TSTP Solution File: GRP294-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP294-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : 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 10:40:49 EDT 2023
% Result : Unsatisfiable 16.07s 6.99s
% Output : CNFRefutation 16.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 40
% Syntax : Number of formulae : 471 ( 385 unt; 10 typ; 0 def)
% Number of atoms : 679 ( 652 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 457 ( 239 ~; 218 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 239 (; 239 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( multiply(X4,sk_c7) != sk_c5 )
| ( inverse(X4) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c7,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
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_26273,plain,
! [X_356,Y_357,Z_358] : ( multiply(multiply(X_356,Y_357),Z_358) = multiply(X_356,multiply(Y_357,Z_358)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_26303,plain,
! [X_2,Z_358] : ( multiply(inverse(X_2),multiply(X_2,Z_358)) = multiply(identity,Z_358) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_26273]) ).
tff(c_26826,plain,
! [X_369,Z_370] : ( multiply(inverse(X_369),multiply(X_369,Z_370)) = Z_370 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26303]) ).
tff(c_26313,plain,
! [X_2,Z_358] : ( multiply(inverse(X_2),multiply(X_2,Z_358)) = Z_358 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26303]) ).
tff(c_27089,plain,
! [X_373,Z_374] : ( multiply(inverse(inverse(X_373)),Z_374) = multiply(X_373,Z_374) ),
inference(superposition,[status(thm),theory(equality)],[c_26826,c_26313]) ).
tff(c_26865,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_26826]) ).
tff(c_27096,plain,
! [X_373] : ( multiply(X_373,identity) = X_373 ),
inference(superposition,[status(thm),theory(equality)],[c_27089,c_26865]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_111,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_18,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_14952,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_32,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_98,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_102,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_14978,plain,
! [X_165,Y_166,Z_167] : ( multiply(multiply(X_165,Y_166),Z_167) = multiply(X_165,multiply(Y_166,Z_167)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_15017,plain,
! [Z_167] : ( multiply(sk_c7,multiply(sk_c1,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_14978]) ).
tff(c_15037,plain,
! [Z_168] : ( multiply(sk_c7,multiply(sk_c1,Z_168)) = Z_168 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15017]) ).
tff(c_15049,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14952,c_15037]) ).
tff(c_15053,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_15049]) ).
tff(c_15060,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15053,c_111]) ).
tff(c_15023,plain,
! [X_2,Z_167] : ( multiply(inverse(X_2),multiply(X_2,Z_167)) = multiply(identity,Z_167) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14978]) ).
tff(c_15102,plain,
! [X_169,Z_170] : ( multiply(inverse(X_169),multiply(X_169,Z_170)) = Z_170 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15023]) ).
tff(c_15120,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15060,c_15102]) ).
tff(c_15154,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15120]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_116,plain,
multiply(sk_c2,sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_64,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_85,plain,
inverse(sk_c2) = sk_c7,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_89,plain,
multiply(sk_c7,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_14635,plain,
! [X_156,Y_157,Z_158] : ( multiply(multiply(X_156,Y_157),Z_158) = multiply(X_156,multiply(Y_157,Z_158)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14674,plain,
! [Z_158] : ( multiply(sk_c7,multiply(sk_c2,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_14635]) ).
tff(c_14704,plain,
! [Z_160] : ( multiply(sk_c7,multiply(sk_c2,Z_160)) = Z_160 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14674]) ).
tff(c_14716,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_116,c_14704]) ).
tff(c_14677,plain,
! [X_2,Z_158] : ( multiply(inverse(X_2),multiply(X_2,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14635]) ).
tff(c_14762,plain,
! [X_162,Z_163] : ( multiply(inverse(X_162),multiply(X_162,Z_163)) = Z_163 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14677]) ).
tff(c_14780,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_14716,c_14762]) ).
tff(c_14814,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14780]) ).
tff(c_42,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_123,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_13682,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_13724,plain,
! [Z_143] : ( multiply(sk_c7,multiply(sk_c2,Z_143)) = multiply(identity,Z_143) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_13682]) ).
tff(c_13754,plain,
! [Z_145] : ( multiply(sk_c7,multiply(sk_c2,Z_145)) = Z_145 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13724]) ).
tff(c_13766,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_116,c_13754]) ).
tff(c_13770,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_123,c_13766]) ).
tff(c_13776,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13770,c_123]) ).
tff(c_13727,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_13682]) ).
tff(c_13932,plain,
! [X_148,Z_149] : ( multiply(inverse(X_148),multiply(X_148,Z_149)) = Z_149 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13727]) ).
tff(c_13956,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_13776,c_13932]) ).
tff(c_13996,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_13956]) ).
tff(c_68,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_13787,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( multiply(sk_c6,sk_c6) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c6 )
| ( multiply(sk_c6,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_13770,c_13770,c_13770,c_13770,c_13770,c_13770,c_13770,c_13770,c_68]) ).
tff(c_13788,plain,
multiply(sk_c6,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_13787]) ).
tff(c_22,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_128,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_154,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_181,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_154]) ).
tff(c_199,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_181]) ).
tff(c_211,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_128,c_199]) ).
tff(c_215,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_211]) ).
tff(c_236,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( multiply(sk_c5,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_215,c_215,c_215,c_215,c_215,c_215,c_215,c_215,c_68]) ).
tff(c_237,plain,
multiply(sk_c5,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_236]) ).
tff(c_220,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_111]) ).
tff(c_245,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_237,c_220]) ).
tff(c_247,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_236]) ).
tff(c_187,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_154]) ).
tff(c_279,plain,
! [X_16,Z_17] : ( multiply(inverse(X_16),multiply(X_16,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_187]) ).
tff(c_300,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_247,c_279]) ).
tff(c_323,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_300]) ).
tff(c_197,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_187]) ).
tff(c_553,plain,
! [X_20,Z_21] : ( multiply(inverse(inverse(X_20)),Z_21) = multiply(X_20,Z_21) ),
inference(superposition,[status(thm),theory(equality)],[c_279,c_197]) ).
tff(c_315,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_279]) ).
tff(c_560,plain,
! [X_20] : ( multiply(X_20,identity) = X_20 ),
inference(superposition,[status(thm),theory(equality)],[c_553,c_315]) ).
tff(c_218,plain,
multiply(sk_c5,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_123]) ).
tff(c_330,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_323,c_218]) ).
tff(c_224,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_85]) ).
tff(c_219,plain,
multiply(sk_c2,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_116]) ).
tff(c_357,plain,
multiply(inverse(sk_c2),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_219,c_197]) ).
tff(c_363,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_330,c_224,c_357]) ).
tff(c_246,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c5,sk_c5) != sk_c6 )
| ( multiply(sk_c6,sk_c5) != sk_c5 )
| ( inverse(X3_6) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_236]) ).
tff(c_8002,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_323,c_560,c_363,c_323,c_560,c_363,c_323,c_323,c_560,c_363,c_363,c_363,c_560,c_363,c_323,c_363,c_2,c_323,c_363,c_2,c_363,c_323,c_246]) ).
tff(c_8004,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8002]) ).
tff(c_222,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_98]) ).
tff(c_232,plain,
multiply(sk_c5,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_222,c_4]) ).
tff(c_369,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_363,c_232]) ).
tff(c_425,plain,
sk_c1 = identity,
inference(superposition,[status(thm),theory(equality)],[c_369,c_2]) ).
tff(c_370,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_363,c_222]) ).
tff(c_436,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_425,c_370]) ).
tff(c_8006,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8004,c_436]) ).
tff(c_8007,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_8002]) ).
tff(c_12846,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8007]) ).
tff(c_12848,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12846,c_436]) ).
tff(c_12849,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_8007]) ).
tff(c_12851,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_12849]) ).
tff(c_12853,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12851,c_436]) ).
tff(c_13623,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_12849]) ).
tff(c_13625,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13623,c_436]) ).
tff(c_13627,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_24,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_13639,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_13627,c_24]) ).
tff(c_26,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_13669,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_13627,c_26]) ).
tff(c_13818,plain,
! [X_146,Z_147] : ( multiply(inverse(X_146),multiply(X_146,Z_147)) = Z_147 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_13727]) ).
tff(c_13851,plain,
multiply(inverse(sk_c4),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_13669,c_13818]) ).
tff(c_13874,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_13639,c_13851]) ).
tff(c_13876,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13788,c_13874]) ).
tff(c_13878,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_13787]) ).
tff(c_14007,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13996,c_13878]) ).
tff(c_13626,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_20,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_13658,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_13627,c_20]) ).
tff(c_13774,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13770,c_13658]) ).
tff(c_13739,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_13727]) ).
tff(c_14023,plain,
multiply(inverse(sk_c3),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_13774,c_13739]) ).
tff(c_14029,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14007,c_13626,c_14023]) ).
tff(c_13780,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13770,c_98]) ).
tff(c_14036,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14029,c_13780]) ).
tff(c_14058,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14036,c_4]) ).
tff(c_14167,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_14058,c_13739]) ).
tff(c_14179,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14167]) ).
tff(c_13775,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13770,c_13627]) ).
tff(c_14032,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_14029,c_14029,c_13775]) ).
tff(c_14253,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14179,c_14032]) ).
tff(c_14255,plain,
multiply(sk_c7,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_38,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_14627,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_14255,c_38]) ).
tff(c_40,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_14291,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_14255,c_40]) ).
tff(c_14254,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_14259,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14254,c_4]) ).
tff(c_14662,plain,
! [Z_158] : ( multiply(sk_c6,multiply(sk_c3,Z_158)) = multiply(identity,Z_158) ),
inference(superposition,[status(thm),theory(equality)],[c_14259,c_14635]) ).
tff(c_14730,plain,
! [Z_161] : ( multiply(sk_c6,multiply(sk_c3,Z_161)) = Z_161 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14662]) ).
tff(c_14742,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14291,c_14730]) ).
tff(c_14746,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14627,c_14742]) ).
tff(c_14722,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14716,c_14255]) ).
tff(c_14748,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14746,c_14722]) ).
tff(c_14818,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_14814,c_14748]) ).
tff(c_14749,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14746,c_14627]) ).
tff(c_14908,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_14814,c_2,c_14814,c_14749]) ).
tff(c_14909,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14818,c_14908]) ).
tff(c_14910,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_14911,plain,
multiply(sk_c2,sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_56,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_14973,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14911,c_56]) ).
tff(c_15132,plain,
multiply(inverse(sk_c4),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_14973,c_15102]) ).
tff(c_15155,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14910,c_15132]) ).
tff(c_15197,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15154,c_2,c_15154,c_15155]) ).
tff(c_15064,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15053,c_85]) ).
tff(c_15091,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15064,c_4]) ).
tff(c_15251,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15197,c_15091]) ).
tff(c_15059,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15053,c_14911]) ).
tff(c_15273,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15251,c_15197,c_15197,c_15059]) ).
tff(c_15274,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_50,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_15285,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_14911,c_50]) ).
tff(c_52,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_14927,plain,
inverse(sk_c3) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14911,c_52]) ).
tff(c_14931,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14927,c_4]) ).
tff(c_15300,plain,
! [X_171,Y_172,Z_173] : ( multiply(multiply(X_171,Y_172),Z_173) = multiply(X_171,multiply(Y_172,Z_173)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_15327,plain,
! [Z_173] : ( multiply(sk_c6,multiply(sk_c3,Z_173)) = multiply(identity,Z_173) ),
inference(superposition,[status(thm),theory(equality)],[c_14931,c_15300]) ).
tff(c_15869,plain,
! [Z_188] : ( multiply(sk_c6,multiply(sk_c3,Z_188)) = Z_188 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15327]) ).
tff(c_15881,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15285,c_15869]) ).
tff(c_15885,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15274,c_15881]) ).
tff(c_15891,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15885,c_15274]) ).
tff(c_15342,plain,
! [X_2,Z_173] : ( multiply(inverse(X_2),multiply(X_2,Z_173)) = multiply(identity,Z_173) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15300]) ).
tff(c_15964,plain,
! [X_189,Z_190] : ( multiply(inverse(X_189),multiply(X_189,Z_190)) = Z_190 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15342]) ).
tff(c_15988,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_15891,c_15964]) ).
tff(c_16035,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15988]) ).
tff(c_16046,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16035,c_102]) ).
tff(c_15354,plain,
! [X_2,Z_173] : ( multiply(inverse(X_2),multiply(X_2,Z_173)) = Z_173 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15342]) ).
tff(c_16091,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_16046,c_15354]) ).
tff(c_16103,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16091]) ).
tff(c_15275,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_15890,plain,
multiply(sk_c1,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15885,c_15275]) ).
tff(c_16041,plain,
multiply(sk_c1,identity) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16035,c_15890]) ).
tff(c_16128,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16103,c_16041]) ).
tff(c_15896,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15885,c_14910]) ).
tff(c_15280,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_15275,c_26]) ).
tff(c_15889,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15885,c_15280]) ).
tff(c_15997,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15889,c_15964]) ).
tff(c_16036,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15896,c_15997]) ).
tff(c_16160,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_16036,c_15354]) ).
tff(c_16166,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16160]) ).
tff(c_16168,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16128,c_16166]) ).
tff(c_16170,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_17674,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_16170,c_8]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_17667,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_16170,c_10]) ).
tff(c_16183,plain,
multiply(sk_c2,sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_17342,plain,
! [X_217,Y_218,Z_219] : ( multiply(multiply(X_217,Y_218),Z_219) = multiply(X_217,multiply(Y_218,Z_219)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17378,plain,
! [Z_219] : ( multiply(sk_c7,multiply(sk_c2,Z_219)) = multiply(identity,Z_219) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_17342]) ).
tff(c_17408,plain,
! [Z_221] : ( multiply(sk_c7,multiply(sk_c2,Z_221)) = Z_221 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17378]) ).
tff(c_17420,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16183,c_17408]) ).
tff(c_17381,plain,
! [X_2,Z_219] : ( multiply(inverse(X_2),multiply(X_2,Z_219)) = multiply(identity,Z_219) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17342]) ).
tff(c_17513,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_17381]) ).
tff(c_17540,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17420,c_17513]) ).
tff(c_17575,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17540]) ).
tff(c_16210,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_16170,c_8]) ).
tff(c_17040,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_17058,plain,
! [X_210,Y_211,Z_212] : ( multiply(multiply(X_210,Y_211),Z_212) = multiply(X_210,multiply(Y_211,Z_212)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17097,plain,
! [Z_212] : ( multiply(sk_c7,multiply(sk_c2,Z_212)) = multiply(identity,Z_212) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_17058]) ).
tff(c_17127,plain,
! [Z_214] : ( multiply(sk_c7,multiply(sk_c2,Z_214)) = Z_214 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17097]) ).
tff(c_17139,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16183,c_17127]) ).
tff(c_17143,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17040,c_17139]) ).
tff(c_17147,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17143,c_17040]) ).
tff(c_17100,plain,
! [X_2,Z_212] : ( multiply(inverse(X_2),multiply(X_2,Z_212)) = multiply(identity,Z_212) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17058]) ).
tff(c_17112,plain,
! [X_2,Z_212] : ( multiply(inverse(X_2),multiply(X_2,Z_212)) = Z_212 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17100]) ).
tff(c_17294,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17147,c_17112]) ).
tff(c_17300,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17294]) ).
tff(c_17151,plain,
multiply(sk_c6,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17143,c_16170]) ).
tff(c_17322,plain,
multiply(sk_c6,sk_c6) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17300,c_17151]) ).
tff(c_17167,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( multiply(sk_c6,sk_c6) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c6 )
| ( multiply(sk_c6,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17143,c_17143,c_17143,c_17143,c_17143,c_17143,c_17143,c_17143,c_68]) ).
tff(c_17168,plain,
multiply(sk_c6,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_17167]) ).
tff(c_17149,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17143,c_16210]) ).
tff(c_17199,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17168,c_17149]) ).
tff(c_17201,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_17167]) ).
tff(c_17323,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17300,c_17201]) ).
tff(c_17324,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17322,c_17323]) ).
tff(c_17325,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_16189,plain,
inverse(sk_c3) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16170,c_12]) ).
tff(c_16193,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16189,c_4]) ).
tff(c_17366,plain,
! [Z_219] : ( multiply(sk_c6,multiply(sk_c3,Z_219)) = multiply(identity,Z_219) ),
inference(superposition,[status(thm),theory(equality)],[c_16193,c_17342]) ).
tff(c_17434,plain,
! [Z_222] : ( multiply(sk_c6,multiply(sk_c3,Z_222)) = Z_222 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17366]) ).
tff(c_17446,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17325,c_17434]) ).
tff(c_17450,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16210,c_17446]) ).
tff(c_17326,plain,
multiply(sk_c7,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_17426,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17420,c_17326]) ).
tff(c_17484,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17450,c_17426]) ).
tff(c_17581,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17575,c_17484]) ).
tff(c_17488,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17450,c_16210]) ).
tff(c_17623,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17575,c_2,c_17575,c_17488]) ).
tff(c_17624,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17581,c_17623]) ).
tff(c_17625,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_17630,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17625,c_4]) ).
tff(c_17685,plain,
! [X_226,Y_227,Z_228] : ( multiply(multiply(X_226,Y_227),Z_228) = multiply(X_226,multiply(Y_227,Z_228)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17715,plain,
! [Z_228] : ( multiply(sk_c6,multiply(sk_c3,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_17630,c_17685]) ).
tff(c_17816,plain,
! [Z_233] : ( multiply(sk_c6,multiply(sk_c3,Z_233)) = Z_233 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17715]) ).
tff(c_17828,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17667,c_17816]) ).
tff(c_17832,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17674,c_17828]) ).
tff(c_17626,plain,
multiply(sk_c2,sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_17660,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_17626,c_56]) ).
tff(c_16169,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_16174,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16169,c_4]) ).
tff(c_17718,plain,
! [Z_228] : ( multiply(sk_c6,multiply(sk_c4,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_16174,c_17685]) ).
tff(c_17780,plain,
! [Z_231] : ( multiply(sk_c6,multiply(sk_c4,Z_231)) = Z_231 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17718]) ).
tff(c_17792,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17660,c_17780]) ).
tff(c_17835,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17832,c_17832,c_17792]) ).
tff(c_17727,plain,
! [X_2,Z_228] : ( multiply(inverse(X_2),multiply(X_2,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17685]) ).
tff(c_17739,plain,
! [X_2,Z_228] : ( multiply(inverse(X_2),multiply(X_2,Z_228)) = Z_228 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17727]) ).
tff(c_17933,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17835,c_17739]) ).
tff(c_17939,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17933]) ).
tff(c_17655,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_17721,plain,
! [Z_228] : ( multiply(sk_c7,multiply(sk_c1,Z_228)) = multiply(identity,Z_228) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_17685]) ).
tff(c_17741,plain,
! [Z_229] : ( multiply(sk_c7,multiply(sk_c1,Z_229)) = Z_229 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17721]) ).
tff(c_17753,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17655,c_17741]) ).
tff(c_17757,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17753,c_16170]) ).
tff(c_17946,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17939,c_17757]) ).
tff(c_17838,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17832,c_17674]) ).
tff(c_17998,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17939,c_2,c_17939,c_17838]) ).
tff(c_17999,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17946,c_17998]) ).
tff(c_18000,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_18006,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17626,c_50]) ).
tff(c_18030,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_18057,plain,
! [Z_238] : ( multiply(sk_c6,multiply(sk_c3,Z_238)) = multiply(identity,Z_238) ),
inference(superposition,[status(thm),theory(equality)],[c_17630,c_18030]) ).
tff(c_18111,plain,
! [Z_241] : ( multiply(sk_c6,multiply(sk_c3,Z_241)) = Z_241 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18057]) ).
tff(c_18123,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18006,c_18111]) ).
tff(c_18127,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18000,c_18123]) ).
tff(c_18132,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18127,c_18000]) ).
tff(c_18069,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_18030]) ).
tff(c_18081,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_18069]) ).
tff(c_18247,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18132,c_18081]) ).
tff(c_18253,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18247]) ).
tff(c_18137,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18127,c_16170]) ).
tff(c_18256,plain,
multiply(identity,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18253,c_18137]) ).
tff(c_18266,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18256]) ).
tff(c_18268,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_36,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_18297,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18268,c_36]) ).
tff(c_34,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_18280,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18268,c_34]) ).
tff(c_18284,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18280,c_4]) ).
tff(c_18330,plain,
! [X_244,Y_245,Z_246] : ( multiply(multiply(X_244,Y_245),Z_246) = multiply(X_244,multiply(Y_245,Z_246)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18354,plain,
! [Z_246] : ( multiply(sk_c6,multiply(sk_c4,Z_246)) = multiply(identity,Z_246) ),
inference(superposition,[status(thm),theory(equality)],[c_18284,c_18330]) ).
tff(c_18376,plain,
! [Z_247] : ( multiply(sk_c6,multiply(sk_c4,Z_247)) = Z_247 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18354]) ).
tff(c_18388,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18297,c_18376]) ).
tff(c_28,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_18302,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_18268,c_28]) ).
tff(c_30,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_18310,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_18268,c_30]) ).
tff(c_18267,plain,
inverse(sk_c3) = sk_c6,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_18272,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18267,c_4]) ).
tff(c_18357,plain,
! [Z_246] : ( multiply(sk_c6,multiply(sk_c3,Z_246)) = multiply(identity,Z_246) ),
inference(superposition,[status(thm),theory(equality)],[c_18272,c_18330]) ).
tff(c_18678,plain,
! [Z_255] : ( multiply(sk_c6,multiply(sk_c3,Z_255)) = Z_255 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18357]) ).
tff(c_18690,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18310,c_18678]) ).
tff(c_18694,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18302,c_18690]) ).
tff(c_18699,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18694,c_18694,c_18388]) ).
tff(c_18363,plain,
! [X_2,Z_246] : ( multiply(inverse(X_2),multiply(X_2,Z_246)) = multiply(identity,Z_246) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18330]) ).
tff(c_18777,plain,
! [X_257,Z_258] : ( multiply(inverse(X_257),multiply(X_257,Z_258)) = Z_258 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18363]) ).
tff(c_18798,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18699,c_18777]) ).
tff(c_18832,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18798]) ).
tff(c_18704,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18694,c_18302]) ).
tff(c_18881,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18832,c_2,c_18832,c_18704]) ).
tff(c_18402,plain,
! [Z_248] : ( multiply(sk_c6,multiply(sk_c3,Z_248)) = Z_248 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18357]) ).
tff(c_18414,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18310,c_18402]) ).
tff(c_18418,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18302,c_18414]) ).
tff(c_18437,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18418,c_18418,c_18388]) ).
tff(c_18480,plain,
! [X_250,Z_251] : ( multiply(inverse(X_250),multiply(X_250,Z_251)) = Z_251 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18363]) ).
tff(c_18501,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18437,c_18480]) ).
tff(c_18526,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18501]) ).
tff(c_18441,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18418,c_18302]) ).
tff(c_18569,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18526,c_2,c_18526,c_18441]) ).
tff(c_18393,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_18302,c_68]) ).
tff(c_18394,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_18393]) ).
tff(c_18438,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18418,c_18394]) ).
tff(c_18609,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18569,c_18526,c_18526,c_18438]) ).
tff(c_18610,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_18393]) ).
tff(c_18677,plain,
multiply(sk_c7,sk_c5) != sk_c6,
inference(splitLeft,[status(thm)],[c_18610]) ).
tff(c_18696,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18694,c_18677]) ).
tff(c_18921,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18881,c_18832,c_18832,c_18696]) ).
tff(c_18923,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_18610]) ).
tff(c_18348,plain,
! [Z_246] : ( multiply(sk_c6,multiply(sk_c7,Z_246)) = multiply(sk_c5,Z_246) ),
inference(superposition,[status(thm),theory(equality)],[c_18302,c_18330]) ).
tff(c_18967,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_18923,c_18348]) ).
tff(c_18973,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18388,c_18967]) ).
tff(c_19607,plain,
! [X_272,Z_273] : ( multiply(inverse(X_272),multiply(X_272,Z_273)) = Z_273 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18363]) ).
tff(c_19634,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18973,c_19607]) ).
tff(c_19656,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19634]) ).
tff(c_18374,plain,
! [X_2,Z_246] : ( multiply(inverse(X_2),multiply(X_2,Z_246)) = Z_246 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18363]) ).
tff(c_19821,plain,
! [X_275,Z_276] : ( multiply(inverse(inverse(X_275)),Z_276) = multiply(X_275,Z_276) ),
inference(superposition,[status(thm),theory(equality)],[c_18374,c_19607]) ).
tff(c_19649,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19607]) ).
tff(c_19828,plain,
! [X_275] : ( multiply(X_275,identity) = X_275 ),
inference(superposition,[status(thm),theory(equality)],[c_19821,c_19649]) ).
tff(c_18993,plain,
! [Z_261] : ( multiply(sk_c6,multiply(sk_c3,Z_261)) = Z_261 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18357]) ).
tff(c_19008,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18310,c_18993]) ).
tff(c_19012,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18302,c_19008]) ).
tff(c_19028,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19012,c_18267]) ).
tff(c_19659,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19656,c_19028]) ).
tff(c_19022,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19012,c_18310]) ).
tff(c_19711,plain,
multiply(sk_c3,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_19656,c_19022]) ).
tff(c_19715,plain,
multiply(inverse(sk_c3),sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19711,c_18374]) ).
tff(c_19721,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19659,c_19715]) ).
tff(c_19090,plain,
! [X_262,Z_263] : ( multiply(inverse(X_262),multiply(X_262,Z_263)) = Z_263 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18363]) ).
tff(c_19318,plain,
! [X_265,Z_266] : ( multiply(inverse(inverse(X_265)),Z_266) = multiply(X_265,Z_266) ),
inference(superposition,[status(thm),theory(equality)],[c_18374,c_19090]) ).
tff(c_19144,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19090]) ).
tff(c_19325,plain,
! [X_265] : ( multiply(X_265,identity) = X_265 ),
inference(superposition,[status(thm),theory(equality)],[c_19318,c_19144]) ).
tff(c_19129,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18973,c_19090]) ).
tff(c_19153,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19129]) ).
tff(c_19023,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19012,c_18302]) ).
tff(c_19108,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_19023,c_19090]) ).
tff(c_19151,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19108]) ).
tff(c_18922,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_18610]) ).
tff(c_19034,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19012,c_19012,c_19012,c_19012,c_19012,c_18922]) ).
tff(c_19035,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_19034]) ).
tff(c_19589,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19325,c_19153,c_19151,c_19151,c_19035]) ).
tff(c_19026,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19012,c_18280]) ).
tff(c_19046,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19026,c_4]) ).
tff(c_19182,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19153,c_19046]) ).
tff(c_19169,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19153,c_19026]) ).
tff(c_19207,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19182,c_19169]) ).
tff(c_19591,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19589,c_19207]) ).
tff(c_19592,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_19034]) ).
tff(c_26193,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19656,c_19828,c_19656,c_19656,c_19828,c_19721,c_19656,c_19656,c_19828,c_19721,c_19656,c_19721,c_19592]) ).
tff(c_26195,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_26193]) ).
tff(c_19603,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19026,c_4]) ).
tff(c_19683,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19656,c_19603]) ).
tff(c_19658,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19656,c_19026]) ).
tff(c_19684,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19683,c_19658]) ).
tff(c_26197,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26195,c_19684]) ).
tff(c_26198,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 ) ),
inference(splitRight,[status(thm)],[c_26193]) ).
tff(c_26200,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_26198]) ).
tff(c_26202,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26200,c_19684]) ).
tff(c_26205,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_26198]) ).
tff(c_26207,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26205,c_19684]) ).
tff(c_26209,plain,
inverse(sk_c2) != sk_c7,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_58,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_26249,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_26209,c_58]) ).
tff(c_60,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_26244,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_26209,c_60]) ).
tff(c_62,plain,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_26221,plain,
inverse(sk_c3) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_26209,c_62]) ).
tff(c_26225,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_26221,c_4]) ).
tff(c_26297,plain,
! [Z_358] : ( multiply(sk_c6,multiply(sk_c3,Z_358)) = multiply(identity,Z_358) ),
inference(superposition,[status(thm),theory(equality)],[c_26225,c_26273]) ).
tff(c_26616,plain,
! [Z_365] : ( multiply(sk_c6,multiply(sk_c3,Z_365)) = Z_365 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26297]) ).
tff(c_26628,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_26244,c_26616]) ).
tff(c_26632,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26249,c_26628]) ).
tff(c_26208,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_26641,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26632,c_26208]) ).
tff(c_66,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_26236,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_26209,c_66]) ).
tff(c_26637,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26632,c_26236]) ).
tff(c_26887,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_26637,c_26313]) ).
tff(c_26893,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26641,c_26887]) ).
tff(c_26937,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_26893,c_26313]) ).
tff(c_26943,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_26937]) ).
tff(c_26635,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26632,c_26249]) ).
tff(c_26847,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_26635,c_26826]) ).
tff(c_26873,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_26847]) ).
tff(c_26707,plain,
! [X_366,Z_367] : ( multiply(inverse(X_366),multiply(X_366,Z_367)) = Z_367 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26303]) ).
tff(c_26728,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_26635,c_26707]) ).
tff(c_26760,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_26728]) ).
tff(c_26369,plain,
! [Z_361] : ( multiply(sk_c6,multiply(sk_c3,Z_361)) = Z_361 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26297]) ).
tff(c_26387,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_26244,c_26369]) ).
tff(c_26391,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26249,c_26387]) ).
tff(c_26397,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26391,c_26249]) ).
tff(c_26470,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_26397,c_26313]) ).
tff(c_26476,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_26470]) ).
tff(c_26316,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26249,c_68]) ).
tff(c_26317,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_26316]) ).
tff(c_26396,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_26391,c_26317]) ).
tff(c_26606,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26476,c_26396]) ).
tff(c_26607,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X1_8) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_26316]) ).
tff(c_26646,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c7,sk_c5) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26632,c_26632,c_26632,c_26632,c_26632,c_26632,c_26607]) ).
tff(c_26647,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(splitLeft,[status(thm)],[c_26646]) ).
tff(c_26772,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26760,c_26647]) ).
tff(c_26773,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(X4_7,sk_c7) != sk_c5 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_26646]) ).
tff(c_35450,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( identity != X2_9 )
| ( inverse(X2_9) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_27096,c_26943,c_26873,c_26873,c_27096,c_26943,c_26873,c_26873,c_27096,c_26943,c_26873,c_26943,c_26943,c_27096,c_26943,c_26943,c_26773]) ).
tff(c_35452,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_35450]) ).
tff(c_26792,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_26641,c_4]) ).
tff(c_26964,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26943,c_26792]) ).
tff(c_26952,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_26943,c_26641]) ).
tff(c_26979,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_26964,c_26952]) ).
tff(c_35454,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_35452,c_26979]) ).
tff(c_35455,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(splitRight,[status(thm)],[c_35450]) ).
tff(c_53119,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_35455]) ).
tff(c_53121,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53119,c_26979]) ).
tff(c_53122,plain,
! [X1_8,X4_7] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 ) ),
inference(splitRight,[status(thm)],[c_35455]) ).
tff(c_53124,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_53122]) ).
tff(c_53126,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53124,c_26979]) ).
tff(c_54227,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_53122]) ).
tff(c_54229,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54227,c_26979]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP294-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n014.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 21:53:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.07/6.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.07/7.03
% 16.07/7.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.43/7.09
% 16.43/7.09 Inference rules
% 16.43/7.09 ----------------------
% 16.43/7.09 #Ref : 0
% 16.43/7.09 #Sup : 13272
% 16.43/7.09 #Fact : 0
% 16.43/7.09 #Define : 0
% 16.43/7.09 #Split : 38
% 16.43/7.09 #Chain : 0
% 16.43/7.09 #Close : 0
% 16.43/7.09
% 16.43/7.09 Ordering : KBO
% 16.43/7.09
% 16.43/7.09 Simplification rules
% 16.43/7.09 ----------------------
% 16.43/7.09 #Subsume : 11
% 16.43/7.09 #Demod : 36543
% 16.43/7.09 #Tautology : 10632
% 16.43/7.09 #SimpNegUnit : 86
% 16.43/7.09 #BackRed : 501
% 16.43/7.09
% 16.43/7.09 #Partial instantiations: 0
% 16.43/7.09 #Strategies tried : 1
% 16.43/7.09
% 16.43/7.09 Timing (in seconds)
% 16.43/7.09 ----------------------
% 16.49/7.09 Preprocessing : 0.49
% 16.49/7.09 Parsing : 0.20
% 16.49/7.09 CNF conversion : 0.03
% 16.49/7.09 Main loop : 5.37
% 16.49/7.09 Inferencing : 1.37
% 16.49/7.09 Reduction : 3.19
% 16.49/7.09 Demodulation : 2.95
% 16.49/7.09 BG Simplification : 0.13
% 16.49/7.09 Subsumption : 0.45
% 16.49/7.09 Abstraction : 0.31
% 16.49/7.09 MUC search : 0.00
% 16.49/7.09 Cooper : 0.00
% 16.49/7.09 Total : 5.98
% 16.49/7.09 Index Insertion : 0.00
% 16.49/7.09 Index Deletion : 0.00
% 16.49/7.09 Index Matching : 0.00
% 16.49/7.09 BG Taut test : 0.00
%------------------------------------------------------------------------------