tff(c_53428,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_53300,c_53392]) ).
tff(c_53459,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_53428]) ).
tff(c_53288,plain,
multiply(sk_c6,identity) = multiply(sk_c5,sk_c3),
inference(superposition,[status(thm),theory(equality)],[c_30415,c_53270]) ).
tff(c_53366,plain,
multiply(sk_c5,sk_c3) = multiply(sk_c5,identity),
inference(demodulation,[status(thm),theory(equality)],[c_53292,c_53288]) ).
tff(c_53413,plain,
multiply(inverse(sk_c5),multiply(sk_c5,identity)) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_53366,c_53392]) ).
tff(c_53456,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_52975,c_53413]) ).
tff(c_53467,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_53456,c_30410]) ).
tff(c_53534,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_53459,c_53467]) ).
tff(c_53596,plain,
! [X_567] : ( multiply(inverse(inverse(X_567)),identity) = X_567 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_53392]) ).
tff(c_53602,plain,
! [X_567] : ( multiply(inverse(inverse(inverse(X_567))),X_567) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_53596,c_52975]) ).
tff(c_53422,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_53296,c_53392]) ).
tff(c_53457,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_53422]) ).
tff(c_53209,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_53001]) ).
tff(c_53242,plain,
! [X2_561] :
( ( multiply(X2_561,sk_c5) != sk_c6 )
| ( inverse(X2_561) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_53209]) ).
tff(c_53249,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_52913,c_53242]) ).
tff(c_53261,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52884,c_53249]) ).
tff(c_53262,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_53209]) ).
tff(c_53332,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_53292,c_53292,c_53292,c_53292,c_53262]) ).
tff(c_53333,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_53332]) ).
tff(c_53655,plain,
! [X3_569] :
( ( inverse(X3_569) != identity )
| ( multiply(X3_569,identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_53459,c_53457,c_53459,c_53333]) ).
tff(c_53659,plain,
inverse(inverse(inverse(inverse(identity)))) != identity,
inference(superposition,[status(thm),theory(equality)],[c_53602,c_53655]) ).
tff(c_53678,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53534,c_53534,c_53534,c_53534,c_53659]) ).
tff(c_53679,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_53332]) ).
tff(c_62969,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_53749,c_53927,c_53749,c_53747,c_53927,c_53747,c_53747,c_53747,c_53679]) ).
tff(c_62971,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_62969]) ).
tff(c_53302,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_53292,c_52884]) ).
tff(c_53311,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_53302,c_4]) ).
tff(c_53776,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_53747,c_53311]) ).
tff(c_53757,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_53747,c_53302]) ).
tff(c_53791,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_53776,c_53757]) ).
tff(c_62973,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62971,c_53791]) ).
tff(c_62975,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_62969]) ).
tff(c_62977,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62975,c_53791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP262-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 21:54:51 EDT 2023
% 0.16/0.37 % CPUTime :
% 15.80/6.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.80/6.67
% 15.80/6.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.80/6.74
% 15.80/6.74 Inference rules
% 15.80/6.74 ----------------------
% 15.80/6.74 #Ref : 0
% 15.80/6.74 #Sup : 15378
% 15.80/6.74 #Fact : 0
% 15.80/6.74 #Define : 0
% 15.80/6.74 #Split : 44
% 15.80/6.74 #Chain : 0
% 15.80/6.74 #Close : 0
% 15.80/6.74
% 15.80/6.74 Ordering : KBO
% 15.80/6.74
% 15.80/6.74 Simplification rules
% 15.80/6.74 ----------------------
% 15.80/6.74 #Subsume : 13
% 15.80/6.74 #Demod : 44717
% 15.80/6.74 #Tautology : 12352
% 15.80/6.74 #SimpNegUnit : 74
% 15.80/6.74 #BackRed : 653
% 15.80/6.74
% 15.80/6.74 #Partial instantiations: 0
% 15.80/6.74 #Strategies tried : 1
% 15.80/6.74
% 15.80/6.74 Timing (in seconds)
% 15.80/6.74 ----------------------
% 15.87/6.75 Preprocessing : 0.50
% 15.87/6.75 Parsing : 0.21
% 15.87/6.75 CNF conversion : 0.02
% 15.87/6.75 Main loop : 4.99
% 15.87/6.75 Inferencing : 1.46
% 15.87/6.75 Reduction : 2.71
% 15.87/6.75 Demodulation : 2.46
% 15.87/6.75 BG Simplification : 0.13
% 15.87/6.75 Subsumption : 0.45
% 15.87/6.75 Abstraction : 0.30
% 15.87/6.75 MUC search : 0.00
% 15.87/6.75 Cooper : 0.00
% 15.87/6.75 Total : 5.63
% 15.87/6.75 Index Insertion : 0.00
% 15.87/6.75 Index Deletion : 0.00
% 15.87/6.75 Index Matching : 0.00
% 15.87/6.75 BG Taut test : 0.00
%------------------------------------------------------------------------------