TSTP Solution File: GRP356-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP356-1 : 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 14.72s 5.66s
% Output : CNFRefutation 15.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 40
% Syntax : Number of formulae : 306 ( 226 unt; 11 typ; 0 def)
% Number of atoms : 464 ( 445 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 336 ( 167 ~; 169 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 155 (; 155 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c8 > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(sk_c8,type,
sk_c8: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X5,X3,X1,X2,X4] :
( ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c8) != sk_c6 )
| ( inverse(X4) != sk_c8 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( multiply(sk_c8,X2) != sk_c7 )
| ( multiply(X5,sk_c8) != X2 )
| ( inverse(X5) != sk_c8 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c8) = sk_c6 )
| ( inverse(sk_c4) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
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_36011,plain,
! [X_347,Y_348,Z_349] : ( multiply(multiply(X_347,Y_348),Z_349) = multiply(X_347,multiply(Y_348,Z_349)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_36047,plain,
! [X_2,Z_349] : ( multiply(inverse(X_2),multiply(X_2,Z_349)) = multiply(identity,Z_349) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_36011]) ).
tff(c_36058,plain,
! [X_2,Z_349] : ( multiply(inverse(X_2),multiply(X_2,Z_349)) = Z_349 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36047]) ).
tff(c_36244,plain,
! [X_353,Z_354] : ( multiply(inverse(X_353),multiply(X_353,Z_354)) = Z_354 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36047]) ).
tff(c_36633,plain,
! [X_358,Z_359] : ( multiply(inverse(inverse(X_358)),Z_359) = multiply(X_358,Z_359) ),
inference(superposition,[status(thm),theory(equality)],[c_36058,c_36244]) ).
tff(c_36274,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_36244]) ).
tff(c_36640,plain,
! [X_358] : ( multiply(X_358,identity) = X_358 ),
inference(superposition,[status(thm),theory(equality)],[c_36633,c_36274]) ).
tff(c_23095,plain,
! [X_218,Y_219,Z_220] : ( multiply(multiply(X_218,Y_219),Z_220) = multiply(X_218,multiply(Y_219,Z_220)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_23131,plain,
! [X_2,Z_220] : ( multiply(inverse(X_2),multiply(X_2,Z_220)) = multiply(identity,Z_220) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_23095]) ).
tff(c_23318,plain,
! [X_224,Z_225] : ( multiply(inverse(X_224),multiply(X_224,Z_225)) = Z_225 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23131]) ).
tff(c_23142,plain,
! [X_2,Z_220] : ( multiply(inverse(X_2),multiply(X_2,Z_220)) = Z_220 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23131]) ).
tff(c_23688,plain,
! [X_230,Z_231] : ( multiply(inverse(inverse(X_230)),Z_231) = multiply(X_230,Z_231) ),
inference(superposition,[status(thm),theory(equality)],[c_23318,c_23142]) ).
tff(c_23363,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_23318]) ).
tff(c_23695,plain,
! [X_230] : ( multiply(X_230,identity) = X_230 ),
inference(superposition,[status(thm),theory(equality)],[c_23688,c_23363]) ).
tff(c_149,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_179,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_149]) ).
tff(c_189,plain,
! [X_2,Z_15] : ( multiply(inverse(X_2),multiply(X_2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_179]) ).
tff(c_237,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_179]) ).
tff(c_698,plain,
! [X_24,Z_25] : ( multiply(inverse(inverse(X_24)),Z_25) = multiply(X_24,Z_25) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_237]) ).
tff(c_291,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_237]) ).
tff(c_705,plain,
! [X_24] : ( multiply(X_24,identity) = X_24 ),
inference(superposition,[status(thm),theory(equality)],[c_698,c_291]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_121,plain,
multiply(sk_c1,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_30]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_98,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_102,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_173,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_149]) ).
tff(c_191,plain,
! [Z_16] : ( multiply(sk_c7,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_173]) ).
tff(c_203,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_121,c_191]) ).
tff(c_261,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_203,c_237]) ).
tff(c_299,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_261]) ).
tff(c_66,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_85,plain,
inverse(sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_419,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_299,c_85]) ).
tff(c_430,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_419,c_4]) ).
tff(c_469,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_430,c_189]) ).
tff(c_481,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_469]) ).
tff(c_485,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_481,c_419]) ).
tff(c_547,plain,
! [X_20] : ( multiply(inverse(inverse(X_20)),identity) = X_20 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_237]) ).
tff(c_553,plain,
! [X_20] : ( multiply(inverse(inverse(inverse(X_20))),X_20) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_547,c_189]) ).
tff(c_48,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_126,plain,
multiply(sk_c2,sk_c8) = sk_c6,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_89,plain,
multiply(sk_c8,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_176,plain,
! [Z_15] : ( multiply(sk_c8,multiply(sk_c2,Z_15)) = multiply(identity,Z_15) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_149]) ).
tff(c_214,plain,
! [Z_17] : ( multiply(sk_c8,multiply(sk_c2,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_176]) ).
tff(c_226,plain,
multiply(sk_c8,sk_c6) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_126,c_214]) ).
tff(c_255,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_226,c_237]) ).
tff(c_298,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_255]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_115,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_68,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(X4_10,sk_c8) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_305,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(X4_10,sk_c8) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_115,c_68]) ).
tff(c_306,plain,
multiply(sk_c8,sk_c7) != sk_c6,
inference(splitLeft,[status(thm)],[c_305]) ).
tff(c_372,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_299,c_298,c_306]) ).
tff(c_315,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_299,c_203]) ).
tff(c_309,plain,
multiply(sk_c7,identity) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_298,c_115]) ).
tff(c_404,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_315,c_299,c_309]) ).
tff(c_405,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_372,c_404]) ).
tff(c_407,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_305]) ).
tff(c_434,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_299,c_298,c_407]) ).
tff(c_406,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c8 )
| ( inverse(X4_10) != sk_c8 )
| ( multiply(X4_10,sk_c8) != sk_c6 )
| ( inverse(X1_8) != sk_c8 )
| ( multiply(X1_8,sk_c8) != sk_c7 )
| ( inverse(X5_6) != sk_c8 )
| ( multiply(sk_c8,multiply(X5_6,sk_c8)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_305]) ).
tff(c_506,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != identity )
| ( inverse(X4_10) != identity )
| ( multiply(X4_10,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X5_6) != identity )
| ( multiply(X5_6,identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_434,c_299,c_2,c_299,c_299,c_434,c_299,c_299,c_299,c_298,c_299,c_434,c_299,c_434,c_406]) ).
tff(c_606,plain,
! [X5_22] :
( ( inverse(X5_22) != identity )
| ( multiply(X5_22,identity) != identity ) ),
inference(splitLeft,[status(thm)],[c_506]) ).
tff(c_610,plain,
inverse(inverse(inverse(inverse(identity)))) != identity,
inference(superposition,[status(thm),theory(equality)],[c_553,c_606]) ).
tff(c_629,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_485,c_485,c_485,c_485,c_610]) ).
tff(c_630,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X4_10) != identity )
| ( multiply(X4_10,identity) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_506]) ).
tff(c_20054,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_705,c_705,c_705,c_630]) ).
tff(c_20056,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_20054]) ).
tff(c_20058,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20056,c_485]) ).
tff(c_20059,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_20054]) ).
tff(c_20061,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_20059]) ).
tff(c_20063,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20061,c_485]) ).
tff(c_20846,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_20059]) ).
tff(c_20848,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20846,c_485]) ).
tff(c_20850,plain,
multiply(sk_c2,sk_c8) != sk_c6,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_50,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_20902,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20850,c_50]) ).
tff(c_52,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_20885,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_20850,c_52]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_20865,plain,
inverse(sk_c4) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_20850,c_54]) ).
tff(c_20869,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20865,c_4]) ).
tff(c_20907,plain,
! [X_178,Y_179,Z_180] : ( multiply(multiply(X_178,Y_179),Z_180) = multiply(X_178,multiply(Y_179,Z_180)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_20934,plain,
! [Z_180] : ( multiply(sk_c8,multiply(sk_c4,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_20869,c_20907]) ).
tff(c_21329,plain,
! [Z_190] : ( multiply(sk_c8,multiply(sk_c4,Z_190)) = Z_190 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20934]) ).
tff(c_21341,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_20885,c_21329]) ).
tff(c_21345,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_20902,c_21341]) ).
tff(c_20946,plain,
! [Z_180] : ( multiply(sk_c7,multiply(sk_c1,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_20907]) ).
tff(c_20966,plain,
! [Z_181] : ( multiply(sk_c7,multiply(sk_c1,Z_181)) = Z_181 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20946]) ).
tff(c_20978,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_121,c_20966]) ).
tff(c_21351,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21345,c_20978]) ).
tff(c_20952,plain,
! [X_2,Z_180] : ( multiply(inverse(X_2),multiply(X_2,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20907]) ).
tff(c_21477,plain,
! [X_191,Z_192] : ( multiply(inverse(X_191),multiply(X_191,Z_192)) = Z_192 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20952]) ).
tff(c_21519,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_21351,c_21477]) ).
tff(c_21559,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21519]) ).
tff(c_21365,plain,
inverse(sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21345,c_85]) ).
tff(c_21396,plain,
multiply(sk_c7,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21365,c_4]) ).
tff(c_21574,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21559,c_21396]) ).
tff(c_20964,plain,
! [X_2,Z_180] : ( multiply(inverse(X_2),multiply(X_2,Z_180)) = Z_180 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20952]) ).
tff(c_21731,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_21574,c_20964]) ).
tff(c_21743,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21731]) ).
tff(c_21363,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21345,c_115]) ).
tff(c_21498,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_21363,c_21477]) ).
tff(c_21554,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21498]) ).
tff(c_21360,plain,
multiply(sk_c2,sk_c7) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_21345,c_20850]) ).
tff(c_21562,plain,
multiply(sk_c2,sk_c7) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_21554,c_21360]) ).
tff(c_21762,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21743,c_21559,c_21562]) ).
tff(c_21764,plain,
multiply(sk_c1,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_26,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_21811,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_21764,c_26]) ).
tff(c_28,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_21798,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_21764,c_28]) ).
tff(c_21763,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_30]) ).
tff(c_21768,plain,
multiply(sk_c8,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21763,c_4]) ).
tff(c_21826,plain,
! [X_194,Y_195,Z_196] : ( multiply(multiply(X_194,Y_195),Z_196) = multiply(X_194,multiply(Y_195,Z_196)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_21859,plain,
! [Z_196] : ( multiply(sk_c8,multiply(sk_c4,Z_196)) = multiply(identity,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_21768,c_21826]) ).
tff(c_22154,plain,
! [Z_203] : ( multiply(sk_c8,multiply(sk_c4,Z_203)) = Z_203 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21859]) ).
tff(c_22166,plain,
multiply(sk_c8,sk_c5) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_21798,c_22154]) ).
tff(c_22170,plain,
sk_c8 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21811,c_22166]) ).
tff(c_22279,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22170,c_115]) ).
tff(c_21871,plain,
! [X_2,Z_196] : ( multiply(inverse(X_2),multiply(X_2,Z_196)) = multiply(identity,Z_196) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_21826]) ).
tff(c_22379,plain,
! [X_205,Z_206] : ( multiply(inverse(X_205),multiply(X_205,Z_206)) = Z_206 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21871]) ).
tff(c_22418,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_22279,c_22379]) ).
tff(c_22456,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22418]) ).
tff(c_20,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_21804,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_21764,c_20]) ).
tff(c_22271,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22170,c_21804]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_21785,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_21764,c_24]) ).
tff(c_22274,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22170,c_21785]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_21818,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_21764,c_22]) ).
tff(c_22269,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22170,c_21818]) ).
tff(c_22400,plain,
multiply(inverse(sk_c3),sk_c7) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22269,c_22379]) ).
tff(c_22453,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22271,c_22274,c_22400]) ).
tff(c_22473,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22453,c_102]) ).
tff(c_22626,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22456,c_22473]) ).
tff(c_22277,plain,
multiply(sk_c1,sk_c7) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_22170,c_21764]) ).
tff(c_22463,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22453,c_22453,c_22277]) ).
tff(c_22668,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22626,c_22456,c_22456,c_22463]) ).
tff(c_22670,plain,
multiply(sk_c7,sk_c6) != sk_c8,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_8,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_22719,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22670,c_8]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_22726,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22670,c_10]) ).
tff(c_22669,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_22674,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22669,c_4]) ).
tff(c_22738,plain,
! [X_209,Y_210,Z_211] : ( multiply(multiply(X_209,Y_210),Z_211) = multiply(X_209,multiply(Y_210,Z_211)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22774,plain,
! [Z_211] : ( multiply(sk_c8,multiply(sk_c3,Z_211)) = multiply(identity,Z_211) ),
inference(superposition,[status(thm),theory(equality)],[c_22674,c_22738]) ).
tff(c_22845,plain,
! [Z_214] : ( multiply(sk_c8,multiply(sk_c3,Z_214)) = Z_214 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22774]) ).
tff(c_22857,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_22726,c_22845]) ).
tff(c_22861,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22719,c_22857]) ).
tff(c_22868,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22861,c_22719]) ).
tff(c_22783,plain,
! [X_2,Z_211] : ( multiply(inverse(X_2),multiply(X_2,Z_211)) = multiply(identity,Z_211) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22738]) ).
tff(c_22795,plain,
! [X_2,Z_211] : ( multiply(inverse(X_2),multiply(X_2,Z_211)) = Z_211 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22783]) ).
tff(c_22998,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22868,c_22795]) ).
tff(c_23007,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22998]) ).
tff(c_22875,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22861,c_22670]) ).
tff(c_23011,plain,
multiply(identity,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23007,c_22875]) ).
tff(c_23017,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23011]) ).
tff(c_23019,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_36,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_23020,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_23028,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23019,c_23020]) ).
tff(c_23030,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_32,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_23066,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_23030,c_32]) ).
tff(c_34,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_23061,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_23030,c_34]) ).
tff(c_23029,plain,
inverse(sk_c3) = sk_c8,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_23041,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_23029,c_4]) ).
tff(c_23122,plain,
! [Z_220] : ( multiply(sk_c8,multiply(sk_c3,Z_220)) = multiply(identity,Z_220) ),
inference(superposition,[status(thm),theory(equality)],[c_23041,c_23095]) ).
tff(c_23144,plain,
! [Z_221] : ( multiply(sk_c8,multiply(sk_c3,Z_221)) = Z_221 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23122]) ).
tff(c_23156,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_23061,c_23144]) ).
tff(c_23160,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23066,c_23156]) ).
tff(c_23163,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_23066]) ).
tff(c_23336,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23163,c_23318]) ).
tff(c_23370,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23336]) ).
tff(c_38,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_23072,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_23030,c_38]) ).
tff(c_23162,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_23072]) ).
tff(c_23405,plain,
multiply(sk_c6,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23370,c_23162]) ).
tff(c_23018,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_23169,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_23018]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_23054,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_23030,c_40]) ).
tff(c_23165,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_23054]) ).
tff(c_23345,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_23165,c_23318]) ).
tff(c_23371,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23169,c_23345]) ).
tff(c_23430,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23405,c_23371]) ).
tff(c_23214,plain,
! [X_222,Z_223] : ( multiply(inverse(X_222),multiply(X_222,Z_223)) = Z_223 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23131]) ).
tff(c_23235,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23163,c_23214]) ).
tff(c_23257,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23235]) ).
tff(c_23183,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_23160,c_23160,c_23160,c_23160,c_23160,c_23160,c_23160,c_23160,c_23160,c_68]) ).
tff(c_23184,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(splitLeft,[status(thm)],[c_23183]) ).
tff(c_23258,plain,
multiply(identity,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23257,c_23184]) ).
tff(c_23263,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23258]) ).
tff(c_23264,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_23183]) ).
tff(c_30751,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_23695,c_23430,c_2,c_23430,c_23370,c_23430,c_23695,c_23430,c_23370,c_23430,c_23695,c_23430,c_23430,c_23430,c_23695,c_23430,c_23370,c_23370,c_23430,c_2,c_23430,c_23370,c_23264]) ).
tff(c_30753,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_30751]) ).
tff(c_23171,plain,
inverse(sk_c2) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23160,c_85]) ).
tff(c_23439,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23430,c_23171]) ).
tff(c_23476,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_23439,c_4]) ).
tff(c_23493,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_23476,c_23142]) ).
tff(c_23505,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23493]) ).
tff(c_23509,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23505,c_23439]) ).
tff(c_30755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_30753,c_23509]) ).
tff(c_30756,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(splitRight,[status(thm)],[c_30751]) ).
tff(c_35918,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_30756]) ).
tff(c_35920,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_35918,c_23509]) ).
tff(c_35921,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_30756]) ).
tff(c_35923,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_35921]) ).
tff(c_35925,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_35923,c_23509]) ).
tff(c_35928,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_35921]) ).
tff(c_35930,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_35928,c_23509]) ).
tff(c_35932,plain,
inverse(sk_c2) != sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_56,plain,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_35958,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_35932,c_56]) ).
tff(c_58,plain,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_35979,plain,
multiply(sk_c3,sk_c8) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_35932,c_58]) ).
tff(c_60,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_35944,plain,
inverse(sk_c3) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_35932,c_60]) ).
tff(c_35948,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_35944,c_4]) ).
tff(c_36041,plain,
! [Z_349] : ( multiply(sk_c8,multiply(sk_c3,Z_349)) = multiply(identity,Z_349) ),
inference(superposition,[status(thm),theory(equality)],[c_35948,c_36011]) ).
tff(c_36060,plain,
! [Z_350] : ( multiply(sk_c8,multiply(sk_c3,Z_350)) = Z_350 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36041]) ).
tff(c_36072,plain,
multiply(sk_c8,sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_35979,c_36060]) ).
tff(c_36076,plain,
sk_c8 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_35958,c_36072]) ).
tff(c_36081,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_35958]) ).
tff(c_36326,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_36081,c_36058]) ).
tff(c_36332,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_36326]) ).
tff(c_62,plain,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_35988,plain,
multiply(sk_c8,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_35932,c_62]) ).
tff(c_36079,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_35988]) ).
tff(c_36390,plain,
multiply(sk_c6,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_36332,c_36079]) ).
tff(c_35931,plain,
inverse(sk_c4) = sk_c8,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_36086,plain,
inverse(sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_35931]) ).
tff(c_64,plain,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( inverse(sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_35994,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_35932,c_64]) ).
tff(c_36078,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_35994]) ).
tff(c_36408,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_36078,c_36058]) ).
tff(c_36414,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_36390,c_36086,c_36408]) ).
tff(c_36121,plain,
! [X_351,Z_352] : ( multiply(inverse(X_351),multiply(X_351,Z_352)) = Z_352 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36047]) ).
tff(c_36139,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_36081,c_36121]) ).
tff(c_36167,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_36139]) ).
tff(c_36091,plain,
! [X5_6,X1_8,X4_10,X3_7] :
( ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_36076,c_36076,c_36076,c_36076,c_36076,c_36076,c_36076,c_36076,c_36076,c_68]) ).
tff(c_36092,plain,
multiply(sk_c7,sk_c6) != sk_c6,
inference(splitLeft,[status(thm)],[c_36091]) ).
tff(c_36234,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36167,c_36092]) ).
tff(c_36235,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( multiply(sk_c6,sk_c7) != sk_c6 )
| ( inverse(X3_7) != sk_c7 )
| ( multiply(X3_7,sk_c7) != sk_c6 )
| ( inverse(X4_10) != sk_c6 )
| ( multiply(X4_10,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X5_6) != sk_c6 )
| ( multiply(sk_c6,multiply(X5_6,sk_c6)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_36091]) ).
tff(c_44319,plain,
! [X3_7,X4_10,X1_8,X5_6] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X5_6) != identity )
| ( identity != X5_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_36640,c_36414,c_2,c_36414,c_36332,c_36414,c_36640,c_36414,c_36332,c_36414,c_36640,c_36414,c_36414,c_36414,c_36640,c_36414,c_36332,c_36332,c_36414,c_2,c_36414,c_36332,c_36235]) ).
tff(c_44321,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_44319]) ).
tff(c_36240,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_36086,c_4]) ).
tff(c_36422,plain,
multiply(identity,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_36414,c_36240]) ).
tff(c_36480,plain,
sk_c4 = identity,
inference(superposition,[status(thm),theory(equality)],[c_36422,c_2]) ).
tff(c_36425,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_36414,c_36086]) ).
tff(c_36490,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_36480,c_36425]) ).
tff(c_44323,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44321,c_36490]) ).
tff(c_44324,plain,
! [X1_8,X4_10,X3_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 ) ),
inference(splitRight,[status(thm)],[c_44319]) ).
tff(c_46170,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_44324]) ).
tff(c_46172,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46170,c_36490]) ).
tff(c_46173,plain,
! [X4_10,X1_8] :
( ( inverse(X4_10) != identity )
| ( identity != X4_10 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_44324]) ).
tff(c_46175,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_46173]) ).
tff(c_46177,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46175,c_36490]) ).
tff(c_46527,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_46173]) ).
tff(c_46529,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46527,c_36490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP356-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 22:23:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 14.72/5.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.72/5.68
% 14.72/5.68 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.00/5.74
% 15.00/5.74 Inference rules
% 15.00/5.74 ----------------------
% 15.00/5.74 #Ref : 0
% 15.00/5.74 #Sup : 11304
% 15.00/5.74 #Fact : 0
% 15.00/5.74 #Define : 0
% 15.00/5.74 #Split : 28
% 15.00/5.74 #Chain : 0
% 15.00/5.74 #Close : 0
% 15.00/5.74
% 15.00/5.74 Ordering : KBO
% 15.00/5.74
% 15.00/5.74 Simplification rules
% 15.00/5.74 ----------------------
% 15.00/5.74 #Subsume : 2
% 15.00/5.74 #Demod : 32749
% 15.00/5.74 #Tautology : 9110
% 15.00/5.74 #SimpNegUnit : 37
% 15.00/5.74 #BackRed : 316
% 15.00/5.74
% 15.00/5.74 #Partial instantiations: 0
% 15.00/5.74 #Strategies tried : 1
% 15.00/5.74
% 15.00/5.74 Timing (in seconds)
% 15.00/5.74 ----------------------
% 15.00/5.74 Preprocessing : 0.51
% 15.00/5.74 Parsing : 0.21
% 15.00/5.74 CNF conversion : 0.03
% 15.00/5.74 Main loop : 4.13
% 15.00/5.74 Inferencing : 1.13
% 15.00/5.74 Reduction : 2.32
% 15.00/5.74 Demodulation : 2.13
% 15.00/5.74 BG Simplification : 0.11
% 15.00/5.74 Subsumption : 0.38
% 15.00/5.74 Abstraction : 0.25
% 15.00/5.74 MUC search : 0.00
% 15.00/5.74 Cooper : 0.00
% 15.00/5.74 Total : 4.73
% 15.00/5.74 Index Insertion : 0.00
% 15.00/5.74 Index Deletion : 0.00
% 15.00/5.74 Index Matching : 0.00
% 15.00/5.74 BG Taut test : 0.00
%------------------------------------------------------------------------------