TSTP Solution File: GRP304-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP304-1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:40:51 EDT 2023
% Result : Unsatisfiable 9.64s 3.36s
% Output : CNFRefutation 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 335 ( 274 unt; 10 typ; 0 def)
% Number of atoms : 429 ( 414 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 204 ( 100 ~; 104 |; 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 : 125 (; 125 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_63,axiom,
multiply(sk_c7,sk_c6) = sk_c5,
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_84,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_78,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_108,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_123,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_153,axiom,
! [X2,X1,X3,X4] :
( ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X1,sk_c7) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( multiply(sk_c7,X3) != sk_c6 )
| ( multiply(X4,sk_c7) != X3 )
| ( inverse(X4) != sk_c7 ) ),
file(unknown,unknown) ).
tff(f_69,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_75,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_66,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_72,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_99,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_105,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_96,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_102,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_90,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
file(unknown,unknown) ).
tff(f_93,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_81,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_111,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_114,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c2) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_117,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c7,sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_120,axiom,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c4 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_8,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_10044,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_10077,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_10044]) ).
tff(c_10336,plain,
! [X_147,Z_148] : ( multiply(inverse(X_147),multiply(X_147,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10077]) ).
tff(c_10091,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_10077]) ).
tff(c_10530,plain,
! [X_150,Z_151] : ( multiply(inverse(inverse(X_150)),Z_151) = multiply(X_150,Z_151) ),
inference(superposition,[status(thm),theory(equality)],[c_10336,c_10091]) ).
tff(c_10390,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10336]) ).
tff(c_10537,plain,
! [X_150] : ( multiply(X_150,identity) = X_150 ),
inference(superposition,[status(thm),theory(equality)],[c_10530,c_10390]) ).
tff(c_123,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_150,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_123]) ).
tff(c_285,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_150]) ).
tff(c_163,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_150]) ).
tff(c_429,plain,
! [X_21,Z_22] : ( multiply(inverse(inverse(X_21)),Z_22) = multiply(X_21,Z_22) ),
inference(superposition,[status(thm),theory(equality)],[c_285,c_163]) ).
tff(c_309,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_285]) ).
tff(c_440,plain,
! [X_21] : ( multiply(X_21,identity) = X_21 ),
inference(superposition,[status(thm),theory(equality)],[c_429,c_309]) ).
tff(c_22,plain,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_86,plain,
inverse(sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_90,plain,
multiply(sk_c5,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_86,c_4]) ).
tff(c_18,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_108,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_38,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_99,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_48,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_73,plain,
inverse(sk_c1) = sk_c6,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_77,plain,
multiply(sk_c6,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73,c_4]) ).
tff(c_147,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_123]) ).
tff(c_188,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_147]) ).
tff(c_200,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_99,c_188]) ).
tff(c_204,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_108,c_200]) ).
tff(c_207,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_204,c_108]) ).
tff(c_212,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_207]) ).
tff(c_210,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_204,c_73]) ).
tff(c_277,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_210]) ).
tff(c_208,plain,
multiply(sk_c1,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_204,c_99]) ).
tff(c_326,plain,
multiply(sk_c1,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_208]) ).
tff(c_330,plain,
multiply(inverse(sk_c1),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_326,c_163]) ).
tff(c_336,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_277,c_330]) ).
tff(c_217,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_204]) ).
tff(c_220,plain,
inverse(sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_86]) ).
tff(c_340,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_336,c_220]) ).
tff(c_50,plain,
! [X4_9,X1_7,X2_6] :
( ( inverse(X4_9) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_9,sk_c7)) != sk_c6 )
| ( inverse(X1_7) != sk_c7 )
| ( multiply(X1_7,sk_c7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c7 )
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_52,plain,
! [X4_9,X1_7,X2_6] :
( ( inverse(X4_9) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_9,sk_c7)) != sk_c6 )
| ( inverse(X1_7) != sk_c7 )
| ( multiply(X1_7,sk_c7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c7 )
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_50]) ).
tff(c_225,plain,
! [X4_9,X1_7,X2_6] :
( ( inverse(X4_9) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_9,sk_c7)) != sk_c6 )
| ( inverse(X1_7) != sk_c7 )
| ( multiply(X1_7,sk_c7) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c7 )
| ( inverse(sk_c7) != identity )
| ( multiply(sk_c6,sk_c7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_212,c_212,c_52]) ).
tff(c_226,plain,
multiply(sk_c6,sk_c7) != identity,
inference(splitLeft,[status(thm)],[c_225]) ).
tff(c_255,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_217,c_226]) ).
tff(c_209,plain,
multiply(sk_c5,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_204,c_77]) ).
tff(c_265,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_212,c_209]) ).
tff(c_256,plain,
multiply(sk_c1,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_212,c_208]) ).
tff(c_266,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_265,c_256]) ).
tff(c_268,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_266]) ).
tff(c_270,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_255,c_268]) ).
tff(c_271,plain,
! [X2_6,X1_7,X4_9] :
( ( inverse(sk_c7) != identity )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c7 )
| ( inverse(X1_7) != sk_c7 )
| ( multiply(X1_7,sk_c7) != sk_c6 )
| ( inverse(X4_9) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_9,sk_c7)) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_225]) ).
tff(c_7953,plain,
! [X2_6,X1_7,X4_9] :
( ( inverse(X2_6) != identity )
| ( identity != X2_6 )
| ( inverse(X1_7) != identity )
| ( identity != X1_7 )
| ( inverse(X4_9) != identity )
| ( identity != X4_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_440,c_336,c_2,c_336,c_217,c_336,c_440,c_336,c_217,c_336,c_440,c_336,c_217,c_217,c_340,c_336,c_271]) ).
tff(c_7955,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_7953]) ).
tff(c_7957,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7955,c_340]) ).
tff(c_7958,plain,
! [X1_7,X2_6] :
( ( inverse(X1_7) != identity )
| ( identity != X1_7 )
| ( inverse(X2_6) != identity )
| ( identity != X2_6 ) ),
inference(splitRight,[status(thm)],[c_7953]) ).
tff(c_7960,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_7958]) ).
tff(c_7962,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7960,c_340]) ).
tff(c_7965,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_7958]) ).
tff(c_7967,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7965,c_340]) ).
tff(c_7969,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_12,plain,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_7983,plain,
inverse(sk_c2) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_7969,c_12]) ).
tff(c_7987,plain,
multiply(sk_c7,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7983,c_4]) ).
tff(c_8014,plain,
! [X_107,Y_108,Z_109] : ( multiply(multiply(X_107,Y_108),Z_109) = multiply(X_107,multiply(Y_108,Z_109)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8047,plain,
! [Z_109] : ( multiply(sk_c5,multiply(sk_c7,Z_109)) = multiply(identity,Z_109) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_8014]) ).
tff(c_8070,plain,
! [Z_110] : ( multiply(sk_c5,multiply(sk_c7,Z_110)) = Z_110 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8047]) ).
tff(c_8085,plain,
multiply(sk_c5,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_7987,c_8070]) ).
tff(c_7968,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_7973,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_7968,c_4]) ).
tff(c_8088,plain,
multiply(sk_c5,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_7973,c_8070]) ).
tff(c_8136,plain,
sk_c3 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8085,c_8088]) ).
tff(c_16,plain,
( ( multiply(sk_c3,sk_c7) = sk_c4 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_7998,plain,
multiply(sk_c3,sk_c7) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_7969,c_16]) ).
tff(c_8145,plain,
multiply(sk_c2,sk_c7) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8136,c_7998]) ).
tff(c_10,plain,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_8009,plain,
multiply(sk_c2,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_7969,c_10]) ).
tff(c_8154,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8145,c_8009]) ).
tff(c_14,plain,
( ( multiply(sk_c7,sk_c4) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_8003,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_7969,c_14]) ).
tff(c_8165,plain,
multiply(sk_c7,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8154,c_8003]) ).
tff(c_8053,plain,
! [X_2,Z_109] : ( multiply(inverse(X_2),multiply(X_2,Z_109)) = multiply(identity,Z_109) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8014]) ).
tff(c_8239,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_8053]) ).
tff(c_8269,plain,
multiply(inverse(sk_c2),sk_c4) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_8145,c_8239]) ).
tff(c_8289,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8165,c_7983,c_8269]) ).
tff(c_8170,plain,
multiply(sk_c7,sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8154,c_8]) ).
tff(c_8211,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8165,c_8170]) ).
tff(c_8227,plain,
inverse(sk_c7) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8211,c_86]) ).
tff(c_8235,plain,
multiply(sk_c4,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8227,c_4]) ).
tff(c_8320,plain,
multiply(sk_c4,sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8289,c_8235]) ).
tff(c_8169,plain,
inverse(sk_c1) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8154,c_73]) ).
tff(c_8167,plain,
multiply(sk_c1,sk_c4) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8154,c_99]) ).
tff(c_8334,plain,
multiply(sk_c1,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8289,c_8167]) ).
tff(c_8068,plain,
! [X_2,Z_109] : ( multiply(inverse(X_2),multiply(X_2,Z_109)) = Z_109 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8053]) ).
tff(c_8338,plain,
multiply(inverse(sk_c1),sk_c4) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_8334,c_8068]) ).
tff(c_8344,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8320,c_8169,c_8338]) ).
tff(c_8351,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8344,c_8211]) ).
tff(c_8350,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8344,c_8289]) ).
tff(c_8166,plain,
multiply(sk_c4,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8154,c_7969]) ).
tff(c_8425,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8351,c_8350,c_2,c_8344,c_8166]) ).
tff(c_8427,plain,
multiply(sk_c1,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_32,plain,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_8441,plain,
inverse(sk_c2) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8427,c_32]) ).
tff(c_8445,plain,
multiply(sk_c7,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8441,c_4]) ).
tff(c_9044,plain,
! [X_124,Y_125,Z_126] : ( multiply(multiply(X_124,Y_125),Z_126) = multiply(X_124,multiply(Y_125,Z_126)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9074,plain,
! [Z_126] : ( multiply(sk_c5,multiply(sk_c7,Z_126)) = multiply(identity,Z_126) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_9044]) ).
tff(c_9097,plain,
! [Z_127] : ( multiply(sk_c5,multiply(sk_c7,Z_127)) = Z_127 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9074]) ).
tff(c_9112,plain,
multiply(sk_c5,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_8445,c_9097]) ).
tff(c_8426,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_8431,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8426,c_4]) ).
tff(c_9115,plain,
multiply(sk_c5,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_8431,c_9097]) ).
tff(c_9156,plain,
sk_c3 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_9112,c_9115]) ).
tff(c_36,plain,
( ( multiply(sk_c3,sk_c7) = sk_c4 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_8459,plain,
multiply(sk_c3,sk_c7) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_8427,c_36]) ).
tff(c_9165,plain,
multiply(sk_c2,sk_c7) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9156,c_8459]) ).
tff(c_30,plain,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_8465,plain,
multiply(sk_c2,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_8427,c_30]) ).
tff(c_9181,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9165,c_8465]) ).
tff(c_8481,plain,
! [X_115,Y_116,Z_117] : ( multiply(multiply(X_115,Y_116),Z_117) = multiply(X_115,multiply(Y_116,Z_117)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8514,plain,
! [Z_117] : ( multiply(sk_c5,multiply(sk_c7,Z_117)) = multiply(identity,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_8481]) ).
tff(c_8537,plain,
! [Z_118] : ( multiply(sk_c5,multiply(sk_c7,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8514]) ).
tff(c_8552,plain,
multiply(sk_c5,identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_8445,c_8537]) ).
tff(c_8555,plain,
multiply(sk_c5,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_8431,c_8537]) ).
tff(c_8805,plain,
sk_c3 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8552,c_8555]) ).
tff(c_8806,plain,
multiply(sk_c2,sk_c7) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8805,c_8459]) ).
tff(c_8871,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8806,c_8465]) ).
tff(c_34,plain,
( ( multiply(sk_c7,sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_8476,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_8427,c_34]) ).
tff(c_8879,plain,
multiply(sk_c7,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8871,c_8476]) ).
tff(c_8471,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_8815,plain,
! [Z_121] : ( multiply(sk_c7,multiply(sk_c6,Z_121)) = multiply(sk_c5,Z_121) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_8481]) ).
tff(c_8830,plain,
multiply(sk_c7,sk_c5) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_8471,c_8815]) ).
tff(c_8837,plain,
multiply(sk_c7,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_8830]) ).
tff(c_8533,plain,
! [Z_117] : ( multiply(sk_c5,multiply(sk_c7,Z_117)) = Z_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8514]) ).
tff(c_8841,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_8837,c_8533]) ).
tff(c_8847,plain,
sk_c5 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8552,c_8841]) ).
tff(c_8858,plain,
multiply(sk_c7,sk_c6) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8847,c_8]) ).
tff(c_8911,plain,
sk_c4 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8879,c_8871,c_8858]) ).
tff(c_8913,plain,
multiply(sk_c7,sk_c2) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8911,c_8911,c_8879]) ).
tff(c_8917,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8445,c_8913]) ).
tff(c_8922,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8917,c_8911]) ).
tff(c_8882,plain,
inverse(sk_c1) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_8871,c_73]) ).
tff(c_8892,plain,
multiply(sk_c4,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8882,c_4]) ).
tff(c_9009,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8922,c_8892]) ).
tff(c_8914,plain,
inverse(sk_c1) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8911,c_8882]) ).
tff(c_8998,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8917,c_8914]) ).
tff(c_9010,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9009,c_8998]) ).
tff(c_8927,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8917,c_8441]) ).
tff(c_9015,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9010,c_8927]) ).
tff(c_8880,plain,
multiply(sk_c1,sk_c4) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_8871,c_8427]) ).
tff(c_9035,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9015,c_2,c_9009,c_8922,c_8880]) ).
tff(c_9036,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_9109,plain,
multiply(sk_c5,sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_9036,c_9097]) ).
tff(c_9191,plain,
multiply(sk_c5,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9181,c_9109]) ).
tff(c_9199,plain,
multiply(sk_c7,sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9181,c_8]) ).
tff(c_9080,plain,
! [X_2,Z_126] : ( multiply(inverse(X_2),multiply(X_2,Z_126)) = multiply(identity,Z_126) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9044]) ).
tff(c_9244,plain,
! [X_129,Z_130] : ( multiply(inverse(X_129),multiply(X_129,Z_130)) = Z_130 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9080]) ).
tff(c_9277,plain,
multiply(inverse(sk_c2),sk_c4) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_9165,c_9244]) ).
tff(c_9309,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9199,c_8441,c_9277]) ).
tff(c_9314,plain,
multiply(sk_c5,sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9309,c_9199]) ).
tff(c_9321,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9191,c_9314]) ).
tff(c_9326,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9321,c_9309]) ).
tff(c_9195,plain,
multiply(sk_c7,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9181,c_9036]) ).
tff(c_9396,plain,
multiply(sk_c4,sk_c4) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_9326,c_9195]) ).
tff(c_9095,plain,
! [X_2,Z_126] : ( multiply(inverse(X_2),multiply(X_2,Z_126)) = Z_126 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9080]) ).
tff(c_9400,plain,
multiply(inverse(sk_c4),sk_c4) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_9396,c_9095]) ).
tff(c_9406,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9400]) ).
tff(c_9037,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_9194,plain,
multiply(sk_c4,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9181,c_9037]) ).
tff(c_9313,plain,
multiply(sk_c4,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9309,c_9194]) ).
tff(c_9492,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9406,c_9313]) ).
tff(c_9494,plain,
inverse(sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_24,plain,
( ( multiply(sk_c7,sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_9523,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9494,c_24]) ).
tff(c_26,plain,
( ( multiply(sk_c3,sk_c7) = sk_c4 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_9535,plain,
multiply(sk_c3,sk_c7) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_9494,c_26]) ).
tff(c_28,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_9502,plain,
inverse(sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_9503,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9494,c_9502]) ).
tff(c_9504,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_9509,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9504,c_4]) ).
tff(c_9549,plain,
! [X_133,Y_134,Z_135] : ( multiply(multiply(X_133,Y_134),Z_135) = multiply(X_133,multiply(Y_134,Z_135)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9573,plain,
! [Z_135] : ( multiply(sk_c7,multiply(sk_c3,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_9509,c_9549]) ).
tff(c_9598,plain,
! [Z_136] : ( multiply(sk_c7,multiply(sk_c3,Z_136)) = Z_136 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9573]) ).
tff(c_9610,plain,
multiply(sk_c7,sk_c4) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_9535,c_9598]) ).
tff(c_9614,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9523,c_9610]) ).
tff(c_9624,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9614,c_8]) ).
tff(c_9493,plain,
inverse(sk_c2) = sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_9623,plain,
inverse(sk_c2) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9614,c_9493]) ).
tff(c_20,plain,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_9530,plain,
multiply(sk_c2,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9494,c_20]) ).
tff(c_9617,plain,
multiply(sk_c2,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_9614,c_9530]) ).
tff(c_9582,plain,
! [X_2,Z_135] : ( multiply(inverse(X_2),multiply(X_2,Z_135)) = multiply(identity,Z_135) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9549]) ).
tff(c_9679,plain,
! [X_137,Z_138] : ( multiply(inverse(X_137),multiply(X_137,Z_138)) = Z_138 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9582]) ).
tff(c_9706,plain,
multiply(inverse(sk_c2),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9617,c_9679]) ).
tff(c_9736,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9624,c_9623,c_9706]) ).
tff(c_9746,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9736,c_9736,c_9624]) ).
tff(c_9596,plain,
! [X_2,Z_135] : ( multiply(inverse(X_2),multiply(X_2,Z_135)) = Z_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9582]) ).
tff(c_9879,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9746,c_9596]) ).
tff(c_9886,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9879]) ).
tff(c_9622,plain,
inverse(sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9614,c_9494]) ).
tff(c_9745,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9736,c_9622]) ).
tff(c_9898,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9886,c_9886,c_9745]) ).
tff(c_9750,plain,
multiply(sk_c5,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9736,c_77]) ).
tff(c_9964,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9886,c_9750]) ).
tff(c_9751,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9736,c_73]) ).
tff(c_9895,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9886,c_9751]) ).
tff(c_9965,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9964,c_9895]) ).
tff(c_9967,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9898,c_9965]) ).
tff(c_9969,plain,
inverse(sk_c1) != sk_c6,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_40,plain,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_10026,plain,
multiply(sk_c2,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9969,c_40]) ).
tff(c_42,plain,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_9970,plain,
inverse(sk_c1) = sk_c6,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_9978,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9969,c_9970]) ).
tff(c_9979,plain,
inverse(sk_c2) = sk_c7,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_9991,plain,
multiply(sk_c7,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9979,c_4]) ).
tff(c_10071,plain,
! [Z_143] : ( multiply(sk_c7,multiply(sk_c2,Z_143)) = multiply(identity,Z_143) ),
inference(superposition,[status(thm),theory(equality)],[c_9991,c_10044]) ).
tff(c_10093,plain,
! [Z_144] : ( multiply(sk_c7,multiply(sk_c2,Z_144)) = Z_144 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10071]) ).
tff(c_10105,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10026,c_10093]) ).
tff(c_10109,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10105]) ).
tff(c_10006,plain,
inverse(sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_10010,plain,
multiply(sk_c5,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10006,c_4]) ).
tff(c_10114,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_10010]) ).
tff(c_10115,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_10006]) ).
tff(c_10120,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_8]) ).
tff(c_10369,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10120,c_10336]) ).
tff(c_10401,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10114,c_10115,c_10369]) ).
tff(c_44,plain,
( ( multiply(sk_c7,sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_10018,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9969,c_44]) ).
tff(c_10113,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_10018]) ).
tff(c_9968,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_10119,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_9968]) ).
tff(c_46,plain,
( ( multiply(sk_c3,sk_c7) = sk_c4 )
| ( inverse(sk_c1) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_10033,plain,
multiply(sk_c3,sk_c7) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_9969,c_46]) ).
tff(c_10111,plain,
multiply(sk_c3,sk_c5) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_10033]) ).
tff(c_10375,plain,
multiply(inverse(sk_c3),sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10111,c_10336]) ).
tff(c_10403,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10113,c_10119,c_10375]) ).
tff(c_10202,plain,
! [X_145,Z_146] : ( multiply(inverse(X_145),multiply(X_145,Z_146)) = Z_146 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10077]) ).
tff(c_10232,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10120,c_10202]) ).
tff(c_10264,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10232]) ).
tff(c_10147,plain,
! [X4_9,X1_7,X2_6] :
( ( inverse(X4_9) != sk_c5 )
| ( multiply(sk_c5,multiply(X4_9,sk_c5)) != sk_c6 )
| ( inverse(X1_7) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10109,c_10115,c_10109,c_10109,c_10109,c_10109,c_10109,c_10109,c_10109,c_52]) ).
tff(c_10148,plain,
multiply(sk_c6,sk_c5) != sk_c5,
inference(splitLeft,[status(thm)],[c_10147]) ).
tff(c_10267,plain,
multiply(identity,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10264,c_10148]) ).
tff(c_10274,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10267]) ).
tff(c_10276,plain,
multiply(sk_c6,sk_c5) = sk_c5,
inference(splitRight,[status(thm)],[c_10147]) ).
tff(c_10404,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10403,c_10276]) ).
tff(c_10409,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10114,c_10404]) ).
tff(c_10275,plain,
! [X2_6,X1_7,X4_9] :
( ( inverse(X2_6) != sk_c6 )
| ( multiply(X2_6,sk_c6) != sk_c5 )
| ( inverse(X1_7) != sk_c5 )
| ( multiply(X1_7,sk_c5) != sk_c6 )
| ( inverse(X4_9) != sk_c5 )
| ( multiply(sk_c5,multiply(X4_9,sk_c5)) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_10147]) ).
tff(c_17989,plain,
! [X2_6,X1_7,X4_9] :
( ( inverse(X2_6) != identity )
| ( identity != X2_6 )
| ( inverse(X1_7) != identity )
| ( identity != X1_7 )
| ( inverse(X4_9) != identity )
| ( identity != X4_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10537,c_10401,c_10409,c_2,c_10409,c_10409,c_10537,c_10401,c_10409,c_10409,c_10537,c_10401,c_10409,c_10401,c_10275]) ).
tff(c_17991,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_17989]) ).
tff(c_10366,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_10113,c_10336]) ).
tff(c_10400,plain,
sk_c5 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_10120,c_10115,c_10366]) ).
tff(c_10428,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10409,c_10400]) ).
tff(c_10135,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10119,c_4]) ).
tff(c_10433,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10409,c_10135]) ).
tff(c_10421,plain,
inverse(sk_c3) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_10400,c_10119]) ).
tff(c_10455,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10428,c_10433,c_10421]) ).
tff(c_17993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17991,c_10455]) ).
tff(c_17994,plain,
! [X1_7,X2_6] :
( ( inverse(X1_7) != identity )
| ( identity != X1_7 )
| ( inverse(X2_6) != identity )
| ( identity != X2_6 ) ),
inference(splitRight,[status(thm)],[c_17989]) ).
tff(c_17996,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_17994]) ).
tff(c_17998,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17996,c_10455]) ).
tff(c_18001,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_17994]) ).
tff(c_18003,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18001,c_10455]) ).
tff(c_18004,plain,
multiply(sk_c2,sk_c7) = sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18035,plain,
! [X_236,Y_237,Z_238] : ( multiply(multiply(X_236,Y_237),Z_238) = multiply(X_236,multiply(Y_237,Z_238)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18059,plain,
! [Z_238] : ( multiply(sk_c7,multiply(sk_c2,Z_238)) = multiply(identity,Z_238) ),
inference(superposition,[status(thm),theory(equality)],[c_9991,c_18035]) ).
tff(c_18080,plain,
! [Z_239] : ( multiply(sk_c7,multiply(sk_c2,Z_239)) = Z_239 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18059]) ).
tff(c_18092,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18004,c_18080]) ).
tff(c_18096,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_18092]) ).
tff(c_18120,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_8]) ).
tff(c_18065,plain,
! [X_2,Z_238] : ( multiply(inverse(X_2),multiply(X_2,Z_238)) = multiply(identity,Z_238) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18035]) ).
tff(c_18211,plain,
! [X_242,Z_243] : ( multiply(inverse(X_242),multiply(X_242,Z_243)) = Z_243 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18065]) ).
tff(c_18247,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18120,c_18211]) ).
tff(c_18269,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18247]) ).
tff(c_18005,plain,
inverse(sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_18019,plain,
multiply(sk_c3,sk_c7) = sk_c4,
inference(negUnitSimplification,[status(thm)],[c_18005,c_26]) ).
tff(c_18112,plain,
multiply(sk_c3,sk_c5) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_18019]) ).
tff(c_9984,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9968,c_4]) ).
tff(c_18062,plain,
! [Z_238] : ( multiply(sk_c7,multiply(sk_c3,Z_238)) = multiply(identity,Z_238) ),
inference(superposition,[status(thm),theory(equality)],[c_9984,c_18035]) ).
tff(c_18077,plain,
! [Z_238] : ( multiply(sk_c7,multiply(sk_c3,Z_238)) = Z_238 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18062]) ).
tff(c_18187,plain,
! [Z_241] : ( multiply(sk_c5,multiply(sk_c3,Z_241)) = Z_241 ),
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_18077]) ).
tff(c_18199,plain,
multiply(sk_c5,sk_c4) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18112,c_18187]) ).
tff(c_18010,plain,
multiply(sk_c7,sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9969,c_44]) ).
tff(c_18113,plain,
multiply(sk_c5,sk_c4) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_18010]) ).
tff(c_18203,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18199,c_18113]) ).
tff(c_18278,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18269,c_18203]) ).
tff(c_18115,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_18005]) ).
tff(c_18290,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_18278,c_18278,c_18115]) ).
tff(c_18117,plain,
multiply(sk_c5,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_9984]) ).
tff(c_18285,plain,
multiply(identity,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18278,c_18117]) ).
tff(c_18078,plain,
! [X_2,Z_238] : ( multiply(inverse(X_2),multiply(X_2,Z_238)) = Z_238 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18065]) ).
tff(c_18365,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_18285,c_18078]) ).
tff(c_18377,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18365]) ).
tff(c_18119,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18096,c_9968]) ).
tff(c_18289,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18278,c_18119]) ).
tff(c_18381,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18377,c_18289]) ).
tff(c_18384,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18290,c_18381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP304-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 21:58:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 9.64/3.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.84/3.39
% 9.84/3.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.84/3.44
% 9.84/3.44 Inference rules
% 9.84/3.44 ----------------------
% 9.84/3.44 #Ref : 0
% 9.84/3.44 #Sup : 4610
% 9.84/3.44 #Fact : 0
% 9.84/3.44 #Define : 0
% 10.20/3.44 #Split : 18
% 10.20/3.44 #Chain : 0
% 10.20/3.44 #Close : 0
% 10.20/3.44
% 10.20/3.44 Ordering : KBO
% 10.20/3.44
% 10.20/3.44 Simplification rules
% 10.20/3.44 ----------------------
% 10.20/3.44 #Subsume : 5
% 10.20/3.44 #Demod : 10109
% 10.20/3.44 #Tautology : 3593
% 10.20/3.44 #SimpNegUnit : 32
% 10.20/3.44 #BackRed : 263
% 10.20/3.44
% 10.20/3.44 #Partial instantiations: 0
% 10.20/3.44 #Strategies tried : 1
% 10.20/3.44
% 10.20/3.44 Timing (in seconds)
% 10.20/3.44 ----------------------
% 10.20/3.45 Preprocessing : 0.48
% 10.20/3.45 Parsing : 0.20
% 10.20/3.45 CNF conversion : 0.02
% 10.20/3.45 Main loop : 1.86
% 10.20/3.45 Inferencing : 0.60
% 10.20/3.45 Reduction : 0.85
% 10.20/3.45 Demodulation : 0.74
% 10.20/3.45 BG Simplification : 0.06
% 10.20/3.45 Subsumption : 0.21
% 10.20/3.45 Abstraction : 0.11
% 10.20/3.45 MUC search : 0.00
% 10.20/3.45 Cooper : 0.00
% 10.20/3.45 Total : 2.44
% 10.20/3.45 Index Insertion : 0.00
% 10.20/3.45 Index Deletion : 0.00
% 10.20/3.45 Index Matching : 0.00
% 10.20/3.45 BG Taut test : 0.00
%------------------------------------------------------------------------------