TSTP Solution File: GRP215-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP215-1 : 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 : n022.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 10:40:30 EDT 2023
% Result : Unsatisfiable 8.99s 3.15s
% Output : CNFRefutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 315 ( 249 unt; 10 typ; 0 def)
% Number of atoms : 404 ( 389 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 214 ( 115 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 167 (; 167 !; 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_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
! [X5,X3,X1,X2,X4] :
( ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(sk_c7,X2) != sk_c6 )
| ( multiply(X5,sk_c7) != X2 )
| ( inverse(X5) != sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_8752,plain,
! [X_180,Y_181,Z_182] : ( multiply(multiply(X_180,Y_181),Z_182) = multiply(X_180,multiply(Y_181,Z_182)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8785,plain,
! [X_2,Z_182] : ( multiply(inverse(X_2),multiply(X_2,Z_182)) = multiply(identity,Z_182) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8752]) ).
tff(c_8796,plain,
! [X_2,Z_182] : ( multiply(inverse(X_2),multiply(X_2,Z_182)) = Z_182 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8785]) ).
tff(c_10427,plain,
! [X_217,Z_218] : ( multiply(inverse(X_217),multiply(X_217,Z_218)) = Z_218 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8785]) ).
tff(c_10687,plain,
! [X_222,Z_223] : ( multiply(inverse(inverse(X_222)),Z_223) = multiply(X_222,Z_223) ),
inference(superposition,[status(thm),theory(equality)],[c_8796,c_10427]) ).
tff(c_10463,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10427]) ).
tff(c_10694,plain,
! [X_222] : ( multiply(X_222,identity) = X_222 ),
inference(superposition,[status(thm),theory(equality)],[c_10687,c_10463]) ).
tff(c_3362,plain,
! [X_82,Y_83,Z_84] : ( multiply(multiply(X_82,Y_83),Z_84) = multiply(X_82,multiply(Y_83,Z_84)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3395,plain,
! [X_2,Z_84] : ( multiply(inverse(X_2),multiply(X_2,Z_84)) = multiply(identity,Z_84) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3362]) ).
tff(c_3406,plain,
! [X_2,Z_84] : ( multiply(inverse(X_2),multiply(X_2,Z_84)) = Z_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3395]) ).
tff(c_5159,plain,
! [X_123,Z_124] : ( multiply(inverse(X_123),multiply(X_123,Z_124)) = Z_124 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3395]) ).
tff(c_5424,plain,
! [X_128,Z_129] : ( multiply(inverse(inverse(X_128)),Z_129) = multiply(X_128,Z_129) ),
inference(superposition,[status(thm),theory(equality)],[c_3406,c_5159]) ).
tff(c_5210,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5159]) ).
tff(c_5431,plain,
! [X_128] : ( multiply(X_128,identity) = X_128 ),
inference(superposition,[status(thm),theory(equality)],[c_5424,c_5210]) ).
tff(c_16,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_91,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_18,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_77,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_81,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_77,c_4]) ).
tff(c_945,plain,
! [X_35,Y_36,Z_37] : ( multiply(multiply(X_35,Y_36),Z_37) = multiply(X_35,multiply(Y_36,Z_37)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_978,plain,
! [Z_37] : ( multiply(sk_c7,multiply(sk_c1,Z_37)) = multiply(identity,Z_37) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_945]) ).
tff(c_998,plain,
! [Z_38] : ( multiply(sk_c7,multiply(sk_c1,Z_38)) = Z_38 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_978]) ).
tff(c_1010,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_91,c_998]) ).
tff(c_1127,plain,
! [Z_42] : ( multiply(sk_c1,multiply(sk_c7,Z_42)) = multiply(sk_c6,Z_42) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_945]) ).
tff(c_1142,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_1010,c_1127]) ).
tff(c_1161,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_91,c_1142]) ).
tff(c_984,plain,
! [X_2,Z_37] : ( multiply(inverse(X_2),multiply(X_2,Z_37)) = multiply(identity,Z_37) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_945]) ).
tff(c_1513,plain,
! [X_49,Z_50] : ( multiply(inverse(X_49),multiply(X_49,Z_50)) = Z_50 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_984]) ).
tff(c_1564,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_1161,c_1513]) ).
tff(c_1591,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1564]) ).
tff(c_46,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_65,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_46]) ).
tff(c_69,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).
tff(c_1611,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1591,c_69]) ).
tff(c_996,plain,
! [X_2,Z_37] : ( multiply(inverse(X_2),multiply(X_2,Z_37)) = Z_37 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_984]) ).
tff(c_1714,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_1611,c_996]) ).
tff(c_1726,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1714]) ).
tff(c_115,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_136,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_115]) ).
tff(c_460,plain,
! [Z_26] : ( multiply(sk_c7,multiply(sk_c1,Z_26)) = Z_26 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_136]) ).
tff(c_472,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_91,c_460]) ).
tff(c_142,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_115]) ).
tff(c_756,plain,
! [X_33,Z_34] : ( multiply(inverse(X_33),multiply(X_33,Z_34)) = Z_34 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_142]) ).
tff(c_807,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_472,c_756]) ).
tff(c_850,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_807]) ).
tff(c_36,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_98,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_139,plain,
! [Z_15] : ( multiply(sk_c6,multiply(sk_c2,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_115]) ).
tff(c_483,plain,
! [Z_27] : ( multiply(sk_c6,multiply(sk_c2,Z_27)) = Z_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_139]) ).
tff(c_501,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_98,c_483]) ).
tff(c_801,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_501,c_756]) ).
tff(c_849,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_801]) ).
tff(c_227,plain,
! [Z_19] : ( multiply(sk_c6,multiply(sk_c2,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_139]) ).
tff(c_239,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_98,c_227]) ).
tff(c_314,plain,
! [X_22,Z_23] : ( multiply(inverse(X_22),multiply(X_22,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_142]) ).
tff(c_347,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_239,c_314]) ).
tff(c_384,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_347]) ).
tff(c_150,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_136]) ).
tff(c_250,plain,
! [Z_20] : ( multiply(sk_c7,multiply(sk_c1,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_136]) ).
tff(c_262,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_91,c_250]) ).
tff(c_338,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_262,c_314]) ).
tff(c_382,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_338]) ).
tff(c_48,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != 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_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_201,plain,
! [X3_18] :
( ( inverse(X3_18) != sk_c7 )
| ( multiply(X3_18,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_211,plain,
inverse(sk_c1) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_91,c_201]) ).
tff(c_224,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_77,c_211]) ).
tff(c_225,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_226,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_225]) ).
tff(c_403,plain,
! [X5_24] :
( ( inverse(X5_24) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_24,sk_c7)) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_226]) ).
tff(c_410,plain,
( ( inverse(sk_c1) != sk_c7 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_403]) ).
tff(c_425,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_77,c_410]) ).
tff(c_442,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_425]) ).
tff(c_443,plain,
! [X1_8,X4_10] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_225]) ).
tff(c_532,plain,
! [X4_28] :
( ( inverse(X4_28) != sk_c6 )
| ( multiply(X4_28,sk_c6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_443]) ).
tff(c_542,plain,
inverse(sk_c2) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_98,c_532]) ).
tff(c_555,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_65,c_542]) ).
tff(c_673,plain,
! [X1_31] :
( ( multiply(X1_31,sk_c6) != sk_c7 )
| ( inverse(X1_31) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_443]) ).
tff(c_686,plain,
inverse(sk_c2) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_98,c_673]) ).
tff(c_697,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_65,c_686]) ).
tff(c_859,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_849,c_697]) ).
tff(c_896,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_850,c_859]) ).
tff(c_898,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_32,plain,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_940,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_898,c_32]) ).
tff(c_34,plain,
( ( multiply(sk_c4,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_934,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_898,c_34]) ).
tff(c_897,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_903,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_897,c_4]) ).
tff(c_972,plain,
! [Z_37] : ( multiply(sk_c7,multiply(sk_c4,Z_37)) = multiply(identity,Z_37) ),
inference(superposition,[status(thm),theory(equality)],[c_903,c_945]) ).
tff(c_1365,plain,
! [Z_47] : ( multiply(sk_c7,multiply(sk_c4,Z_47)) = Z_47 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_972]) ).
tff(c_1380,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_934,c_1365]) ).
tff(c_1384,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_940,c_1380]) ).
tff(c_1414,plain,
multiply(sk_c2,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_1384,c_898]) ).
tff(c_1601,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_1591,c_1591,c_1414]) ).
tff(c_1744,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1726,c_1601]) ).
tff(c_1746,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_1790,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_1746,c_10]) ).
tff(c_8,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1760,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_1746,c_8]) ).
tff(c_1764,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_1760,c_4]) ).
tff(c_1800,plain,
! [X_52,Y_53,Z_54] : ( multiply(multiply(X_52,Y_53),Z_54) = multiply(X_52,multiply(Y_53,Z_54)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1827,plain,
! [Z_54] : ( multiply(sk_c7,multiply(sk_c3,Z_54)) = multiply(identity,Z_54) ),
inference(superposition,[status(thm),theory(equality)],[c_1764,c_1800]) ).
tff(c_2331,plain,
! [Z_65] : ( multiply(sk_c7,multiply(sk_c3,Z_65)) = Z_65 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1827]) ).
tff(c_2343,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_1790,c_2331]) ).
tff(c_1778,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_1836,plain,
! [Z_54] : ( multiply(sk_c6,multiply(sk_c2,Z_54)) = multiply(identity,Z_54) ),
inference(superposition,[status(thm),theory(equality)],[c_69,c_1800]) ).
tff(c_1866,plain,
! [Z_56] : ( multiply(sk_c6,multiply(sk_c2,Z_56)) = Z_56 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1836]) ).
tff(c_1878,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_1778,c_1866]) ).
tff(c_1824,plain,
! [Z_54] : ( multiply(sk_c2,multiply(sk_c6,Z_54)) = multiply(sk_c7,Z_54) ),
inference(superposition,[status(thm),theory(equality)],[c_1778,c_1800]) ).
tff(c_2316,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_1878,c_1824]) ).
tff(c_2322,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_1778,c_2316]) ).
tff(c_2347,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2343,c_2322]) ).
tff(c_2355,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2347,c_2347,c_2343]) ).
tff(c_1839,plain,
! [X_2,Z_54] : ( multiply(inverse(X_2),multiply(X_2,Z_54)) = multiply(identity,Z_54) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1800]) ).
tff(c_2446,plain,
! [X_66,Z_67] : ( multiply(inverse(X_66),multiply(X_66,Z_67)) = Z_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1839]) ).
tff(c_2473,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2355,c_2446]) ).
tff(c_2513,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2473]) ).
tff(c_2370,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2347,c_77]) ).
tff(c_2380,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2370,c_4]) ).
tff(c_2547,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2513,c_2380]) ).
tff(c_2367,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2347,c_1746]) ).
tff(c_2586,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2547,c_2513,c_2513,c_2367]) ).
tff(c_2588,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_2593,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_2588,c_32]) ).
tff(c_2587,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_1745,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_1750,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_1745,c_4]) ).
tff(c_2609,plain,
! [X_68,Y_69,Z_70] : ( multiply(multiply(X_68,Y_69),Z_70) = multiply(X_68,multiply(Y_69,Z_70)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2636,plain,
! [Z_70] : ( multiply(sk_c7,multiply(sk_c4,Z_70)) = multiply(identity,Z_70) ),
inference(superposition,[status(thm),theory(equality)],[c_1750,c_2609]) ).
tff(c_2920,plain,
! [Z_78] : ( multiply(sk_c7,multiply(sk_c4,Z_78)) = Z_78 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2636]) ).
tff(c_2932,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_2587,c_2920]) ).
tff(c_2936,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2593,c_2932]) ).
tff(c_2598,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_1746,c_10]) ).
tff(c_2633,plain,
! [Z_70] : ( multiply(sk_c7,multiply(sk_c3,Z_70)) = multiply(identity,Z_70) ),
inference(superposition,[status(thm),theory(equality)],[c_1764,c_2609]) ).
tff(c_2685,plain,
! [Z_73] : ( multiply(sk_c7,multiply(sk_c3,Z_73)) = Z_73 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2633]) ).
tff(c_2697,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2598,c_2685]) ).
tff(c_2979,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2936,c_2936,c_2697]) ).
tff(c_2645,plain,
! [X_2,Z_70] : ( multiply(inverse(X_2),multiply(X_2,Z_70)) = multiply(identity,Z_70) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_2609]) ).
tff(c_3073,plain,
! [X_80,Z_81] : ( multiply(inverse(X_80),multiply(X_80,Z_81)) = Z_81 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2645]) ).
tff(c_3103,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_2979,c_3073]) ).
tff(c_3141,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3103]) ).
tff(c_2992,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2936,c_77]) ).
tff(c_3014,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_2992,c_4]) ).
tff(c_3174,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3141,c_3014]) ).
tff(c_2989,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2936,c_1746]) ).
tff(c_3148,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3141,c_3141,c_2989]) ).
tff(c_3307,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3174,c_3148]) ).
tff(c_3309,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_22,plain,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_3351,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_3309,c_22]) ).
tff(c_24,plain,
( ( multiply(sk_c4,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_3343,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3309,c_24]) ).
tff(c_26,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_3321,plain,
inverse(sk_c4) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_3309,c_26]) ).
tff(c_3325,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3321,c_4]) ).
tff(c_3386,plain,
! [Z_84] : ( multiply(sk_c7,multiply(sk_c4,Z_84)) = multiply(identity,Z_84) ),
inference(superposition,[status(thm),theory(equality)],[c_3325,c_3362]) ).
tff(c_3498,plain,
! [Z_87] : ( multiply(sk_c7,multiply(sk_c4,Z_87)) = Z_87 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3386]) ).
tff(c_3510,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_3343,c_3498]) ).
tff(c_3514,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3351,c_3510]) ).
tff(c_3308,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_3313,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3308,c_4]) ).
tff(c_3521,plain,
multiply(sk_c6,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3313]) ).
tff(c_20,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_3336,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_3309,c_20]) ).
tff(c_3383,plain,
! [Z_84] : ( multiply(sk_c3,multiply(sk_c6,Z_84)) = multiply(sk_c7,Z_84) ),
inference(superposition,[status(thm),theory(equality)],[c_3336,c_3362]) ).
tff(c_5091,plain,
! [Z_120] : ( multiply(sk_c3,multiply(sk_c6,Z_120)) = multiply(sk_c6,Z_120) ),
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3383]) ).
tff(c_5103,plain,
multiply(sk_c6,sk_c3) = multiply(sk_c3,identity),
inference(superposition,[status(thm),theory(equality)],[c_3521,c_5091]) ).
tff(c_5116,plain,
multiply(sk_c3,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3521,c_5103]) ).
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_5123,plain,
! [Z_5] : ( multiply(sk_c3,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_5116,c_6]) ).
tff(c_5126,plain,
! [Z_5] : ( multiply(sk_c3,Z_5) = Z_5 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_5123]) ).
tff(c_3523,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3308]) ).
tff(c_5192,plain,
! [Z_124] : ( multiply(sk_c6,multiply(sk_c3,Z_124)) = Z_124 ),
inference(superposition,[status(thm),theory(equality)],[c_3523,c_5159]) ).
tff(c_5220,plain,
! [Z_124] : ( multiply(sk_c6,Z_124) = Z_124 ),
inference(demodulation,[status(thm),theory(equality)],[c_5126,c_5192]) ).
tff(c_3516,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3351]) ).
tff(c_5189,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3516,c_5159]) ).
tff(c_5219,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5189]) ).
tff(c_5223,plain,
multiply(sk_c6,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_5219,c_3516]) ).
tff(c_5288,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5220,c_5223]) ).
tff(c_3652,plain,
! [X_91,Z_92] : ( multiply(inverse(X_91),multiply(X_91,Z_92)) = Z_92 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3395]) ).
tff(c_3917,plain,
! [X_96,Z_97] : ( multiply(inverse(inverse(X_96)),Z_97) = multiply(X_96,Z_97) ),
inference(superposition,[status(thm),theory(equality)],[c_3406,c_3652]) ).
tff(c_3703,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3652]) ).
tff(c_3924,plain,
! [X_96] : ( multiply(X_96,identity) = X_96 ),
inference(superposition,[status(thm),theory(equality)],[c_3917,c_3703]) ).
tff(c_3584,plain,
! [Z_88] : ( multiply(sk_c3,multiply(sk_c6,Z_88)) = multiply(sk_c6,Z_88) ),
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3383]) ).
tff(c_3596,plain,
multiply(sk_c6,sk_c3) = multiply(sk_c3,identity),
inference(superposition,[status(thm),theory(equality)],[c_3521,c_3584]) ).
tff(c_3609,plain,
multiply(sk_c3,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3521,c_3596]) ).
tff(c_3616,plain,
! [Z_5] : ( multiply(sk_c3,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_3609,c_6]) ).
tff(c_3619,plain,
! [Z_5] : ( multiply(sk_c3,Z_5) = Z_5 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_3616]) ).
tff(c_3685,plain,
! [Z_92] : ( multiply(sk_c6,multiply(sk_c3,Z_92)) = Z_92 ),
inference(superposition,[status(thm),theory(equality)],[c_3523,c_3652]) ).
tff(c_3713,plain,
! [Z_92] : ( multiply(sk_c6,Z_92) = Z_92 ),
inference(demodulation,[status(thm),theory(equality)],[c_3619,c_3685]) ).
tff(c_3682,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3516,c_3652]) ).
tff(c_3712,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_3682]) ).
tff(c_3716,plain,
multiply(sk_c6,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3712,c_3516]) ).
tff(c_3781,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3713,c_3716]) ).
tff(c_3409,plain,
! [Z_85] : ( multiply(sk_c7,multiply(sk_c4,Z_85)) = Z_85 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3386]) ).
tff(c_3421,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_3343,c_3409]) ).
tff(c_3425,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3351,c_3421]) ).
tff(c_3434,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3425,c_3308]) ).
tff(c_3429,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_3425,c_3336]) ).
tff(c_3408,plain,
! [X3_7] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_3477,plain,
! [X3_86] :
( ( inverse(X3_86) != sk_c6 )
| ( multiply(X3_86,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3425,c_3425,c_3408]) ).
tff(c_3480,plain,
inverse(sk_c3) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3429,c_3477]) ).
tff(c_3496,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3434,c_3480]) ).
tff(c_3497,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_3565,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3514,c_3514,c_3514,c_3514,c_3514,c_3514,c_3497]) ).
tff(c_3566,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_3565]) ).
tff(c_5070,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_3924,c_3781,c_3781,c_2,c_3781,c_3781,c_3566]) ).
tff(c_3782,plain,
! [Z_94] : ( multiply(sk_c6,Z_94) = Z_94 ),
inference(demodulation,[status(thm),theory(equality)],[c_3619,c_3685]) ).
tff(c_3794,plain,
sk_c3 = identity,
inference(superposition,[status(thm),theory(equality)],[c_3782,c_3521]) ).
tff(c_3827,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3781,c_3523]) ).
tff(c_3876,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_3794,c_3827]) ).
tff(c_5072,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5070,c_3876]) ).
tff(c_5073,plain,
! [X1_8,X4_10] :
( ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_3565]) ).
tff(c_8677,plain,
! [X1_8,X4_10] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5431,c_5288,c_5288,c_5288,c_5288,c_5431,c_5288,c_5288,c_5073]) ).
tff(c_8679,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8677]) ).
tff(c_5289,plain,
! [Z_126] : ( multiply(sk_c6,Z_126) = Z_126 ),
inference(demodulation,[status(thm),theory(equality)],[c_5126,c_5192]) ).
tff(c_5301,plain,
sk_c3 = identity,
inference(superposition,[status(thm),theory(equality)],[c_5289,c_3521]) ).
tff(c_5334,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5288,c_3523]) ).
tff(c_5383,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5301,c_5334]) ).
tff(c_8681,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8679,c_5383]) ).
tff(c_8683,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_8677]) ).
tff(c_8685,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8683,c_5383]) ).
tff(c_8687,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_42,plain,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_8726,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_8687,c_42]) ).
tff(c_44,plain,
( ( multiply(sk_c4,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_8734,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_8687,c_44]) ).
tff(c_8686,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_8691,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8686,c_4]) ).
tff(c_8782,plain,
! [Z_182] : ( multiply(sk_c7,multiply(sk_c4,Z_182)) = multiply(identity,Z_182) ),
inference(superposition,[status(thm),theory(equality)],[c_8691,c_8752]) ).
tff(c_8964,plain,
! [Z_188] : ( multiply(sk_c7,multiply(sk_c4,Z_188)) = Z_188 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8782]) ).
tff(c_8976,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_8734,c_8964]) ).
tff(c_8980,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8726,c_8976]) ).
tff(c_40,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_8741,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8687,c_40]) ).
tff(c_38,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_8712,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8687,c_38]) ).
tff(c_8716,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8712,c_4]) ).
tff(c_8776,plain,
! [Z_182] : ( multiply(sk_c7,multiply(sk_c3,Z_182)) = multiply(identity,Z_182) ),
inference(superposition,[status(thm),theory(equality)],[c_8716,c_8752]) ).
tff(c_8798,plain,
! [Z_183] : ( multiply(sk_c7,multiply(sk_c3,Z_183)) = Z_183 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8776]) ).
tff(c_8810,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8741,c_8798]) ).
tff(c_8996,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8980,c_8980,c_8810]) ).
tff(c_10496,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8996,c_8796]) ).
tff(c_10502,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10496]) ).
tff(c_9089,plain,
! [X_190,Z_191] : ( multiply(inverse(X_190),multiply(X_190,Z_191)) = Z_191 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8785]) ).
tff(c_9409,plain,
! [X_195,Z_196] : ( multiply(inverse(inverse(X_195)),Z_196) = multiply(X_195,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_8796,c_9089]) ).
tff(c_9140,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9089]) ).
tff(c_9416,plain,
! [X_195] : ( multiply(X_195,identity) = X_195 ),
inference(superposition,[status(thm),theory(equality)],[c_9409,c_9140]) ).
tff(c_9116,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8996,c_9089]) ).
tff(c_9148,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9116]) ).
tff(c_8822,plain,
! [Z_184] : ( multiply(sk_c7,multiply(sk_c4,Z_184)) = Z_184 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8782]) ).
tff(c_8834,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_8734,c_8822]) ).
tff(c_8838,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8726,c_8834]) ).
tff(c_8846,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8838,c_8712]) ).
tff(c_8842,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8838,c_8741]) ).
tff(c_8814,plain,
! [X3_7] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_8855,plain,
! [X3_7] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8838,c_8838,c_8814]) ).
tff(c_8945,plain,
inverse(sk_c3) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8842,c_8855]) ).
tff(c_8955,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8846,c_8945]) ).
tff(c_8956,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X5_6) != sk_c7 )
| ( multiply(sk_c7,multiply(X5_6,sk_c7)) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_9040,plain,
! [X4_10,X1_8,X5_6] :
( ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8980,c_8980,c_8980,c_8980,c_8980,c_8980,c_8956]) ).
tff(c_9041,plain,
! [X5_6] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_9040]) ).
tff(c_10416,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9416,c_9148,c_9148,c_2,c_9148,c_9148,c_9041]) ).
tff(c_9004,plain,
multiply(sk_c6,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8980,c_8691]) ).
tff(c_9157,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9148,c_9004]) ).
tff(c_9276,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_9157,c_8796]) ).
tff(c_9288,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9276]) ).
tff(c_9006,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8980,c_8686]) ).
tff(c_9159,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9148,c_9006]) ).
tff(c_9293,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9288,c_9159]) ).
tff(c_10418,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10416,c_9293]) ).
tff(c_10419,plain,
! [X1_8,X4_10] :
( ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_9040]) ).
tff(c_14226,plain,
! [X1_8,X4_10] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10694,c_10502,c_10502,c_10502,c_10502,c_10694,c_10502,c_10502,c_10419]) ).
tff(c_14228,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_14226]) ).
tff(c_9002,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_8980,c_8712]) ).
tff(c_9014,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9002,c_4]) ).
tff(c_10584,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10502,c_9014]) ).
tff(c_10512,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10502,c_9002]) ).
tff(c_10585,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10584,c_10512]) ).
tff(c_14230,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14228,c_10585]) ).
tff(c_14232,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_14226]) ).
tff(c_14234,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14232,c_10585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP215-1 : 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
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 3 21:57:33 EDT 2023
% 0.17/0.34 % CPUTime :
% 8.99/3.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.09/3.18
% 9.09/3.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.36/3.23
% 9.36/3.23 Inference rules
% 9.36/3.23 ----------------------
% 9.36/3.23 #Ref : 0
% 9.36/3.23 #Sup : 3604
% 9.36/3.23 #Fact : 0
% 9.36/3.23 #Define : 0
% 9.36/3.23 #Split : 26
% 9.36/3.23 #Chain : 0
% 9.36/3.23 #Close : 0
% 9.36/3.23
% 9.36/3.23 Ordering : KBO
% 9.36/3.23
% 9.36/3.23 Simplification rules
% 9.36/3.23 ----------------------
% 9.36/3.23 #Subsume : 5
% 9.36/3.23 #Demod : 5281
% 9.36/3.23 #Tautology : 2790
% 9.36/3.23 #SimpNegUnit : 31
% 9.36/3.23 #BackRed : 349
% 9.36/3.23
% 9.36/3.23 #Partial instantiations: 0
% 9.36/3.23 #Strategies tried : 1
% 9.36/3.23
% 9.36/3.23 Timing (in seconds)
% 9.36/3.23 ----------------------
% 9.36/3.23 Preprocessing : 0.51
% 9.36/3.23 Parsing : 0.22
% 9.36/3.23 CNF conversion : 0.03
% 9.36/3.23 Main loop : 1.62
% 9.36/3.23 Inferencing : 0.59
% 9.36/3.23 Reduction : 0.62
% 9.36/3.23 Demodulation : 0.50
% 9.36/3.23 BG Simplification : 0.06
% 9.36/3.23 Subsumption : 0.20
% 9.36/3.23 Abstraction : 0.08
% 9.36/3.23 MUC search : 0.00
% 9.36/3.23 Cooper : 0.00
% 9.36/3.23 Total : 2.23
% 9.36/3.23 Index Insertion : 0.00
% 9.36/3.23 Index Deletion : 0.00
% 9.36/3.23 Index Matching : 0.00
% 9.36/3.23 BG Taut test : 0.00
%------------------------------------------------------------------------------