TSTP Solution File: GRP374-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP374-1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:41:06 EDT 2023
% Result : Unsatisfiable 11.97s 4.16s
% Output : CNFRefutation 12.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 43
% Syntax : Number of formulae : 480 ( 390 unt; 11 typ; 0 def)
% Number of atoms : 654 ( 632 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 373 ( 188 ~; 185 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 210 (; 210 !; 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_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_161,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_206,axiom,
! [X5,X3,X1,X2,X4] :
( ( inverse(sk_c8) != sk_c7 )
| ( multiply(X3,sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,X2) != sk_c7 )
| ( multiply(X5,sk_c8) != X2 )
| ( inverse(X5) != sk_c8 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_164,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_170,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_158,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_155,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
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_11234,plain,
! [X_171,Y_172,Z_173] : ( multiply(multiply(X_171,Y_172),Z_173) = multiply(X_171,multiply(Y_172,Z_173)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_11273,plain,
! [X_2,Z_173] : ( multiply(inverse(X_2),multiply(X_2,Z_173)) = multiply(identity,Z_173) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11234]) ).
tff(c_12966,plain,
! [X_204,Z_205] : ( multiply(inverse(X_204),multiply(X_204,Z_205)) = Z_205 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11273]) ).
tff(c_11285,plain,
! [X_2,Z_173] : ( multiply(inverse(X_2),multiply(X_2,Z_173)) = Z_173 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11273]) ).
tff(c_13136,plain,
! [X_207,Z_208] : ( multiply(inverse(inverse(X_207)),Z_208) = multiply(X_207,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_12966,c_11285]) ).
tff(c_13017,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12966]) ).
tff(c_13143,plain,
! [X_207] : ( multiply(X_207,identity) = X_207 ),
inference(superposition,[status(thm),theory(equality)],[c_13136,c_13017]) ).
tff(c_72,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_97,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_66,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_138,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_9801,plain,
! [X_143,Y_144,Z_145] : ( multiply(multiply(X_143,Y_144),Z_145) = multiply(X_143,multiply(Y_144,Z_145)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9849,plain,
! [X_2,Z_145] : ( multiply(inverse(X_2),multiply(X_2,Z_145)) = multiply(identity,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9801]) ).
tff(c_9954,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_9849]) ).
tff(c_9996,plain,
multiply(inverse(sk_c2),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_138,c_9954]) ).
tff(c_10014,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_9996]) ).
tff(c_9862,plain,
! [X_2,Z_145] : ( multiply(inverse(X_2),multiply(X_2,Z_145)) = Z_145 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9849]) ).
tff(c_10019,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10014,c_9862]) ).
tff(c_10025,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10019]) ).
tff(c_179,plain,
! [X_13,Y_14,Z_15] : ( multiply(multiply(X_13,Y_14),Z_15) = multiply(X_13,multiply(Y_14,Z_15)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_212,plain,
! [X_2,Z_15] : ( multiply(inverse(X_2),multiply(X_2,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_179]) ).
tff(c_1734,plain,
! [X_47,Z_48] : ( multiply(inverse(X_47),multiply(X_47,Z_48)) = Z_48 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_212]) ).
tff(c_223,plain,
! [X_2,Z_15] : ( multiply(inverse(X_2),multiply(X_2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_212]) ).
tff(c_1969,plain,
! [X_51,Z_52] : ( multiply(inverse(inverse(X_51)),Z_52) = multiply(X_51,Z_52) ),
inference(superposition,[status(thm),theory(equality)],[c_1734,c_223]) ).
tff(c_1770,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1734]) ).
tff(c_1976,plain,
! [X_51] : ( multiply(X_51,identity) = X_51 ),
inference(superposition,[status(thm),theory(equality)],[c_1969,c_1770]) ).
tff(c_1761,plain,
multiply(inverse(sk_c2),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_138,c_1734]) ).
tff(c_1777,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_1761]) ).
tff(c_1782,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_1777,c_223]) ).
tff(c_1788,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1782]) ).
tff(c_1790,plain,
multiply(sk_c6,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_1788,c_1777]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_144,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_36,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_121,plain,
inverse(sk_c1) = sk_c8,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_126,plain,
multiply(sk_c8,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_121,c_4]) ).
tff(c_203,plain,
! [Z_15] : ( multiply(sk_c8,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_126,c_179]) ).
tff(c_228,plain,
! [Z_16] : ( multiply(sk_c8,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_203]) ).
tff(c_240,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_144,c_228]) ).
tff(c_268,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_212]) ).
tff(c_289,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_240,c_268]) ).
tff(c_332,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_289]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_109,plain,
inverse(sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_143,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_301,plain,
multiply(inverse(sk_c8),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_143,c_268]) ).
tff(c_335,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_109,c_301]) ).
tff(c_360,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_332,c_2,c_332,c_335]) ).
tff(c_80,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_226,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_109,c_143,c_80]) ).
tff(c_227,plain,
multiply(sk_c8,sk_c7) != sk_c6,
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_244,plain,
sk_c8 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_240,c_227]) ).
tff(c_362,plain,
sk_c8 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_360,c_244]) ).
tff(c_345,plain,
inverse(sk_c8) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_332,c_109]) ).
tff(c_356,plain,
multiply(identity,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_345,c_4]) ).
tff(c_382,plain,
sk_c8 = identity,
inference(superposition,[status(thm),theory(equality)],[c_2,c_356]) ).
tff(c_387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_362,c_382]) ).
tff(c_389,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_397,plain,
! [Z_20] : ( multiply(sk_c8,multiply(sk_c1,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_203]) ).
tff(c_409,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_144,c_397]) ).
tff(c_413,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_389,c_409]) ).
tff(c_421,plain,
inverse(sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_413,c_109]) ).
tff(c_1791,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1788,c_421]) ).
tff(c_419,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_413,c_121]) ).
tff(c_1723,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_419,c_4]) ).
tff(c_1810,plain,
multiply(inverse(sk_c6),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_1723,c_223]) ).
tff(c_1816,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1791,c_1810]) ).
tff(c_418,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_413,c_126]) ).
tff(c_1860,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1790,c_1816,c_418]) ).
tff(c_481,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_212]) ).
tff(c_720,plain,
! [X_25,Z_26] : ( multiply(inverse(inverse(X_25)),Z_26) = multiply(X_25,Z_26) ),
inference(superposition,[status(thm),theory(equality)],[c_223,c_481]) ).
tff(c_532,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_481]) ).
tff(c_727,plain,
! [X_25] : ( multiply(X_25,identity) = X_25 ),
inference(superposition,[status(thm),theory(equality)],[c_720,c_532]) ).
tff(c_415,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_413,c_389]) ).
tff(c_499,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_415,c_481]) ).
tff(c_539,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_499]) ).
tff(c_549,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_539,c_421]) ).
tff(c_561,plain,
multiply(identity,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_549,c_4]) ).
tff(c_575,plain,
multiply(inverse(identity),identity) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_561,c_223]) ).
tff(c_587,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_575]) ).
tff(c_388,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_426,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_413,c_413,c_413,c_413,c_413,c_413,c_413,c_388]) ).
tff(c_427,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_426]) ).
tff(c_1716,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_727,c_587,c_2,c_587,c_539,c_587,c_427]) ).
tff(c_101,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_97,c_4]) ).
tff(c_526,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_101,c_481]) ).
tff(c_544,plain,
multiply(sk_c7,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_421,c_526]) ).
tff(c_565,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_539,c_544]) ).
tff(c_567,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_565,c_97]) ).
tff(c_606,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_587,c_567]) ).
tff(c_1718,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1716,c_606]) ).
tff(c_1719,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_426]) ).
tff(c_9475,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1976,c_1860,c_1788,c_1860,c_1976,c_1860,c_1788,c_1860,c_1976,c_1860,c_1788,c_1860,c_1719]) ).
tff(c_9477,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_9475]) ).
tff(c_1864,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1860,c_1791]) ).
tff(c_9479,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9477,c_1864]) ).
tff(c_9480,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_9475]) ).
tff(c_9482,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_9480]) ).
tff(c_9484,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9482,c_1864]) ).
tff(c_9487,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_9480]) ).
tff(c_9489,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9487,c_1864]) ).
tff(c_9491,plain,
multiply(sk_c1,sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_113,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_109,c_4]) ).
tff(c_9560,plain,
! [X_137,Y_138,Z_139] : ( multiply(multiply(X_137,Y_138),Z_139) = multiply(X_137,multiply(Y_138,Z_139)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9602,plain,
! [Z_139] : ( multiply(sk_c7,multiply(sk_c8,Z_139)) = multiply(identity,Z_139) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_9560]) ).
tff(c_9636,plain,
! [Z_141] : ( multiply(sk_c7,multiply(sk_c8,Z_141)) = Z_141 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9602]) ).
tff(c_9666,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_126,c_9636]) ).
tff(c_9490,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_9495,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9490,c_4]) ).
tff(c_9660,plain,
multiply(sk_c7,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_9495,c_9636]) ).
tff(c_9724,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_9666,c_9660]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_9537,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9491,c_22]) ).
tff(c_9725,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9724,c_9537]) ).
tff(c_9729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9491,c_9725]) ).
tff(c_9731,plain,
multiply(sk_c8,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_44,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_9778,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9731,c_44]) ).
tff(c_9743,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_9840,plain,
! [Z_145] : ( multiply(sk_c8,multiply(sk_c1,Z_145)) = multiply(identity,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_126,c_9801]) ).
tff(c_9866,plain,
! [Z_146] : ( multiply(sk_c8,multiply(sk_c1,Z_146)) = Z_146 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9840]) ).
tff(c_9878,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_9743,c_9866]) ).
tff(c_9882,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9778,c_9878]) ).
tff(c_9897,plain,
inverse(sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9882,c_109]) ).
tff(c_9920,plain,
multiply(sk_c7,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9897,c_4]) ).
tff(c_10045,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10025,c_9920]) ).
tff(c_9892,plain,
multiply(sk_c6,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9882,c_9731]) ).
tff(c_10148,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10045,c_2,c_10045,c_10025,c_9892]) ).
tff(c_10150,plain,
multiply(sk_c1,sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_10210,plain,
! [X_150,Y_151,Z_152] : ( multiply(multiply(X_150,Y_151),Z_152) = multiply(X_150,multiply(Y_151,Z_152)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10249,plain,
! [Z_152] : ( multiply(sk_c7,multiply(sk_c8,Z_152)) = multiply(identity,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_10210]) ).
tff(c_10283,plain,
! [Z_154] : ( multiply(sk_c7,multiply(sk_c8,Z_154)) = Z_154 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10249]) ).
tff(c_10310,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_126,c_10283]) ).
tff(c_10149,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_10154,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10149,c_4]) ).
tff(c_10304,plain,
multiply(sk_c7,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_10154,c_10283]) ).
tff(c_10364,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10310,c_10304]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_10193,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9731,c_46]) ).
tff(c_10365,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10364,c_10193]) ).
tff(c_10369,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10150,c_10365]) ).
tff(c_10371,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_56,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_10426,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10371,c_56]) ).
tff(c_28,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_10419,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_10446,plain,
! [X_156,Y_157,Z_158] : ( multiply(multiply(X_156,Y_157),Z_158) = multiply(X_156,multiply(Y_157,Z_158)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10485,plain,
! [Z_158] : ( multiply(sk_c8,multiply(sk_c1,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_126,c_10446]) ).
tff(c_10509,plain,
! [Z_159] : ( multiply(sk_c8,multiply(sk_c1,Z_159)) = Z_159 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10485]) ).
tff(c_10521,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_10419,c_10509]) ).
tff(c_10525,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10426,c_10521]) ).
tff(c_10529,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10525,c_10426]) ).
tff(c_10494,plain,
! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10446]) ).
tff(c_10507,plain,
! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = Z_158 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10494]) ).
tff(c_10696,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10529,c_10507]) ).
tff(c_10702,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10696]) ).
tff(c_10540,plain,
inverse(sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10525,c_109]) ).
tff(c_10742,plain,
inverse(sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10702,c_10540]) ).
tff(c_60,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_10401,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_10371,c_60]) ).
tff(c_10405,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10401,c_4]) ).
tff(c_10532,plain,
multiply(sk_c6,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10525,c_10405]) ).
tff(c_10761,plain,
multiply(inverse(sk_c6),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_10532,c_10507]) ).
tff(c_10767,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10742,c_10761]) ).
tff(c_58,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_10414,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_10371,c_58]) ).
tff(c_10531,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10525,c_10414]) ).
tff(c_10841,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10767,c_10702,c_10531]) ).
tff(c_10538,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10525,c_121]) ).
tff(c_10847,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10841,c_10538]) ).
tff(c_10877,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10847,c_4]) ).
tff(c_10919,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_10877,c_10507]) ).
tff(c_10931,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10919]) ).
tff(c_10578,plain,
! [X_160,Z_161] : ( multiply(inverse(X_160),multiply(X_160,Z_161)) = Z_161 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10494]) ).
tff(c_10611,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_101,c_10578]) ).
tff(c_10624,plain,
multiply(sk_c7,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_10540,c_10611]) ).
tff(c_10567,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10538,c_4]) ).
tff(c_10651,plain,
multiply(inverse(sk_c6),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_10567,c_10507]) ).
tff(c_10657,plain,
sk_c2 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10624,c_10540,c_10651]) ).
tff(c_10661,plain,
multiply(sk_c1,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_10657,c_10371]) ).
tff(c_10975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10931,c_10841,c_10702,c_10661]) ).
tff(c_10977,plain,
multiply(sk_c1,sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_11004,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_11043,plain,
! [Z_167] : ( multiply(sk_c7,multiply(sk_c8,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_11004]) ).
tff(c_11080,plain,
! [Z_169] : ( multiply(sk_c7,multiply(sk_c8,Z_169)) = Z_169 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11043]) ).
tff(c_11107,plain,
multiply(sk_c7,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_126,c_11080]) ).
tff(c_11098,plain,
multiply(sk_c7,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_10405,c_11080]) ).
tff(c_11155,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_11107,c_11098]) ).
tff(c_11156,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11155,c_10414]) ).
tff(c_11160,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10977,c_11156]) ).
tff(c_11161,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_11166,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11161,c_4]) ).
tff(c_11267,plain,
! [Z_173] : ( multiply(sk_c7,multiply(sk_c8,Z_173)) = multiply(identity,Z_173) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_11234]) ).
tff(c_11287,plain,
! [Z_174] : ( multiply(sk_c7,multiply(sk_c8,Z_174)) = Z_174 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11267]) ).
tff(c_11308,plain,
multiply(sk_c7,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_11166,c_11287]) ).
tff(c_11162,plain,
inverse(sk_c1) != sk_c8,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_11170,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_11162,c_42]) ).
tff(c_11174,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11170,c_4]) ).
tff(c_11305,plain,
multiply(sk_c7,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_11174,c_11287]) ).
tff(c_11632,plain,
sk_c4 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_11308,c_11305]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_11210,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_11162,c_40]) ).
tff(c_11641,plain,
multiply(sk_c3,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11632,c_11210]) ).
tff(c_34,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_11196,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_11162,c_34]) ).
tff(c_12899,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11641,c_11196]) ).
tff(c_38,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_11205,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_11162,c_38]) ).
tff(c_11302,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11205,c_11287]) ).
tff(c_12911,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_12899,c_12899,c_11302]) ).
tff(c_12990,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_12911,c_12966]) ).
tff(c_13025,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12990]) ).
tff(c_13034,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13025,c_12899]) ).
tff(c_12913,plain,
multiply(sk_c8,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_12899,c_11205]) ).
tff(c_13002,plain,
multiply(inverse(sk_c3),sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_11641,c_12966]) ).
tff(c_13026,plain,
sk_c8 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_12913,c_11161,c_13002]) ).
tff(c_13044,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13025,c_13026]) ).
tff(c_11726,plain,
! [X_179,Z_180] : ( multiply(inverse(X_179),multiply(X_179,Z_180)) = Z_180 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11273]) ).
tff(c_11896,plain,
! [X_182,Z_183] : ( multiply(inverse(inverse(X_182)),Z_183) = multiply(X_182,Z_183) ),
inference(superposition,[status(thm),theory(equality)],[c_11726,c_11285]) ).
tff(c_11777,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11726]) ).
tff(c_11903,plain,
! [X_182] : ( multiply(X_182,identity) = X_182 ),
inference(superposition,[status(thm),theory(equality)],[c_11896,c_11777]) ).
tff(c_11659,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11641,c_11196]) ).
tff(c_11671,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11659,c_11659,c_11302]) ).
tff(c_11750,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11671,c_11726]) ).
tff(c_11785,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11750]) ).
tff(c_11794,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11785,c_11659]) ).
tff(c_11673,plain,
multiply(sk_c8,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11659,c_11205]) ).
tff(c_11762,plain,
multiply(inverse(sk_c3),sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_11641,c_11726]) ).
tff(c_11786,plain,
sk_c8 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11673,c_11161,c_11762]) ).
tff(c_11804,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11785,c_11786]) ).
tff(c_11337,plain,
sk_c4 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_11308,c_11305]) ).
tff(c_11346,plain,
multiply(sk_c3,sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11337,c_11210]) ).
tff(c_11378,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11346,c_11196]) ).
tff(c_11389,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11378,c_11378,c_11302]) ).
tff(c_11422,plain,
! [X_176,Z_177] : ( multiply(inverse(X_176),multiply(X_176,Z_177)) = Z_177 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11273]) ).
tff(c_11440,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11389,c_11422]) ).
tff(c_11474,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11440]) ).
tff(c_11395,plain,
inverse(sk_c8) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11378,c_109]) ).
tff(c_11403,plain,
multiply(sk_c5,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11395,c_4]) ).
tff(c_11499,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11474,c_11403]) ).
tff(c_32,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_11215,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_11162,c_32]) ).
tff(c_11392,plain,
multiply(sk_c8,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11378,c_11215]) ).
tff(c_11523,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11499,c_11474,c_11392]) ).
tff(c_11335,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_109,c_11215,c_80]) ).
tff(c_11336,plain,
multiply(sk_c8,sk_c6) != sk_c7,
inference(splitLeft,[status(thm)],[c_11335]) ).
tff(c_11388,plain,
multiply(sk_c8,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11378,c_11336]) ).
tff(c_11575,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11523,c_2,c_11499,c_11474,c_11388]) ).
tff(c_11577,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_11335]) ).
tff(c_11283,plain,
! [Z_173] : ( multiply(sk_c7,multiply(sk_c8,Z_173)) = Z_173 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11267]) ).
tff(c_11581,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11577,c_11283]) ).
tff(c_11587,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11302,c_11581]) ).
tff(c_11576,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_11335]) ).
tff(c_11657,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c5 )
| ( multiply(X4_10,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_11587,c_11587,c_11576]) ).
tff(c_11658,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_11657]) ).
tff(c_12895,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11903,c_11794,c_11804,c_2,c_11804,c_11804,c_11658]) ).
tff(c_11668,plain,
multiply(sk_c5,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_11659,c_11308]) ).
tff(c_11788,plain,
multiply(identity,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_11785,c_11668]) ).
tff(c_11798,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11788]) ).
tff(c_11807,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11804,c_11161]) ).
tff(c_11834,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11798,c_11807]) ).
tff(c_12897,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12895,c_11834]) ).
tff(c_12898,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c5 )
| ( multiply(X4_10,sk_c5) != sk_c7 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_11657]) ).
tff(c_19981,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_13143,c_13034,c_13044,c_13044,c_13143,c_13034,c_13025,c_13025,c_13143,c_13034,c_13044,c_13044,c_12898]) ).
tff(c_19983,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_19981]) ).
tff(c_12908,plain,
multiply(sk_c5,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_12899,c_11308]) ).
tff(c_13028,plain,
multiply(identity,identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_13025,c_12908]) ).
tff(c_13038,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13028]) ).
tff(c_13047,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13044,c_11161]) ).
tff(c_13074,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13038,c_13047]) ).
tff(c_19985,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19983,c_13074]) ).
tff(c_19986,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_19981]) ).
tff(c_19988,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_19986]) ).
tff(c_19990,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19988,c_13074]) ).
tff(c_19993,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_19986]) ).
tff(c_19995,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19993,c_13074]) ).
tff(c_19997,plain,
inverse(sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_14,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_20038,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19997,c_14]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_20043,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_19997,c_16]) ).
tff(c_18,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_20011,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_19997,c_18]) ).
tff(c_20015,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20011,c_4]) ).
tff(c_20070,plain,
! [X_289,Y_290,Z_291] : ( multiply(multiply(X_289,Y_290),Z_291) = multiply(X_289,multiply(Y_290,Z_291)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_20097,plain,
! [Z_291] : ( multiply(sk_c8,multiply(sk_c4,Z_291)) = multiply(identity,Z_291) ),
inference(superposition,[status(thm),theory(equality)],[c_20015,c_20070]) ).
tff(c_20119,plain,
! [Z_292] : ( multiply(sk_c8,multiply(sk_c4,Z_292)) = Z_292 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20097]) ).
tff(c_20131,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_20043,c_20119]) ).
tff(c_20135,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20038,c_20131]) ).
tff(c_8,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_20024,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_19997,c_8]) ).
tff(c_20140,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20135,c_20024]) ).
tff(c_19996,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_20145,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20135,c_19996]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_20030,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_19997,c_10]) ).
tff(c_20139,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20135,c_20030]) ).
tff(c_20106,plain,
! [X_2,Z_291] : ( multiply(inverse(X_2),multiply(X_2,Z_291)) = multiply(identity,Z_291) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20070]) ).
tff(c_20224,plain,
! [X_294,Z_295] : ( multiply(inverse(X_294),multiply(X_294,Z_295)) = Z_295 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20106]) ).
tff(c_20254,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20139,c_20224]) ).
tff(c_20286,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20140,c_20145,c_20254]) ).
tff(c_20291,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20286,c_20286,c_20140]) ).
tff(c_20117,plain,
! [X_2,Z_291] : ( multiply(inverse(X_2),multiply(X_2,Z_291)) = Z_291 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20106]) ).
tff(c_20431,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_20291,c_20117]) ).
tff(c_20437,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20431]) ).
tff(c_20144,plain,
inverse(sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20135,c_19997]) ).
tff(c_20296,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20286,c_20286,c_20144]) ).
tff(c_20447,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_20437,c_20437,c_20296]) ).
tff(c_20142,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20135,c_20011]) ).
tff(c_20297,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20286,c_20142]) ).
tff(c_20363,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20297,c_4]) ).
tff(c_20498,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20437,c_20363]) ).
tff(c_20445,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20437,c_20297]) ).
tff(c_20499,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20498,c_20445]) ).
tff(c_20501,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20447,c_20499]) ).
tff(c_20503,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_74,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_31431,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20503,c_74]) ).
tff(c_20599,plain,
! [X_297,Y_298,Z_299] : ( multiply(multiply(X_297,Y_298),Z_299) = multiply(X_297,multiply(Y_298,Z_299)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_20638,plain,
! [X_2,Z_299] : ( multiply(inverse(X_2),multiply(X_2,Z_299)) = multiply(identity,Z_299) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20599]) ).
tff(c_22239,plain,
! [X_330,Z_331] : ( multiply(inverse(X_330),multiply(X_330,Z_331)) = Z_331 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20638]) ).
tff(c_20650,plain,
! [X_2,Z_299] : ( multiply(inverse(X_2),multiply(X_2,Z_299)) = Z_299 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20638]) ).
tff(c_22469,plain,
! [X_334,Z_335] : ( multiply(inverse(inverse(X_334)),Z_335) = multiply(X_334,Z_335) ),
inference(superposition,[status(thm),theory(equality)],[c_22239,c_20650]) ).
tff(c_22293,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22239]) ).
tff(c_22476,plain,
! [X_334] : ( multiply(X_334,identity) = X_334 ),
inference(superposition,[status(thm),theory(equality)],[c_22469,c_22293]) ).
tff(c_20568,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20503,c_74]) ).
tff(c_76,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_20579,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_20503,c_76]) ).
tff(c_78,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_20530,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_20503,c_78]) ).
tff(c_20534,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20530,c_4]) ).
tff(c_20629,plain,
! [Z_299] : ( multiply(sk_c8,multiply(sk_c4,Z_299)) = multiply(identity,Z_299) ),
inference(superposition,[status(thm),theory(equality)],[c_20534,c_20599]) ).
tff(c_20652,plain,
! [Z_300] : ( multiply(sk_c8,multiply(sk_c4,Z_300)) = Z_300 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20629]) ).
tff(c_20664,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_20579,c_20652]) ).
tff(c_20668,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20568,c_20664]) ).
tff(c_20516,plain,
inverse(sk_c8) = sk_c7,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_20520,plain,
multiply(sk_c7,sk_c8) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20516,c_4]) ).
tff(c_20847,plain,
multiply(sk_c7,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20520]) ).
tff(c_20502,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_20850,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20502]) ).
tff(c_70,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_20574,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20503,c_70]) ).
tff(c_20840,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20574]) ).
tff(c_22269,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20840,c_22239]) ).
tff(c_22304,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20847,c_20850,c_22269]) ).
tff(c_68,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_20555,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_20503,c_68]) ).
tff(c_20842,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20555]) ).
tff(c_22224,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20847,c_20842]) ).
tff(c_20990,plain,
! [X_304,Z_305] : ( multiply(inverse(X_304),multiply(X_304,Z_305)) = Z_305 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20638]) ).
tff(c_21217,plain,
! [X_308,Z_309] : ( multiply(inverse(inverse(X_308)),Z_309) = multiply(X_308,Z_309) ),
inference(superposition,[status(thm),theory(equality)],[c_20990,c_20650]) ).
tff(c_21050,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20990]) ).
tff(c_21224,plain,
! [X_308] : ( multiply(X_308,identity) = X_308 ),
inference(superposition,[status(thm),theory(equality)],[c_21217,c_21050]) ).
tff(c_20507,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20502,c_4]) ).
tff(c_20635,plain,
! [Z_299] : ( multiply(sk_c8,multiply(sk_c3,Z_299)) = multiply(identity,Z_299) ),
inference(superposition,[status(thm),theory(equality)],[c_20507,c_20599]) ).
tff(c_20649,plain,
! [Z_299] : ( multiply(sk_c8,multiply(sk_c3,Z_299)) = Z_299 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20635]) ).
tff(c_20973,plain,
! [Z_303] : ( multiply(sk_c7,multiply(sk_c3,Z_303)) = Z_303 ),
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20649]) ).
tff(c_20985,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20840,c_20973]) ).
tff(c_20989,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20847,c_20985]) ).
tff(c_20670,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_20516,c_20555,c_80]) ).
tff(c_20671,plain,
multiply(sk_c8,sk_c6) != sk_c7,
inference(splitLeft,[status(thm)],[c_20670]) ).
tff(c_20725,plain,
multiply(sk_c7,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20671]) ).
tff(c_20682,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20516]) ).
tff(c_20676,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20555]) ).
tff(c_20827,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20676,c_20650]) ).
tff(c_20833,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20682,c_20827]) ).
tff(c_20835,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20725,c_20833]) ).
tff(c_20836,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c8 )
| ( multiply(X3_7,sk_c8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_20670]) ).
tff(c_20936,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c7 )
| ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20668,c_20668,c_20668,c_20668,c_20668,c_20668,c_20836]) ).
tff(c_20937,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_20936]) ).
tff(c_22212,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_21224,c_20989,c_20989,c_2,c_20989,c_20989,c_20937]) ).
tff(c_20946,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20847,c_20842]) ).
tff(c_20837,plain,
multiply(sk_c8,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_20670]) ).
tff(c_20869,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20837]) ).
tff(c_20955,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20946,c_20869]) ).
tff(c_20848,plain,
inverse(sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20516]) ).
tff(c_20846,plain,
inverse(sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20530]) ).
tff(c_20858,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20846,c_4]) ).
tff(c_21029,plain,
multiply(inverse(sk_c7),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_20858,c_20990]) ).
tff(c_21064,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_20955,c_20848,c_21029]) ).
tff(c_21151,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20989,c_21064]) ).
tff(c_20849,plain,
multiply(sk_c7,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20668,c_20507]) ).
tff(c_21023,plain,
multiply(inverse(sk_c7),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_20849,c_20990]) ).
tff(c_21062,plain,
sk_c7 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_20955,c_20848,c_21023]) ).
tff(c_21090,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20989,c_21062]) ).
tff(c_21084,plain,
inverse(sk_c4) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_21062,c_20846]) ).
tff(c_21156,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21151,c_21090,c_21084]) ).
tff(c_22214,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22212,c_21156]) ).
tff(c_22215,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_20936]) ).
tff(c_31053,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22476,c_22304,c_22304,c_22304,c_22476,c_22304,c_22224,c_22224,c_22476,c_22304,c_22304,c_22304,c_22215]) ).
tff(c_31055,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_31053]) ).
tff(c_20865,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20850,c_4]) ).
tff(c_22332,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22304,c_20865]) ).
tff(c_22316,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22304,c_20850]) ).
tff(c_22347,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22332,c_22316]) ).
tff(c_31057,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31055,c_22347]) ).
tff(c_31058,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_31053]) ).
tff(c_31060,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_31058]) ).
tff(c_31062,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31060,c_22347]) ).
tff(c_31391,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_31058]) ).
tff(c_31393,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31391,c_22347]) ).
tff(c_31395,plain,
inverse(sk_c8) != sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_31411,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_31395,c_16]) ).
tff(c_31394,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_31399,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31394,c_4]) ).
tff(c_31461,plain,
! [X_430,Y_431,Z_432] : ( multiply(multiply(X_430,Y_431),Z_432) = multiply(X_430,multiply(Y_431,Z_432)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_31488,plain,
! [Z_432] : ( multiply(sk_c8,multiply(sk_c4,Z_432)) = multiply(identity,Z_432) ),
inference(superposition,[status(thm),theory(equality)],[c_31399,c_31461]) ).
tff(c_31506,plain,
! [Z_433] : ( multiply(sk_c8,multiply(sk_c4,Z_433)) = Z_433 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31488]) ).
tff(c_31518,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_31411,c_31506]) ).
tff(c_31522,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_31431,c_31518]) ).
tff(c_31416,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_20503,c_68]) ).
tff(c_31528,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31522,c_31416]) ).
tff(c_31534,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_31522,c_20502]) ).
tff(c_31422,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_31395,c_10]) ).
tff(c_31527,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_31522,c_31422]) ).
tff(c_31494,plain,
! [X_2,Z_432] : ( multiply(inverse(X_2),multiply(X_2,Z_432)) = multiply(identity,Z_432) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_31461]) ).
tff(c_31560,plain,
! [X_434,Z_435] : ( multiply(inverse(X_434),multiply(X_434,Z_435)) = Z_435 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31494]) ).
tff(c_31578,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_31527,c_31560]) ).
tff(c_31597,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_31534,c_31578]) ).
tff(c_31674,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31528,c_31597]) ).
tff(c_31679,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31674,c_31674,c_31528]) ).
tff(c_31504,plain,
! [X_2,Z_432] : ( multiply(inverse(X_2),multiply(X_2,Z_432)) = Z_432 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31494]) ).
tff(c_31795,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_31679,c_31504]) ).
tff(c_31802,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_31795]) ).
tff(c_31531,plain,
inverse(sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_31522,c_31395]) ).
tff(c_31683,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31674,c_31674,c_31531]) ).
tff(c_31809,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_31802,c_31802,c_31683]) ).
tff(c_31682,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_31674,c_31534]) ).
tff(c_31720,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_31682,c_4]) ).
tff(c_31823,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_31802,c_31720]) ).
tff(c_31810,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31802,c_31682]) ).
tff(c_31836,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_31823,c_31810]) ).
tff(c_31837,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31809,c_31836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP374-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 21:43:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 11.97/4.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.29/4.20
% 12.29/4.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.29/4.26
% 12.29/4.26 Inference rules
% 12.29/4.26 ----------------------
% 12.29/4.26 #Ref : 0
% 12.29/4.26 #Sup : 7869
% 12.29/4.26 #Fact : 0
% 12.29/4.26 #Define : 0
% 12.29/4.26 #Split : 27
% 12.29/4.26 #Chain : 0
% 12.29/4.26 #Close : 0
% 12.29/4.26
% 12.29/4.26 Ordering : KBO
% 12.29/4.26
% 12.29/4.26 Simplification rules
% 12.29/4.26 ----------------------
% 12.29/4.26 #Subsume : 4
% 12.29/4.26 #Demod : 17423
% 12.29/4.26 #Tautology : 6404
% 12.29/4.26 #SimpNegUnit : 75
% 12.29/4.26 #BackRed : 389
% 12.29/4.26
% 12.29/4.26 #Partial instantiations: 0
% 12.29/4.26 #Strategies tried : 1
% 12.29/4.26
% 12.29/4.26 Timing (in seconds)
% 12.29/4.26 ----------------------
% 12.29/4.26 Preprocessing : 0.53
% 12.29/4.26 Parsing : 0.21
% 12.29/4.26 CNF conversion : 0.03
% 12.29/4.26 Main loop : 2.60
% 12.29/4.26 Inferencing : 0.82
% 12.29/4.26 Reduction : 1.24
% 12.29/4.26 Demodulation : 1.08
% 12.29/4.26 BG Simplification : 0.09
% 12.29/4.26 Subsumption : 0.28
% 12.29/4.26 Abstraction : 0.16
% 12.29/4.26 MUC search : 0.00
% 12.29/4.26 Cooper : 0.00
% 12.29/4.26 Total : 3.24
% 12.29/4.26 Index Insertion : 0.00
% 12.29/4.26 Index Deletion : 0.00
% 12.29/4.26 Index Matching : 0.00
% 12.29/4.26 BG Taut test : 0.00
%------------------------------------------------------------------------------