TSTP Solution File: GRP352-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP352-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n023.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 10:41:02 EDT 2023
% Result : Unsatisfiable 15.70s 6.65s
% Output : CNFRefutation 15.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 38
% Syntax : Number of formulae : 484 ( 394 unt; 10 typ; 0 def)
% Number of atoms : 659 ( 632 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 401 ( 216 ~; 185 |; 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 : 233 (; 233 !; 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_113,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_167,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c5 )
| ( inverse(X4) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c4,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = 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_22494,plain,
! [X_310,Y_311,Z_312] : ( multiply(multiply(X_310,Y_311),Z_312) = multiply(X_310,multiply(Y_311,Z_312)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22527,plain,
! [X_2,Z_312] : ( multiply(inverse(X_2),multiply(X_2,Z_312)) = multiply(identity,Z_312) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22494]) ).
tff(c_22910,plain,
! [X_318,Z_319] : ( multiply(inverse(X_318),multiply(X_318,Z_319)) = Z_319 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22527]) ).
tff(c_22538,plain,
! [X_2,Z_312] : ( multiply(inverse(X_2),multiply(X_2,Z_312)) = Z_312 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22527]) ).
tff(c_23189,plain,
! [X_321,Z_322] : ( multiply(inverse(inverse(X_321)),Z_322) = multiply(X_321,Z_322) ),
inference(superposition,[status(thm),theory(equality)],[c_22910,c_22538]) ).
tff(c_22958,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22910]) ).
tff(c_23196,plain,
! [X_321] : ( multiply(X_321,identity) = X_321 ),
inference(superposition,[status(thm),theory(equality)],[c_23189,c_22958]) ).
tff(c_7497,plain,
! [X_168,Y_169,Z_170] : ( multiply(multiply(X_168,Y_169),Z_170) = multiply(X_168,multiply(Y_169,Z_170)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_7530,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_7497]) ).
tff(c_7962,plain,
! [X_177,Z_178] : ( multiply(inverse(X_177),multiply(X_177,Z_178)) = Z_178 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7530]) ).
tff(c_7541,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = Z_170 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7530]) ).
tff(c_8298,plain,
! [X_182,Z_183] : ( multiply(inverse(inverse(X_182)),Z_183) = multiply(X_182,Z_183) ),
inference(superposition,[status(thm),theory(equality)],[c_7962,c_7541]) ).
tff(c_8004,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_7962]) ).
tff(c_8305,plain,
! [X_182] : ( multiply(X_182,identity) = X_182 ),
inference(superposition,[status(thm),theory(equality)],[c_8298,c_8004]) ).
tff(c_40,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_4353,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_50,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_75,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_79,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).
tff(c_4395,plain,
! [X_94,Y_95,Z_96] : ( multiply(multiply(X_94,Y_95),Z_96) = multiply(X_94,multiply(Y_95,Z_96)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4434,plain,
! [Z_96] : ( multiply(sk_c6,multiply(sk_c2,Z_96)) = multiply(identity,Z_96) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_4395]) ).
tff(c_4464,plain,
! [Z_98] : ( multiply(sk_c6,multiply(sk_c2,Z_98)) = Z_98 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4434]) ).
tff(c_4476,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4353,c_4464]) ).
tff(c_4437,plain,
! [X_2,Z_96] : ( multiply(inverse(X_2),multiply(X_2,Z_96)) = multiply(identity,Z_96) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4395]) ).
tff(c_4573,plain,
! [X_100,Z_101] : ( multiply(inverse(X_100),multiply(X_100,Z_101)) = Z_101 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4437]) ).
tff(c_4606,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_4476,c_4573]) ).
tff(c_4638,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4606]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_102,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_4480,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4476,c_102]) ).
tff(c_116,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_134,plain,
! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_161,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_134]) ).
tff(c_519,plain,
! [Z_24] : ( multiply(sk_c6,multiply(sk_c2,Z_24)) = Z_24 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_531,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_116,c_519]) ).
tff(c_561,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_531,c_102]) ).
tff(c_179,plain,
! [Z_15] : ( multiply(sk_c6,multiply(sk_c2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_191,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_116,c_179]) ).
tff(c_195,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_191,c_102]) ).
tff(c_30,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_87,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_223,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_195,c_87]) ).
tff(c_26,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_108,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_221,plain,
multiply(sk_c1,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_195,c_108]) ).
tff(c_164,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_134]) ).
tff(c_250,plain,
! [X_17,Z_18] : ( multiply(inverse(X_17),multiply(X_17,Z_18)) = Z_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_268,plain,
multiply(inverse(sk_c1),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_221,c_250]) ).
tff(c_302,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_223,c_268]) ).
tff(c_277,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_191,c_250]) ).
tff(c_303,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_277]) ).
tff(c_58,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_177,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_58]) ).
tff(c_178,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitLeft,[status(thm)],[c_177]) ).
tff(c_220,plain,
multiply(sk_c6,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_195,c_178]) ).
tff(c_306,plain,
multiply(sk_c6,sk_c6) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_303,c_220]) ).
tff(c_342,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_302,c_306]) ).
tff(c_174,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_346,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_302,c_174]) ).
tff(c_352,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_346]) ).
tff(c_354,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_342,c_352]) ).
tff(c_356,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_572,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_356]) ).
tff(c_91,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_87,c_4]) ).
tff(c_158,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_134]) ).
tff(c_496,plain,
! [Z_23] : ( multiply(sk_c7,multiply(sk_c1,Z_23)) = Z_23 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_158]) ).
tff(c_508,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_108,c_496]) ).
tff(c_570,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_561,c_508]) ).
tff(c_1107,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_572,c_570]) ).
tff(c_1108,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1107,c_1107,c_572]) ).
tff(c_1200,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_1108,c_174]) ).
tff(c_1206,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1200]) ).
tff(c_1214,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1206,c_1107]) ).
tff(c_1122,plain,
! [X_36,Z_37] : ( multiply(inverse(X_36),multiply(X_36,Z_37)) = Z_37 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_1354,plain,
! [X_40,Z_41] : ( multiply(inverse(inverse(X_40)),Z_41) = multiply(X_40,Z_41) ),
inference(superposition,[status(thm),theory(equality)],[c_174,c_1122]) ).
tff(c_1143,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1122]) ).
tff(c_1361,plain,
! [X_40] : ( multiply(X_40,identity) = X_40 ),
inference(superposition,[status(thm),theory(equality)],[c_1354,c_1143]) ).
tff(c_676,plain,
! [X_26,Z_27] : ( multiply(inverse(X_26),multiply(X_26,Z_27)) = Z_27 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_164]) ).
tff(c_835,plain,
! [X_29,Z_30] : ( multiply(inverse(inverse(X_29)),Z_30) = multiply(X_29,Z_30) ),
inference(superposition,[status(thm),theory(equality)],[c_174,c_676]) ).
tff(c_715,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_676]) ).
tff(c_842,plain,
! [X_29] : ( multiply(X_29,identity) = X_29 ),
inference(superposition,[status(thm),theory(equality)],[c_835,c_715]) ).
tff(c_611,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_572,c_570]) ).
tff(c_617,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_611,c_611,c_531]) ).
tff(c_694,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_617,c_676]) ).
tff(c_722,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_694]) ).
tff(c_731,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_722,c_611]) ).
tff(c_388,plain,
! [Z_20] : ( multiply(sk_c6,multiply(sk_c2,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_161]) ).
tff(c_400,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_116,c_388]) ).
tff(c_430,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_400,c_102]) ).
tff(c_444,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_430,c_87]) ).
tff(c_442,plain,
multiply(sk_c1,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_430,c_108]) ).
tff(c_355,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_364,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_355]) ).
tff(c_472,plain,
! [X2_22] :
( ( inverse(X2_22) != sk_c6 )
| ( multiply(X2_22,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_364]) ).
tff(c_475,plain,
inverse(sk_c1) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_442,c_472]) ).
tff(c_494,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_444,c_475]) ).
tff(c_495,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_355]) ).
tff(c_602,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_561,c_561,c_561,c_561,c_495]) ).
tff(c_603,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_602]) ).
tff(c_1096,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_842,c_731,c_731,c_731,c_603]) ).
tff(c_621,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_611,c_75]) ).
tff(c_642,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_621,c_4]) ).
tff(c_745,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_722,c_642]) ).
tff(c_728,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_722,c_621]) ).
tff(c_760,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_745,c_728]) ).
tff(c_1098,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1096,c_760]) ).
tff(c_1099,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_602]) ).
tff(c_3810,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1214,c_1361,c_1214,c_1214,c_1361,c_1214,c_1206,c_1214,c_1099]) ).
tff(c_3812,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_3810]) ).
tff(c_575,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_87]) ).
tff(c_1111,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1107,c_575]) ).
tff(c_1170,plain,
multiply(sk_c5,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_1111,c_4]) ).
tff(c_1267,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1206,c_1170]) ).
tff(c_1211,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1206,c_1111]) ).
tff(c_1268,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1267,c_1211]) ).
tff(c_3814,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3812,c_1268]) ).
tff(c_3816,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_3810]) ).
tff(c_3818,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3816,c_1268]) ).
tff(c_3820,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_38,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_3861,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_3820,c_38]) ).
tff(c_44,plain,
( ( multiply(sk_c4,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_3855,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_3820,c_44]) ).
tff(c_46,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_3828,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_46]) ).
tff(c_3834,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3828,c_3820]) ).
tff(c_3835,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_3840,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3835,c_4]) ).
tff(c_3876,plain,
! [X_83,Y_84,Z_85] : ( multiply(multiply(X_83,Y_84),Z_85) = multiply(X_83,multiply(Y_84,Z_85)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_3900,plain,
! [Z_85] : ( multiply(sk_c6,multiply(sk_c4,Z_85)) = multiply(identity,Z_85) ),
inference(superposition,[status(thm),theory(equality)],[c_3840,c_3876]) ).
tff(c_3968,plain,
! [Z_88] : ( multiply(sk_c6,multiply(sk_c4,Z_88)) = Z_88 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3900]) ).
tff(c_3980,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_3855,c_3968]) ).
tff(c_3984,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3861,c_3980]) ).
tff(c_3912,plain,
! [Z_85] : ( multiply(sk_c7,multiply(sk_c1,Z_85)) = multiply(identity,Z_85) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_3876]) ).
tff(c_3932,plain,
! [Z_86] : ( multiply(sk_c7,multiply(sk_c1,Z_86)) = Z_86 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_3912]) ).
tff(c_3944,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_108,c_3932]) ).
tff(c_3987,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_3984,c_3944]) ).
tff(c_3918,plain,
! [X_2,Z_85] : ( multiply(inverse(X_2),multiply(X_2,Z_85)) = multiply(identity,Z_85) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_3876]) ).
tff(c_4181,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_3918]) ).
tff(c_4199,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_3987,c_4181]) ).
tff(c_4236,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4199]) ).
tff(c_3997,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3984,c_75]) ).
tff(c_4155,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_3997,c_4]) ).
tff(c_4261,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4236,c_4155]) ).
tff(c_3992,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_3984,c_3820]) ).
tff(c_4337,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4261,c_4236,c_4236,c_3992]) ).
tff(c_4339,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_18,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_4387,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_4339,c_18]) ).
tff(c_4495,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4480,c_4387]) ).
tff(c_4672,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4638,c_4495]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_4358,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_4339,c_20]) ).
tff(c_4499,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4480,c_4358]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_4382,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_4339,c_22]) ).
tff(c_4496,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4480,c_4382]) ).
tff(c_4449,plain,
! [X_2,Z_96] : ( multiply(inverse(X_2),multiply(X_2,Z_96)) = Z_96 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4437]) ).
tff(c_4652,plain,
multiply(inverse(sk_c3),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4496,c_4449]) ).
tff(c_4658,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4499,c_4652]) ).
tff(c_4714,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4672,c_4658]) ).
tff(c_4501,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4480,c_91]) ).
tff(c_4721,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4714,c_4501]) ).
tff(c_4879,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_4721,c_4449]) ).
tff(c_4891,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4879]) ).
tff(c_4500,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_4480,c_4339]) ).
tff(c_4719,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_4714,c_4714,c_4500]) ).
tff(c_4913,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4891,c_4719]) ).
tff(c_4914,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_4915,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_42,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_4946,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_4915,c_42]) ).
tff(c_4934,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_4915,c_38]) ).
tff(c_24,plain,
( ( multiply(sk_c4,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_4939,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_4339,c_24]) ).
tff(c_4338,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_4344,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4338,c_4]) ).
tff(c_4958,plain,
! [X_103,Y_104,Z_105] : ( multiply(multiply(X_103,Y_104),Z_105) = multiply(X_103,multiply(Y_104,Z_105)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4985,plain,
! [Z_105] : ( multiply(sk_c6,multiply(sk_c4,Z_105)) = multiply(identity,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_4344,c_4958]) ).
tff(c_5577,plain,
! [Z_123] : ( multiply(sk_c6,multiply(sk_c4,Z_123)) = Z_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4985]) ).
tff(c_5589,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4939,c_5577]) ).
tff(c_5593,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4934,c_5589]) ).
tff(c_5613,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5593,c_4934]) ).
tff(c_4997,plain,
! [X_2,Z_105] : ( multiply(inverse(X_2),multiply(X_2,Z_105)) = multiply(identity,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4958]) ).
tff(c_5714,plain,
! [X_126,Z_127] : ( multiply(inverse(X_126),multiply(X_126,Z_127)) = Z_127 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4997]) ).
tff(c_5732,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5613,c_5714]) ).
tff(c_5784,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5732]) ).
tff(c_5617,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5593,c_4338]) ).
tff(c_5612,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_5593,c_4939]) ).
tff(c_5416,plain,
! [Z_118] : ( multiply(sk_c6,multiply(sk_c4,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4985]) ).
tff(c_5428,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4939,c_5416]) ).
tff(c_5432,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4934,c_5428]) ).
tff(c_5443,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_4338]) ).
tff(c_5438,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_4939]) ).
tff(c_5076,plain,
! [Z_110] : ( multiply(sk_c6,multiply(sk_c4,Z_110)) = Z_110 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4985]) ).
tff(c_5088,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4939,c_5076]) ).
tff(c_5092,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_4934,c_5088]) ).
tff(c_5099,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5092,c_4934]) ).
tff(c_5196,plain,
! [X_112,Z_113] : ( multiply(inverse(X_112),multiply(X_112,Z_113)) = Z_113 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4997]) ).
tff(c_5214,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5099,c_5196]) ).
tff(c_5266,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_5214]) ).
tff(c_4919,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_4914,c_4]) ).
tff(c_4982,plain,
! [Z_105] : ( multiply(sk_c7,multiply(sk_c3,Z_105)) = multiply(identity,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_4919,c_4958]) ).
tff(c_5040,plain,
! [Z_108] : ( multiply(sk_c7,multiply(sk_c3,Z_108)) = Z_108 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4982]) ).
tff(c_5052,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4946,c_5040]) ).
tff(c_5094,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5092,c_5052]) ).
tff(c_5276,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5266,c_5266,c_5094]) ).
tff(c_5284,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5276]) ).
tff(c_5103,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5092,c_4338]) ).
tff(c_5114,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_5103,c_4]) ).
tff(c_5302,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5284,c_5114]) ).
tff(c_5292,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5284,c_5103]) ).
tff(c_5317,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5302,c_5292]) ).
tff(c_5012,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_4934,c_58]) ).
tff(c_5013,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_5012]) ).
tff(c_5125,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5092,c_5013]) ).
tff(c_5148,plain,
inverse(sk_c7) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5094,c_5125]) ).
tff(c_5275,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_5266,c_5266,c_5148]) ).
tff(c_5351,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5317,c_5275]) ).
tff(c_5352,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_5012]) ).
tff(c_5353,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_5352]) ).
tff(c_5465,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5432,c_5432,c_5353]) ).
tff(c_5516,plain,
inverse(sk_c4) != sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_5438,c_5465]) ).
tff(c_5525,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5443,c_5516]) ).
tff(c_5526,plain,
! [X1_8,X4_7] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_5352]) ).
tff(c_5553,plain,
! [X4_7] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_5526]) ).
tff(c_5649,plain,
! [X4_7] :
( ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5593,c_5593,c_5553]) ).
tff(c_5681,plain,
( ( inverse(sk_c4) != sk_c5 )
| ( sk_c7 != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_5612,c_5649]) ).
tff(c_5688,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5617,c_5681]) ).
tff(c_5790,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_5784,c_5688]) ).
tff(c_5554,plain,
! [Z_122] : ( multiply(sk_c7,multiply(sk_c3,Z_122)) = Z_122 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_4982]) ).
tff(c_5566,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_4946,c_5554]) ).
tff(c_5609,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5593,c_5566]) ).
tff(c_5826,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_5784,c_2,c_5784,c_5609]) ).
tff(c_5827,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5790,c_5826]) ).
tff(c_5869,plain,
! [X1_130] :
( ( multiply(X1_130,sk_c6) != sk_c7 )
| ( inverse(X1_130) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_5526]) ).
tff(c_5876,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_4946,c_5869]) ).
tff(c_5891,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4914,c_5876]) ).
tff(c_5893,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_7116,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_5893,c_8]) ).
tff(c_6762,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_5893,c_8]) ).
tff(c_5940,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_5893,c_8]) ).
tff(c_14,plain,
( ( multiply(sk_c4,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_5945,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_5893,c_14]) ).
tff(c_16,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_5911,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_5893,c_16]) ).
tff(c_5915,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_5911,c_4]) ).
tff(c_5955,plain,
! [X_131,Y_132,Z_133] : ( multiply(multiply(X_131,Y_132),Z_133) = multiply(X_131,multiply(Y_132,Z_133)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_5982,plain,
! [Z_133] : ( multiply(sk_c6,multiply(sk_c4,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_5915,c_5955]) ).
tff(c_6060,plain,
! [Z_136] : ( multiply(sk_c6,multiply(sk_c4,Z_136)) = Z_136 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5982]) ).
tff(c_6072,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_5945,c_6060]) ).
tff(c_6076,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_5940,c_6072]) ).
tff(c_6114,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6076,c_5940]) ).
tff(c_5997,plain,
! [X_2,Z_133] : ( multiply(inverse(X_2),multiply(X_2,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_5955]) ).
tff(c_6009,plain,
! [X_2,Z_133] : ( multiply(inverse(X_2),multiply(X_2,Z_133)) = Z_133 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5997]) ).
tff(c_6237,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_6114,c_6009]) ).
tff(c_6243,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6237]) ).
tff(c_5931,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_5994,plain,
! [Z_133] : ( multiply(sk_c6,multiply(sk_c2,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_5955]) ).
tff(c_6034,plain,
! [Z_135] : ( multiply(sk_c6,multiply(sk_c2,Z_135)) = Z_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5994]) ).
tff(c_6046,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_5931,c_6034]) ).
tff(c_6052,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_6046,c_5893]) ).
tff(c_6108,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6076,c_6052]) ).
tff(c_6248,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_6243,c_6108]) ).
tff(c_5906,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_5991,plain,
! [Z_133] : ( multiply(sk_c7,multiply(sk_c1,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_5955]) ).
tff(c_6011,plain,
! [Z_134] : ( multiply(sk_c7,multiply(sk_c1,Z_134)) = Z_134 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5991]) ).
tff(c_6023,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5906,c_6011]) ).
tff(c_6111,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_6076,c_6023]) ).
tff(c_6304,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_6243,c_2,c_6243,c_6111]) ).
tff(c_6305,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6248,c_6304]) ).
tff(c_6307,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_6313,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_6307,c_38]) ).
tff(c_6306,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_6330,plain,
! [X_141,Y_142,Z_143] : ( multiply(multiply(X_141,Y_142),Z_143) = multiply(X_141,multiply(Y_142,Z_143)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_6354,plain,
! [Z_143] : ( multiply(sk_c6,multiply(sk_c4,Z_143)) = multiply(identity,Z_143) ),
inference(superposition,[status(thm),theory(equality)],[c_5915,c_6330]) ).
tff(c_6444,plain,
! [Z_147] : ( multiply(sk_c6,multiply(sk_c4,Z_147)) = Z_147 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6354]) ).
tff(c_6456,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_6306,c_6444]) ).
tff(c_6460,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6313,c_6456]) ).
tff(c_6363,plain,
! [Z_143] : ( multiply(sk_c7,multiply(sk_c1,Z_143)) = multiply(identity,Z_143) ),
inference(superposition,[status(thm),theory(equality)],[c_91,c_6330]) ).
tff(c_6383,plain,
! [Z_144] : ( multiply(sk_c7,multiply(sk_c1,Z_144)) = Z_144 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6363]) ).
tff(c_6395,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_5906,c_6383]) ).
tff(c_6464,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_6460,c_6395]) ).
tff(c_6369,plain,
! [X_2,Z_143] : ( multiply(inverse(X_2),multiply(X_2,Z_143)) = multiply(identity,Z_143) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_6330]) ).
tff(c_6381,plain,
! [X_2,Z_143] : ( multiply(inverse(X_2),multiply(X_2,Z_143)) = Z_143 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6369]) ).
tff(c_6662,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_6464,c_6381]) ).
tff(c_6669,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6662]) ).
tff(c_6472,plain,
multiply(sk_c5,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_6460,c_5893]) ).
tff(c_6679,plain,
multiply(identity,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_6669,c_6669,c_6472]) ).
tff(c_6684,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6679]) ).
tff(c_6466,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6460,c_6313]) ).
tff(c_6721,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_6669,c_2,c_6669,c_6466]) ).
tff(c_6722,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6684,c_6721]) ).
tff(c_6724,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_6753,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_6724,c_24]) ).
tff(c_6723,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_6728,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_6723,c_4]) ).
tff(c_6774,plain,
! [X_151,Y_152,Z_153] : ( multiply(multiply(X_151,Y_152),Z_153) = multiply(X_151,multiply(Y_152,Z_153)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_6801,plain,
! [Z_153] : ( multiply(sk_c6,multiply(sk_c4,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_6728,c_6774]) ).
tff(c_6866,plain,
! [Z_156] : ( multiply(sk_c6,multiply(sk_c4,Z_156)) = Z_156 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6801]) ).
tff(c_6878,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_6753,c_6866]) ).
tff(c_6882,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6762,c_6878]) ).
tff(c_6887,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6762]) ).
tff(c_6813,plain,
! [X_2,Z_153] : ( multiply(inverse(X_2),multiply(X_2,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_6774]) ).
tff(c_6825,plain,
! [X_2,Z_153] : ( multiply(inverse(X_2),multiply(X_2,Z_153)) = Z_153 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6813]) ).
tff(c_7001,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_6887,c_6825]) ).
tff(c_7007,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7001]) ).
tff(c_6752,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_6810,plain,
! [Z_153] : ( multiply(sk_c6,multiply(sk_c2,Z_153)) = multiply(identity,Z_153) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_6774]) ).
tff(c_6840,plain,
! [Z_155] : ( multiply(sk_c6,multiply(sk_c2,Z_155)) = Z_155 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6810]) ).
tff(c_6852,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_6752,c_6840]) ).
tff(c_6858,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_6852,c_5893]) ).
tff(c_6884,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6858]) ).
tff(c_7012,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_7007,c_6884]) ).
tff(c_6885,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_6882,c_6882,c_6852]) ).
tff(c_7100,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_6885,c_6825]) ).
tff(c_7107,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7100]) ).
tff(c_7109,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7012,c_7107]) ).
tff(c_7110,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_7131,plain,
! [X_160,Y_161,Z_162] : ( multiply(multiply(X_160,Y_161),Z_162) = multiply(X_160,multiply(Y_161,Z_162)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_7155,plain,
! [Z_162] : ( multiply(sk_c6,multiply(sk_c4,Z_162)) = multiply(identity,Z_162) ),
inference(superposition,[status(thm),theory(equality)],[c_6728,c_7131]) ).
tff(c_7207,plain,
! [Z_165] : ( multiply(sk_c6,multiply(sk_c4,Z_165)) = Z_165 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7155]) ).
tff(c_7219,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7110,c_7207]) ).
tff(c_7223,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7116,c_7219]) ).
tff(c_7228,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7223,c_7116]) ).
tff(c_7167,plain,
! [X_2,Z_162] : ( multiply(inverse(X_2),multiply(X_2,Z_162)) = multiply(identity,Z_162) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_7131]) ).
tff(c_7179,plain,
! [X_2,Z_162] : ( multiply(inverse(X_2),multiply(X_2,Z_162)) = Z_162 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7167]) ).
tff(c_7343,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_7228,c_7179]) ).
tff(c_7349,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7343]) ).
tff(c_5892,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_7356,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_7349,c_5892]) ).
tff(c_6746,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_6724,c_22]) ).
tff(c_7231,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_7223,c_6746]) ).
tff(c_7384,plain,
multiply(sk_c3,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_7349,c_7231]) ).
tff(c_7388,plain,
multiply(inverse(sk_c3),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_7384,c_7179]) ).
tff(c_7394,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7356,c_7388]) ).
tff(c_7235,plain,
multiply(sk_c5,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_7223,c_5893]) ).
tff(c_7434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7394,c_2,c_7394,c_7349,c_7235]) ).
tff(c_7436,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_28,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_7469,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_7436,c_28]) ).
tff(c_34,plain,
( ( multiply(sk_c4,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_7481,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_7436,c_34]) ).
tff(c_36,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_7444,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_7445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7436,c_7444]) ).
tff(c_7446,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_7451,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7446,c_4]) ).
tff(c_7521,plain,
! [Z_170] : ( multiply(sk_c6,multiply(sk_c4,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_7451,c_7497]) ).
tff(c_7543,plain,
! [Z_171] : ( multiply(sk_c6,multiply(sk_c4,Z_171)) = Z_171 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7521]) ).
tff(c_7555,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_7481,c_7543]) ).
tff(c_7559,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7469,c_7555]) ).
tff(c_7562,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7559,c_7469]) ).
tff(c_7986,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_7562,c_7962]) ).
tff(c_8012,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7986]) ).
tff(c_7435,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_32,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_7464,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_7436,c_32]) ).
tff(c_7563,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_7559,c_7464]) ).
tff(c_7983,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_7563,c_7962]) ).
tff(c_8011,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7435,c_7983]) ).
tff(c_8133,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8012,c_2,c_8012,c_8011]) ).
tff(c_7651,plain,
! [X_173,Z_174] : ( multiply(inverse(X_173),multiply(X_173,Z_174)) = Z_174 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7530]) ).
tff(c_7687,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_7562,c_7651]) ).
tff(c_7714,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_7687]) ).
tff(c_7440,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7435,c_4]) ).
tff(c_7524,plain,
! [Z_170] : ( multiply(sk_c7,multiply(sk_c3,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_7440,c_7497]) ).
tff(c_7628,plain,
! [Z_172] : ( multiply(sk_c7,multiply(sk_c3,Z_172)) = Z_172 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7524]) ).
tff(c_7640,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_7563,c_7628]) ).
tff(c_7716,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_7714,c_7714,c_7640]) ).
tff(c_7725,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7716]) ).
tff(c_7594,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( multiply(sk_c5,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_7559,c_7559,c_7559,c_7559,c_7562,c_7559,c_7559,c_7559,c_7559,c_58]) ).
tff(c_7595,plain,
multiply(sk_c5,sk_c5) != sk_c7,
inference(splitLeft,[status(thm)],[c_7594]) ).
tff(c_7719,plain,
multiply(sk_c5,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_7714,c_7595]) ).
tff(c_7945,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7725,c_2,c_7725,c_7719]) ).
tff(c_7946,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_7594]) ).
tff(c_16827,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8305,c_8133,c_8012,c_8133,c_8012,c_8305,c_8133,c_8012,c_8305,c_8133,c_8133,c_8133,c_8305,c_8133,c_8012,c_8012,c_7946]) ).
tff(c_16829,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16827]) ).
tff(c_8016,plain,
multiply(identity,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8012,c_7440]) ).
tff(c_8072,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_8016,c_7541]) ).
tff(c_8084,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8072]) ).
tff(c_8018,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8012,c_7435]) ).
tff(c_8088,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8084,c_8018]) ).
tff(c_16831,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16829,c_8088]) ).
tff(c_16832,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_16827]) ).
tff(c_21607,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16832]) ).
tff(c_21609,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21607,c_8088]) ).
tff(c_21610,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_16832]) ).
tff(c_21612,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_21610]) ).
tff(c_21614,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21612,c_8088]) ).
tff(c_22420,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_21610]) ).
tff(c_22422,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22420,c_8088]) ).
tff(c_22424,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_48,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_22479,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_22424,c_48]) ).
tff(c_54,plain,
( ( multiply(sk_c4,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_22462,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22424,c_54]) ).
tff(c_56,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_22449,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22424,c_56]) ).
tff(c_22453,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22449,c_4]) ).
tff(c_22518,plain,
! [Z_312] : ( multiply(sk_c6,multiply(sk_c4,Z_312)) = multiply(identity,Z_312) ),
inference(superposition,[status(thm),theory(equality)],[c_22453,c_22494]) ).
tff(c_22540,plain,
! [Z_313] : ( multiply(sk_c6,multiply(sk_c4,Z_313)) = Z_313 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22518]) ).
tff(c_22552,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_22462,c_22540]) ).
tff(c_22556,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_22479,c_22552]) ).
tff(c_22558,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_22556,c_22479]) ).
tff(c_22970,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22558,c_22538]) ).
tff(c_22976,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22970]) ).
tff(c_22423,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_22985,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22976,c_22423]) ).
tff(c_22996,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22985,c_4]) ).
tff(c_23003,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_22996,c_22538]) ).
tff(c_23015,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23003]) ).
tff(c_52,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_22469,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22424,c_52]) ).
tff(c_22559,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22556,c_22469]) ).
tff(c_22980,plain,
multiply(sk_c3,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22976,c_22559]) ).
tff(c_23050,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23015,c_22980]) ).
tff(c_22630,plain,
! [X_315,Z_316] : ( multiply(inverse(X_315),multiply(X_315,Z_316)) = Z_316 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22527]) ).
tff(c_22663,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22558,c_22630]) ).
tff(c_22693,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22663]) ).
tff(c_22428,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22423,c_4]) ).
tff(c_22524,plain,
! [Z_312] : ( multiply(sk_c7,multiply(sk_c3,Z_312)) = multiply(identity,Z_312) ),
inference(superposition,[status(thm),theory(equality)],[c_22428,c_22494]) ).
tff(c_22607,plain,
! [Z_314] : ( multiply(sk_c7,multiply(sk_c3,Z_314)) = Z_314 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22524]) ).
tff(c_22619,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_22559,c_22607]) ).
tff(c_22695,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_22693,c_22693,c_22619]) ).
tff(c_22705,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22695]) ).
tff(c_22575,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( multiply(sk_c5,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22556,c_22556,c_22556,c_22556,c_22556,c_22556,c_22556,c_22556,c_58]) ).
tff(c_22576,plain,
multiply(sk_c5,sk_c5) != sk_c7,
inference(splitLeft,[status(thm)],[c_22575]) ).
tff(c_22697,plain,
multiply(sk_c5,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22693,c_22576]) ).
tff(c_22877,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22705,c_2,c_22705,c_22697]) ).
tff(c_22878,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c5,sk_c7) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_22575]) ).
tff(c_30926,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_23196,c_23050,c_22976,c_23050,c_22976,c_23196,c_23050,c_22976,c_23196,c_23050,c_23050,c_23050,c_23196,c_23050,c_22976,c_22976,c_23050,c_2,c_23050,c_22976,c_22878]) ).
tff(c_30928,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_30926]) ).
tff(c_23019,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23015,c_22985]) ).
tff(c_30930,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30928,c_23019]) ).
tff(c_30931,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_30926]) ).
tff(c_54730,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_30931]) ).
tff(c_54732,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54730,c_23019]) ).
tff(c_54733,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_30931]) ).
tff(c_54735,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_54733]) ).
tff(c_54737,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54735,c_23019]) ).
tff(c_54739,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_54733]) ).
tff(c_54741,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54739,c_23019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP352-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 3 22:31:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 15.70/6.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.70/6.69
% 15.70/6.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.89/6.76
% 15.89/6.76 Inference rules
% 15.89/6.76 ----------------------
% 15.89/6.76 #Ref : 0
% 15.89/6.76 #Sup : 13363
% 15.89/6.76 #Fact : 0
% 15.89/6.76 #Define : 0
% 15.89/6.76 #Split : 29
% 15.89/6.76 #Chain : 0
% 15.89/6.76 #Close : 0
% 15.89/6.76
% 15.89/6.76 Ordering : KBO
% 15.89/6.76
% 15.89/6.76 Simplification rules
% 15.89/6.76 ----------------------
% 15.89/6.76 #Subsume : 6
% 15.89/6.76 #Demod : 38275
% 15.89/6.76 #Tautology : 10766
% 15.89/6.76 #SimpNegUnit : 63
% 15.89/6.76 #BackRed : 447
% 15.89/6.76
% 15.89/6.76 #Partial instantiations: 0
% 15.89/6.76 #Strategies tried : 1
% 15.89/6.76
% 15.89/6.76 Timing (in seconds)
% 15.89/6.76 ----------------------
% 15.89/6.76 Preprocessing : 0.47
% 15.89/6.76 Parsing : 0.20
% 15.89/6.76 CNF conversion : 0.02
% 15.89/6.76 Main loop : 5.16
% 15.89/6.76 Inferencing : 1.30
% 15.89/6.76 Reduction : 3.11
% 15.89/6.76 Demodulation : 2.89
% 15.89/6.76 BG Simplification : 0.11
% 15.89/6.76 Subsumption : 0.41
% 15.89/6.76 Abstraction : 0.28
% 15.89/6.76 MUC search : 0.00
% 15.89/6.76 Cooper : 0.00
% 15.89/6.76 Total : 5.75
% 15.89/6.76 Index Insertion : 0.00
% 15.89/6.76 Index Deletion : 0.00
% 15.89/6.76 Index Matching : 0.00
% 15.89/6.76 BG Taut test : 0.00
%------------------------------------------------------------------------------