TSTP Solution File: GRP376-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP376-1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:41:07 EDT 2023
% Result : Unsatisfiable 12.53s 4.23s
% Output : CNFRefutation 12.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 39
% Syntax : Number of formulae : 412 ( 320 unt; 10 typ; 0 def)
% Number of atoms : 585 ( 562 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 368 ( 185 ~; 183 |; 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 : 184 (; 184 !; 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_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_68,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X3,X4,X1,X2] :
( ( inverse(sk_c7) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(X4,sk_c5) != sk_c7 )
| ( inverse(X4) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( 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_110,axiom,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = 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_107,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_12924,plain,
! [X_150,Y_151,Z_152] : ( multiply(multiply(X_150,Y_151),Z_152) = multiply(X_150,multiply(Y_151,Z_152)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12954,plain,
! [X_2,Z_152] : ( multiply(inverse(X_2),multiply(X_2,Z_152)) = multiply(identity,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12924]) ).
tff(c_13312,plain,
! [X_158,Z_159] : ( multiply(inverse(X_158),multiply(X_158,Z_159)) = Z_159 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12954]) ).
tff(c_12966,plain,
! [X_2,Z_152] : ( multiply(inverse(X_2),multiply(X_2,Z_152)) = Z_152 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12954]) ).
tff(c_14454,plain,
! [X_182,Z_183] : ( multiply(inverse(inverse(X_182)),Z_183) = multiply(X_182,Z_183) ),
inference(superposition,[status(thm),theory(equality)],[c_13312,c_12966]) ).
tff(c_13372,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_13312]) ).
tff(c_14490,plain,
! [X_182] : ( multiply(X_182,identity) = X_182 ),
inference(superposition,[status(thm),theory(equality)],[c_14454,c_13372]) ).
tff(c_13716,plain,
! [X_167,Z_168] : ( multiply(inverse(inverse(X_167)),Z_168) = multiply(X_167,Z_168) ),
inference(superposition,[status(thm),theory(equality)],[c_12966,c_13312]) ).
tff(c_13744,plain,
! [X_167] : ( multiply(X_167,identity) = X_167 ),
inference(superposition,[status(thm),theory(equality)],[c_13716,c_13372]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_98,plain,
inverse(sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_102,plain,
multiply(sk_c6,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_20,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_136,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_34,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_111,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_115,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_111,c_4]) ).
tff(c_160,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_184,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_160]) ).
tff(c_206,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_184]) ).
tff(c_218,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_136,c_206]) ).
tff(c_187,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c7,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_160]) ).
tff(c_229,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c7,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_187]) ).
tff(c_241,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_218,c_229]) ).
tff(c_251,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_241]) ).
tff(c_193,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_160]) ).
tff(c_483,plain,
! [X_19,Z_20] : ( multiply(inverse(X_19),multiply(X_19,Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_193]) ).
tff(c_204,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_193]) ).
tff(c_569,plain,
! [X_23,Z_24] : ( multiply(inverse(inverse(X_23)),Z_24) = multiply(X_23,Z_24) ),
inference(superposition,[status(thm),theory(equality)],[c_483,c_204]) ).
tff(c_507,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_483]) ).
tff(c_580,plain,
! [X_23] : ( multiply(X_23,identity) = X_23 ),
inference(superposition,[status(thm),theory(equality)],[c_569,c_507]) ).
tff(c_44,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_130,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_68,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(sk_c7) != sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_253,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( sk_c5 != identity )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_130,c_102,c_68]) ).
tff(c_254,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_253]) ).
tff(c_260,plain,
inverse(sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_98]) ).
tff(c_268,plain,
multiply(identity,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_260,c_4]) ).
tff(c_278,plain,
sk_c7 = identity,
inference(superposition,[status(thm),theory(equality)],[c_268,c_2]) ).
tff(c_258,plain,
multiply(sk_c5,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_130]) ).
tff(c_363,plain,
multiply(sk_c5,identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_278,c_258]) ).
tff(c_64,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_85,plain,
inverse(sk_c2) = sk_c5,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_125,plain,
multiply(sk_c2,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_54]) ).
tff(c_289,plain,
multiply(sk_c2,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_278,c_125]) ).
tff(c_379,plain,
multiply(inverse(sk_c2),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_289,c_204]) ).
tff(c_385,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_363,c_85,c_379]) ).
tff(c_387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_254,c_385]) ).
tff(c_389,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_253]) ).
tff(c_390,plain,
multiply(identity,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_389,c_130]) ).
tff(c_394,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_390]) ).
tff(c_419,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_394]) ).
tff(c_388,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_253]) ).
tff(c_694,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_251,c_580,c_251,c_389,c_419,c_580,c_419,c_251,c_580,c_419,c_389,c_389,c_580,c_419,c_251,c_419,c_388]) ).
tff(c_774,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_694]) ).
tff(c_406,plain,
inverse(sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_394,c_98]) ).
tff(c_440,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_251,c_251,c_406]) ).
tff(c_776,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_774,c_440]) ).
tff(c_777,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_694]) ).
tff(c_11824,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_777]) ).
tff(c_11826,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11824,c_440]) ).
tff(c_11827,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_777]) ).
tff(c_11829,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_11827]) ).
tff(c_11831,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11829,c_440]) ).
tff(c_11834,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_11827]) ).
tff(c_11836,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11834,c_440]) ).
tff(c_11838,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_20]) ).
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_11875,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_18]) ).
tff(c_11876,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_11838,c_11875]) ).
tff(c_89,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_11879,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11876,c_89]) ).
tff(c_11944,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_11879,c_2]) ).
tff(c_11877,plain,
multiply(identity,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11876,c_130]) ).
tff(c_11881,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11877]) ).
tff(c_11878,plain,
multiply(sk_c2,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11876,c_125]) ).
tff(c_11935,plain,
multiply(sk_c2,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11881,c_11878]) ).
tff(c_11952,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11944,c_11935]) ).
tff(c_11955,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11952]) ).
tff(c_11889,plain,
multiply(sk_c6,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11881,c_115]) ).
tff(c_12012,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11955,c_11889]) ).
tff(c_11887,plain,
multiply(sk_c1,sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11881,c_11838]) ).
tff(c_12011,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11955,c_11955,c_11887]) ).
tff(c_12013,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12012,c_12011]) ).
tff(c_12017,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12013]) ).
tff(c_12019,plain,
multiply(sk_c5,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_38,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_12064,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_38]) ).
tff(c_12065,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_12019,c_12064]) ).
tff(c_12069,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12065,c_89]) ).
tff(c_12162,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_12069,c_2]) ).
tff(c_12096,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_12069,c_2]) ).
tff(c_52,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_12087,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,identity) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12065,c_52]) ).
tff(c_12088,plain,
multiply(sk_c2,identity) = sk_c7,
inference(splitLeft,[status(thm)],[c_12087]) ).
tff(c_12104,plain,
multiply(identity,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12096,c_12088]) ).
tff(c_12107,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12104]) ).
tff(c_12067,plain,
multiply(identity,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12065,c_12019]) ).
tff(c_12071,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12067]) ).
tff(c_12114,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12107,c_12071]) ).
tff(c_12070,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12065,c_85]) ).
tff(c_12105,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12096,c_12070]) ).
tff(c_12120,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_12107,c_98]) ).
tff(c_12155,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12105,c_12120]) ).
tff(c_12156,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12114,c_12155]) ).
tff(c_12158,plain,
multiply(sk_c2,identity) != sk_c7,
inference(splitRight,[status(thm)],[c_12087]) ).
tff(c_12191,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12162,c_12158]) ).
tff(c_12068,plain,
multiply(sk_c2,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12065,c_125]) ).
tff(c_12194,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12162,c_12068]) ).
tff(c_12195,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12191,c_12194]) ).
tff(c_12197,plain,
multiply(sk_c2,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_48,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_12560,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_12561,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_12197,c_12560]) ).
tff(c_12564,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12561,c_89]) ).
tff(c_12580,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_12564,c_2]) ).
tff(c_12563,plain,
multiply(sk_c2,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12561,c_12197]) ).
tff(c_12604,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12580,c_12563]) ).
tff(c_12618,plain,
! [X_143,Y_144,Z_145] : ( multiply(multiply(X_143,Y_144),Z_145) = multiply(X_143,multiply(Y_144,Z_145)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12648,plain,
! [Z_145] : ( multiply(sk_c6,multiply(sk_c7,Z_145)) = multiply(identity,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_12618]) ).
tff(c_12679,plain,
! [Z_147] : ( multiply(sk_c6,multiply(sk_c7,Z_147)) = Z_147 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12648]) ).
tff(c_12697,plain,
multiply(sk_c6,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_12679]) ).
tff(c_50,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_12217,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12197,c_50]) ).
tff(c_12221,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12217,c_4]) ).
tff(c_12694,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_12221,c_12679]) ).
tff(c_12712,plain,
sk_c3 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_12697,c_12694]) ).
tff(c_12244,plain,
( ( sk_c5 = identity )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_48]) ).
tff(c_12245,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_12197,c_12244]) ).
tff(c_12248,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12245,c_89]) ).
tff(c_12264,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_12248,c_2]) ).
tff(c_12288,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( sk_c7 = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12264,c_12245,c_52]) ).
tff(c_12289,plain,
sk_c7 = identity,
inference(splitLeft,[status(thm)],[c_12288]) ).
tff(c_12247,plain,
multiply(sk_c2,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12245,c_12197]) ).
tff(c_12336,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12289,c_2,c_12264,c_12247]) ).
tff(c_12338,plain,
sk_c7 != identity,
inference(splitRight,[status(thm)],[c_12288]) ).
tff(c_12249,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12245,c_85]) ).
tff(c_12273,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12264,c_12249]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_12233,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_12352,plain,
! [X_136,Y_137,Z_138] : ( multiply(multiply(X_136,Y_137),Z_138) = multiply(X_136,multiply(Y_137,Z_138)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12382,plain,
! [Z_138] : ( multiply(sk_c7,multiply(sk_c1,Z_138)) = multiply(identity,Z_138) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_12352]) ).
tff(c_12403,plain,
! [Z_139] : ( multiply(sk_c7,multiply(sk_c1,Z_139)) = Z_139 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12382]) ).
tff(c_12415,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12233,c_12403]) ).
tff(c_12385,plain,
! [Z_138] : ( multiply(sk_c6,multiply(sk_c7,Z_138)) = multiply(identity,Z_138) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_12352]) ).
tff(c_12429,plain,
! [Z_140] : ( multiply(sk_c6,multiply(sk_c7,Z_140)) = Z_140 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12385]) ).
tff(c_12441,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_12415,c_12429]) ).
tff(c_12454,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_12441]) ).
tff(c_12464,plain,
inverse(sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12454,c_98]) ).
tff(c_12388,plain,
! [X_2,Z_138] : ( multiply(inverse(X_2),multiply(X_2,Z_138)) = multiply(identity,Z_138) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12352]) ).
tff(c_12483,plain,
! [X_141,Z_142] : ( multiply(inverse(X_141),multiply(X_141,Z_142)) = Z_142 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12388]) ).
tff(c_12522,plain,
multiply(inverse(sk_c7),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_115,c_12483]) ).
tff(c_12538,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12464,c_12522]) ).
tff(c_12543,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12538,c_111]) ).
tff(c_12545,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12273,c_12543]) ).
tff(c_12547,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12338,c_12545]) ).
tff(c_12548,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_12713,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12712,c_12548]) ).
tff(c_12645,plain,
! [Z_145] : ( multiply(sk_c7,multiply(sk_c1,Z_145)) = multiply(identity,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_12618]) ).
tff(c_12662,plain,
! [Z_145] : ( multiply(sk_c7,multiply(sk_c1,Z_145)) = Z_145 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12645]) ).
tff(c_12725,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_12713,c_12662]) ).
tff(c_12663,plain,
! [Z_145] : ( multiply(sk_c6,multiply(sk_c7,Z_145)) = Z_145 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12648]) ).
tff(c_12735,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12725,c_12663]) ).
tff(c_12196,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_54]) ).
tff(c_12549,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
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_12605,plain,
( ( multiply(sk_c4,identity) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12561,c_26]) ).
tff(c_12606,plain,
multiply(sk_c4,identity) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_12549,c_12605]) ).
tff(c_12651,plain,
! [X_2,Z_145] : ( multiply(inverse(X_2),multiply(X_2,Z_145)) = multiply(identity,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12618]) ).
tff(c_12749,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_12651]) ).
tff(c_12788,plain,
multiply(inverse(sk_c4),sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12606,c_12749]) ).
tff(c_12822,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12735,c_12196,c_12788]) ).
tff(c_12824,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12604,c_12822]) ).
tff(c_12826,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_28,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_12863,plain,
( ( sk_c5 = identity )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_28]) ).
tff(c_12864,plain,
sk_c5 = identity,
inference(negUnitSimplification,[status(thm)],[c_12826,c_12863]) ).
tff(c_36,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_12908,plain,
( ( multiply(sk_c4,identity) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12864,c_36]) ).
tff(c_12909,plain,
multiply(sk_c4,identity) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_12826,c_12908]) ).
tff(c_12939,plain,
! [Z_152] : ( multiply(sk_c4,multiply(identity,Z_152)) = multiply(sk_c6,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_12909,c_12924]) ).
tff(c_12962,plain,
! [Z_152] : ( multiply(sk_c6,Z_152) = multiply(sk_c4,Z_152) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12939]) ).
tff(c_12992,plain,
! [Z_154] : ( multiply(sk_c6,Z_154) = multiply(sk_c4,Z_154) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12939]) ).
tff(c_30,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_12838,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12826,c_30]) ).
tff(c_12842,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12838,c_4]) ).
tff(c_12951,plain,
! [Z_152] : ( multiply(sk_c6,multiply(sk_c7,Z_152)) = multiply(identity,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_12924]) ).
tff(c_12968,plain,
! [Z_153] : ( multiply(sk_c6,multiply(sk_c7,Z_153)) = Z_153 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12951]) ).
tff(c_12980,plain,
multiply(sk_c6,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_12842,c_12968]) ).
tff(c_12998,plain,
multiply(sk_c4,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_12992,c_12980]) ).
tff(c_32,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_12853,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12826,c_32]) ).
tff(c_12942,plain,
! [Z_152] : ( multiply(sk_c3,multiply(sk_c6,Z_152)) = multiply(sk_c7,Z_152) ),
inference(superposition,[status(thm),theory(equality)],[c_12853,c_12924]) ).
tff(c_13049,plain,
! [Z_155] : ( multiply(sk_c3,multiply(sk_c4,Z_155)) = multiply(sk_c7,Z_155) ),
inference(demodulation,[status(thm),theory(equality)],[c_12962,c_12942]) ).
tff(c_13067,plain,
multiply(sk_c7,identity) = multiply(sk_c3,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_12909,c_13049]) ).
tff(c_13071,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_12853,c_13067]) ).
tff(c_13086,plain,
sk_c6 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_12998,c_12909]) ).
tff(c_12825,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_13105,plain,
inverse(sk_c4) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_13086,c_12825]) ).
tff(c_13184,plain,
multiply(sk_c3,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_13105,c_4]) ).
tff(c_13191,plain,
multiply(inverse(sk_c3),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_13184,c_12966]) ).
tff(c_13197,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_13071,c_12838,c_13191]) ).
tff(c_13202,plain,
multiply(sk_c4,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_13197,c_13197,c_13071]) ).
tff(c_13209,plain,
sk_c4 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_12998,c_13202]) ).
tff(c_13030,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 )
| ( sk_c7 != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_2,c_12864,c_12864,c_12864,c_12864,c_102,c_12864,c_68]) ).
tff(c_13031,plain,
sk_c7 != sk_c6,
inference(splitLeft,[status(thm)],[c_13030]) ).
tff(c_13099,plain,
sk_c7 != sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_13086,c_13031]) ).
tff(c_13201,plain,
sk_c4 != sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_13197,c_13099]) ).
tff(c_13229,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13209,c_13201]) ).
tff(c_13231,plain,
sk_c7 = sk_c6,
inference(splitRight,[status(thm)],[c_13030]) ).
tff(c_13237,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13231,c_102]) ).
tff(c_13268,plain,
multiply(sk_c4,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12962,c_13237]) ).
tff(c_13235,plain,
inverse(sk_c3) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13231,c_12838]) ).
tff(c_13233,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13231,c_12853]) ).
tff(c_13336,plain,
multiply(inverse(sk_c3),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_13233,c_13312]) ).
tff(c_13381,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13268,c_12962,c_13235,c_13336]) ).
tff(c_13238,plain,
inverse(sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_13231,c_98]) ).
tff(c_12830,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12825,c_4]) ).
tff(c_13366,plain,
multiply(inverse(sk_c6),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_12830,c_13312]) ).
tff(c_13389,plain,
sk_c6 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_12909,c_12962,c_13238,c_13366]) ).
tff(c_13415,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13381,c_13389]) ).
tff(c_13398,plain,
sk_c7 = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_13389,c_13231]) ).
tff(c_13445,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_13415,c_13398]) ).
tff(c_13230,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_13030]) ).
tff(c_13556,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_13381,c_13381,c_13445,c_13445,c_13381,c_13445,c_13445,c_13381,c_13445,c_13230]) ).
tff(c_13557,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_13556]) ).
tff(c_14161,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_13744,c_13557]) ).
tff(c_12865,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12864,c_89]) ).
tff(c_12881,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_12865,c_2]) ).
tff(c_12866,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12864,c_85]) ).
tff(c_12889,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12881,c_12866]) ).
tff(c_14163,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14161,c_12889]) ).
tff(c_14164,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_13556]) ).
tff(c_22261,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14490,c_14490,c_14490,c_14164]) ).
tff(c_22263,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22261]) ).
tff(c_22265,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22263,c_12889]) ).
tff(c_22266,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_22261]) ).
tff(c_22268,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_22266]) ).
tff(c_22270,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22268,c_12889]) ).
tff(c_22273,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_22266]) ).
tff(c_22275,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22273,c_12889]) ).
tff(c_22277,plain,
inverse(sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_16,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_22320,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22277,c_16]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_22302,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22277,c_14]) ).
tff(c_22306,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22302,c_4]) ).
tff(c_22350,plain,
! [X_268,Y_269,Z_270] : ( multiply(multiply(X_268,Y_269),Z_270) = multiply(X_268,multiply(Y_269,Z_270)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22371,plain,
! [Z_270] : ( multiply(sk_c6,multiply(sk_c4,Z_270)) = multiply(identity,Z_270) ),
inference(superposition,[status(thm),theory(equality)],[c_22306,c_22350]) ).
tff(c_22415,plain,
! [Z_272] : ( multiply(sk_c6,multiply(sk_c4,Z_272)) = Z_272 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22371]) ).
tff(c_22427,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_22320,c_22415]) ).
tff(c_12,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_22310,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22277,c_12]) ).
tff(c_22276,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_22281,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22276,c_4]) ).
tff(c_22380,plain,
! [Z_270] : ( multiply(sk_c7,multiply(sk_c3,Z_270)) = multiply(identity,Z_270) ),
inference(superposition,[status(thm),theory(equality)],[c_22281,c_22350]) ).
tff(c_22463,plain,
! [Z_274] : ( multiply(sk_c7,multiply(sk_c3,Z_274)) = Z_274 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22380]) ).
tff(c_22478,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_22310,c_22463]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_22326,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_22277,c_8]) ).
tff(c_22744,plain,
! [Z_279] : ( multiply(sk_c6,multiply(sk_c7,Z_279)) = multiply(sk_c5,Z_279) ),
inference(superposition,[status(thm),theory(equality)],[c_22326,c_22350]) ).
tff(c_22762,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_22478,c_22744]) ).
tff(c_22769,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_22427,c_22762]) ).
tff(c_22386,plain,
! [X_2,Z_270] : ( multiply(inverse(X_2),multiply(X_2,Z_270)) = multiply(identity,Z_270) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22350]) ).
tff(c_22398,plain,
! [X_2,Z_270] : ( multiply(inverse(X_2),multiply(X_2,Z_270)) = Z_270 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22386]) ).
tff(c_22773,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_22769,c_22398]) ).
tff(c_22779,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22773]) ).
tff(c_22787,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22779,c_22779,c_22478]) ).
tff(c_22794,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22787]) ).
tff(c_22791,plain,
inverse(identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_22779,c_22277]) ).
tff(c_22857,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22794,c_22791]) ).
tff(c_22800,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_22794,c_22794,c_22427]) ).
tff(c_22805,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22800]) ).
tff(c_22515,plain,
! [X_275,Z_276] : ( multiply(inverse(X_275),multiply(X_275,Z_276)) = Z_276 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22386]) ).
tff(c_22590,plain,
multiply(inverse(sk_c5),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_89,c_22515]) ).
tff(c_22834,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_22805,c_22590]) ).
tff(c_22839,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_22834]) ).
tff(c_22837,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22805,c_85]) ).
tff(c_22863,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22839,c_22837]) ).
tff(c_22864,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22857,c_22863]) ).
tff(c_22866,plain,
inverse(sk_c2) != sk_c5,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_66,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_32889,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22866,c_66]) ).
tff(c_22865,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_22870,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22865,c_4]) ).
tff(c_32907,plain,
! [X_400,Y_401,Z_402] : ( multiply(multiply(X_400,Y_401),Z_402) = multiply(X_400,multiply(Y_401,Z_402)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_32937,plain,
! [Z_402] : ( multiply(sk_c6,multiply(sk_c4,Z_402)) = multiply(identity,Z_402) ),
inference(superposition,[status(thm),theory(equality)],[c_22870,c_32907]) ).
tff(c_32978,plain,
! [Z_404] : ( multiply(sk_c6,multiply(sk_c4,Z_404)) = Z_404 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32937]) ).
tff(c_32990,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_32889,c_32978]) ).
tff(c_32940,plain,
! [X_2,Z_402] : ( multiply(inverse(X_2),multiply(X_2,Z_402)) = multiply(identity,Z_402) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_32907]) ).
tff(c_33014,plain,
! [X_406,Z_407] : ( multiply(inverse(X_406),multiply(X_406,Z_407)) = Z_407 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32940]) ).
tff(c_33035,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32990,c_33014]) ).
tff(c_22960,plain,
! [X_281,Y_282,Z_283] : ( multiply(multiply(X_281,Y_282),Z_283) = multiply(X_281,multiply(Y_282,Z_283)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_22993,plain,
! [X_2,Z_283] : ( multiply(inverse(X_2),multiply(X_2,Z_283)) = multiply(identity,Z_283) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22960]) ).
tff(c_23006,plain,
! [X_2,Z_283] : ( multiply(inverse(X_2),multiply(X_2,Z_283)) = Z_283 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22993]) ).
tff(c_23300,plain,
! [X_290,Z_291] : ( multiply(inverse(X_290),multiply(X_290,Z_291)) = Z_291 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22993]) ).
tff(c_24048,plain,
! [X_307,Z_308] : ( multiply(inverse(inverse(X_307)),Z_308) = multiply(X_307,Z_308) ),
inference(superposition,[status(thm),theory(equality)],[c_23006,c_23300]) ).
tff(c_23327,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_23300]) ).
tff(c_24069,plain,
! [X_307] : ( multiply(X_307,identity) = X_307 ),
inference(superposition,[status(thm),theory(equality)],[c_24048,c_23327]) ).
tff(c_23496,plain,
! [X_293,Z_294] : ( multiply(inverse(inverse(X_293)),Z_294) = multiply(X_293,Z_294) ),
inference(superposition,[status(thm),theory(equality)],[c_23006,c_23300]) ).
tff(c_23503,plain,
! [X_293] : ( multiply(X_293,identity) = X_293 ),
inference(superposition,[status(thm),theory(equality)],[c_23496,c_23327]) ).
tff(c_22895,plain,
inverse(sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_22899,plain,
multiply(sk_c6,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22895,c_4]) ).
tff(c_58,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_22903,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_22866,c_58]) ).
tff(c_22908,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22899,c_22903]) ).
tff(c_22913,plain,
inverse(sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22908,c_22866]) ).
tff(c_22942,plain,
( ( multiply(sk_c4,identity) = sk_c6 )
| ( inverse(sk_c2) = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22908,c_22908,c_66]) ).
tff(c_22943,plain,
multiply(sk_c4,identity) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_22913,c_22942]) ).
tff(c_22990,plain,
! [Z_283] : ( multiply(sk_c6,multiply(sk_c4,Z_283)) = multiply(identity,Z_283) ),
inference(superposition,[status(thm),theory(equality)],[c_22870,c_22960]) ).
tff(c_23034,plain,
! [Z_285] : ( multiply(sk_c6,multiply(sk_c4,Z_285)) = Z_285 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22990]) ).
tff(c_23046,plain,
multiply(sk_c6,sk_c6) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22943,c_23034]) ).
tff(c_62,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_22935,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22908,c_62]) ).
tff(c_22936,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22913,c_22935]) ).
tff(c_60,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_22874,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_22866,c_60]) ).
tff(c_22878,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_22874,c_4]) ).
tff(c_22987,plain,
! [Z_283] : ( multiply(sk_c7,multiply(sk_c3,Z_283)) = multiply(identity,Z_283) ),
inference(superposition,[status(thm),theory(equality)],[c_22878,c_22960]) ).
tff(c_23008,plain,
! [Z_284] : ( multiply(sk_c7,multiply(sk_c3,Z_284)) = Z_284 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22987]) ).
tff(c_23020,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_22936,c_23008]) ).
tff(c_22984,plain,
! [Z_283] : ( multiply(sk_c6,multiply(sk_c7,Z_283)) = multiply(identity,Z_283) ),
inference(superposition,[status(thm),theory(equality)],[c_22899,c_22960]) ).
tff(c_23058,plain,
! [Z_286] : ( multiply(sk_c6,multiply(sk_c7,Z_286)) = Z_286 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22984]) ).
tff(c_23070,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_23020,c_23058]) ).
tff(c_23083,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23046,c_23070]) ).
tff(c_23086,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23083,c_23083,c_23020]) ).
tff(c_23096,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23086]) ).
tff(c_23032,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 )
| ( sk_c7 != sk_c6 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22895,c_2,c_22908,c_22908,c_22908,c_22908,c_22899,c_22908,c_68]) ).
tff(c_23033,plain,
sk_c7 != sk_c6,
inference(splitLeft,[status(thm)],[c_23032]) ).
tff(c_23085,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_23083,c_23033]) ).
tff(c_23157,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23096,c_23085]) ).
tff(c_23159,plain,
sk_c7 = sk_c6,
inference(splitRight,[status(thm)],[c_23032]) ).
tff(c_23165,plain,
multiply(sk_c6,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23159,c_22899]) ).
tff(c_23160,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23159,c_23159,c_23020]) ).
tff(c_23268,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23165,c_23160]) ).
tff(c_23277,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23268,c_23159]) ).
tff(c_23158,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,identity) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_23032]) ).
tff(c_23422,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_23268,c_23268,c_23277,c_23277,c_23268,c_23277,c_23277,c_23268,c_23277,c_23158]) ).
tff(c_23423,plain,
! [X2_9] :
( ( multiply(X2_9,identity) != identity )
| ( inverse(X2_9) != identity ) ),
inference(splitLeft,[status(thm)],[c_23422]) ).
tff(c_23860,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_23503,c_23423]) ).
tff(c_23166,plain,
inverse(sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_23159,c_22895]) ).
tff(c_23274,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_23268,c_23268,c_23166]) ).
tff(c_23862,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_23860,c_23274]) ).
tff(c_23863,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(X3_6) != identity )
| ( multiply(X3_6,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_23422]) ).
tff(c_32441,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_24069,c_24069,c_24069,c_23863]) ).
tff(c_32443,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_32441]) ).
tff(c_32445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32443,c_23274]) ).
tff(c_32446,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_32441]) ).
tff(c_32448,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_32446]) ).
tff(c_32450,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32448,c_23274]) ).
tff(c_32854,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_32446]) ).
tff(c_32856,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32854,c_23274]) ).
tff(c_32858,plain,
inverse(sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_32864,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_32858,c_8]) ).
tff(c_33059,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32864,c_33014]) ).
tff(c_33324,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33035,c_33059]) ).
tff(c_32857,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_32934,plain,
! [Z_402] : ( multiply(sk_c7,multiply(sk_c3,Z_402)) = multiply(identity,Z_402) ),
inference(superposition,[status(thm),theory(equality)],[c_22878,c_32907]) ).
tff(c_32953,plain,
! [Z_403] : ( multiply(sk_c7,multiply(sk_c3,Z_403)) = Z_403 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_32934]) ).
tff(c_32965,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_32857,c_32953]) ).
tff(c_33041,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_32965,c_33014]) ).
tff(c_33335,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33324,c_33324,c_33041]) ).
tff(c_33345,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33335]) ).
tff(c_33068,plain,
multiply(inverse(sk_c6),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_22870,c_33014]) ).
tff(c_33357,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_33345,c_33068]) ).
tff(c_33364,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_33357]) ).
tff(c_33362,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33345,c_22865]) ).
tff(c_33403,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_33364,c_33362]) ).
tff(c_33344,plain,
inverse(sk_c6) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_33324,c_32858]) ).
tff(c_33423,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_33403,c_33345,c_33345,c_33344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP376-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 22:00:52 EDT 2023
% 0.21/0.35 % CPUTime :
% 12.53/4.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.87/4.27
% 12.87/4.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.99/4.32
% 12.99/4.32 Inference rules
% 12.99/4.32 ----------------------
% 12.99/4.32 #Ref : 0
% 12.99/4.32 #Sup : 8134
% 12.99/4.32 #Fact : 0
% 12.99/4.32 #Define : 0
% 12.99/4.32 #Split : 31
% 12.99/4.32 #Chain : 0
% 12.99/4.32 #Close : 0
% 12.99/4.32
% 12.99/4.32 Ordering : KBO
% 12.99/4.32
% 12.99/4.32 Simplification rules
% 12.99/4.32 ----------------------
% 12.99/4.32 #Subsume : 4
% 12.99/4.32 #Demod : 20748
% 12.99/4.32 #Tautology : 6710
% 12.99/4.32 #SimpNegUnit : 50
% 12.99/4.32 #BackRed : 308
% 12.99/4.32
% 12.99/4.32 #Partial instantiations: 0
% 12.99/4.32 #Strategies tried : 1
% 12.99/4.32
% 12.99/4.32 Timing (in seconds)
% 12.99/4.32 ----------------------
% 12.99/4.33 Preprocessing : 0.50
% 12.99/4.33 Parsing : 0.21
% 12.99/4.33 CNF conversion : 0.02
% 12.99/4.33 Main loop : 2.66
% 12.99/4.33 Inferencing : 0.83
% 12.99/4.33 Reduction : 1.32
% 12.99/4.33 Demodulation : 1.17
% 12.99/4.33 BG Simplification : 0.08
% 12.99/4.33 Subsumption : 0.28
% 12.99/4.33 Abstraction : 0.15
% 12.99/4.33 MUC search : 0.00
% 12.99/4.33 Cooper : 0.00
% 12.99/4.33 Total : 3.28
% 12.99/4.33 Index Insertion : 0.00
% 12.99/4.33 Index Deletion : 0.00
% 12.99/4.33 Index Matching : 0.00
% 12.99/4.33 BG Taut test : 0.00
%------------------------------------------------------------------------------