TSTP Solution File: GRP341-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP341-1 : 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 : n019.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 10:40:59 EDT 2023
% Result : Unsatisfiable 12.75s 4.25s
% Output : CNFRefutation 13.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 41
% Syntax : Number of formulae : 433 ( 345 unt; 10 typ; 0 def)
% Number of atoms : 628 ( 606 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 421 ( 216 ~; 205 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 215 (; 215 !; 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_155,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
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,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_161,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_203,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( multiply(X4,sk_c5) != sk_c6 )
| ( multiply(X1,sk_c7) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( inverse(sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c7 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c1,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_158,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_164,axiom,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_98,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_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_68,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_10093,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_164,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_194,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_164]) ).
tff(c_1490,plain,
! [X_39,Z_40] : ( multiply(inverse(X_39),multiply(X_39,Z_40)) = Z_40 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_194]) ).
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_194]) ).
tff(c_1704,plain,
! [X_42,Z_43] : ( multiply(inverse(inverse(X_42)),Z_43) = multiply(X_42,Z_43) ),
inference(superposition,[status(thm),theory(equality)],[c_1490,c_204]) ).
tff(c_1532,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1490]) ).
tff(c_1711,plain,
! [X_42] : ( multiply(X_42,identity) = X_42 ),
inference(superposition,[status(thm),theory(equality)],[c_1704,c_1532]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_123,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_58,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_95,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_99,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_95,c_4]) ).
tff(c_749,plain,
! [X_29,Z_30] : ( multiply(inverse(X_29),multiply(X_29,Z_30)) = Z_30 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_194]) ).
tff(c_809,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_99,c_749]) ).
tff(c_72,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_129,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_191,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_164]) ).
tff(c_209,plain,
! [Z_15] : ( multiply(sk_c6,multiply(sk_c2,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_191]) ).
tff(c_221,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_129,c_209]) ).
tff(c_271,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_194]) ).
tff(c_298,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_221,c_271]) ).
tff(c_313,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_123,c_271]) ).
tff(c_490,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_298,c_313]) ).
tff(c_44,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_135,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_108,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_112,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_108,c_4]) ).
tff(c_188,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_164]) ).
tff(c_248,plain,
! [Z_17] : ( multiply(sk_c7,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_188]) ).
tff(c_260,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_135,c_248]) ).
tff(c_537,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_490,c_490,c_260]) ).
tff(c_544,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_221,c_537]) ).
tff(c_551,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_544,c_544,c_298]) ).
tff(c_561,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_551]) ).
tff(c_78,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_207,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(sk_c5) != sk_c6 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_78]) ).
tff(c_208,plain,
inverse(sk_c5) != sk_c6,
inference(splitLeft,[status(thm)],[c_207]) ).
tff(c_557,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_544,c_208]) ).
tff(c_653,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_561,c_557]) ).
tff(c_598,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_544]) ).
tff(c_542,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_490,c_108]) ).
tff(c_612,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_598,c_542]) ).
tff(c_328,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_271]) ).
tff(c_616,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_612,c_328]) ).
tff(c_625,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_616]) ).
tff(c_627,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_625,c_612]) ).
tff(c_655,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_653,c_627]) ).
tff(c_657,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_207]) ).
tff(c_949,plain,
! [X_33] : ( multiply(inverse(inverse(X_33)),identity) = X_33 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_749]) ).
tff(c_964,plain,
multiply(inverse(sk_c6),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_657,c_949]) ).
tff(c_974,plain,
sk_c5 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_809,c_964]) ).
tff(c_697,plain,
! [Z_26] : ( multiply(sk_c6,multiply(sk_c2,Z_26)) = Z_26 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_191]) ).
tff(c_709,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_129,c_697]) ).
tff(c_981,plain,
multiply(sk_c6,sk_c6) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_974,c_709]) ).
tff(c_673,plain,
! [Z_25] : ( multiply(sk_c7,multiply(sk_c1,Z_25)) = Z_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_188]) ).
tff(c_685,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_135,c_673]) ).
tff(c_185,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c7,Z_14)) = multiply(sk_c5,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_123,c_164]) ).
tff(c_1052,plain,
! [Z_34] : ( multiply(sk_c6,multiply(sk_c7,Z_34)) = multiply(sk_c2,Z_34) ),
inference(demodulation,[status(thm),theory(equality)],[c_974,c_185]) ).
tff(c_1070,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c2,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_685,c_1052]) ).
tff(c_1080,plain,
multiply(sk_c2,sk_c7) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_981,c_1070]) ).
tff(c_1187,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_1080,c_204]) ).
tff(c_1193,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1187]) ).
tff(c_803,plain,
multiply(inverse(sk_c7),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_112,c_749]) ).
tff(c_1217,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_1193,c_803]) ).
tff(c_885,plain,
! [Z_32] : ( multiply(sk_c1,multiply(sk_c6,Z_32)) = multiply(sk_c7,Z_32) ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_164]) ).
tff(c_915,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c1,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_123,c_885]) ).
tff(c_923,plain,
multiply(sk_c1,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_685,c_915]) ).
tff(c_977,plain,
multiply(sk_c1,sk_c2) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_974,c_923]) ).
tff(c_202,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_188]) ).
tff(c_1000,plain,
multiply(sk_c7,sk_c6) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_977,c_202]) ).
tff(c_179,plain,
! [Z_14] : ( multiply(sk_c1,multiply(sk_c6,Z_14)) = multiply(sk_c7,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_164]) ).
tff(c_1011,plain,
multiply(sk_c7,sk_c6) = multiply(sk_c1,sk_c2),
inference(superposition,[status(thm),theory(equality)],[c_981,c_179]) ).
tff(c_1020,plain,
multiply(sk_c7,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_977,c_1011]) ).
tff(c_1095,plain,
sk_c6 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_1000,c_1020]) ).
tff(c_1163,plain,
multiply(sk_c1,sk_c2) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_1095,c_135]) ).
tff(c_1271,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1217,c_1193,c_1163]) ).
tff(c_656,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_207]) ).
tff(c_696,plain,
multiply(sk_c5,sk_c6) != sk_c7,
inference(splitLeft,[status(thm)],[c_656]) ).
tff(c_982,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_974,c_696]) ).
tff(c_1153,plain,
multiply(sk_c2,sk_c2) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_1095,c_982]) ).
tff(c_1312,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1271,c_2,c_1271,c_1193,c_1153]) ).
tff(c_1314,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_656]) ).
tff(c_661,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_657,c_4]) ).
tff(c_6,plain,
! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_668,plain,
! [Z_5] : ( multiply(sk_c6,multiply(sk_c5,Z_5)) = multiply(identity,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_661,c_6]) ).
tff(c_1345,plain,
! [Z_37] : ( multiply(sk_c6,multiply(sk_c5,Z_37)) = Z_37 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_668]) ).
tff(c_1357,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_1314,c_1345]) ).
tff(c_1361,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_123,c_1357]) ).
tff(c_1403,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_661]) ).
tff(c_1322,plain,
! [Z_36] : ( multiply(sk_c6,multiply(sk_c2,Z_36)) = Z_36 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_191]) ).
tff(c_1334,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_129,c_1322]) ).
tff(c_1399,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_1361,c_1334]) ).
tff(c_1543,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1403,c_1399]) ).
tff(c_1401,plain,
multiply(sk_c5,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_1314]) ).
tff(c_1451,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1399,c_1401]) ).
tff(c_1559,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1543,c_1451]) ).
tff(c_1313,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_656]) ).
tff(c_1446,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(sk_c5,sk_c7) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_1361,c_1361,c_1361,c_1361,c_1361,c_1361,c_1313]) ).
tff(c_1447,plain,
multiply(sk_c5,sk_c7) != sk_c5,
inference(splitLeft,[status(thm)],[c_1446]) ).
tff(c_1407,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_123]) ).
tff(c_1448,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1447,c_1407]) ).
tff(c_1449,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_1446]) ).
tff(c_8762,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( identity != X3_6 )
| ( inverse(X3_6) != identity )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1711,c_1543,c_1543,c_1543,c_1711,c_1559,c_1543,c_1559,c_1543,c_1711,c_1543,c_1543,c_1559,c_1711,c_1559,c_1543,c_1449]) ).
tff(c_8764,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8762]) ).
tff(c_1404,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_1361,c_657]) ).
tff(c_1563,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1543,c_1543,c_1404]) ).
tff(c_8766,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8764,c_1563]) ).
tff(c_8767,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( identity != X3_6 )
| ( inverse(X3_6) != identity ) ),
inference(splitRight,[status(thm)],[c_8762]) ).
tff(c_9176,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8767]) ).
tff(c_9178,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9176,c_1563]) ).
tff(c_9179,plain,
! [X4_7,X1_8] :
( ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_8767]) ).
tff(c_9181,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_9179]) ).
tff(c_9183,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9181,c_1563]) ).
tff(c_9571,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_9179]) ).
tff(c_9573,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9571,c_1563]) ).
tff(c_9575,plain,
multiply(sk_c1,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_40,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_9607,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9575,c_40]) ).
tff(c_9611,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9607,c_4]) ).
tff(c_42,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_9631,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_9575,c_42]) ).
tff(c_9574,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_9579,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9574,c_4]) ).
tff(c_9649,plain,
! [X_131,Y_132,Z_133] : ( multiply(multiply(X_131,Y_132),Z_133) = multiply(X_131,multiply(Y_132,Z_133)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9682,plain,
! [Z_133] : ( multiply(sk_c6,multiply(sk_c4,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_9579,c_9649]) ).
tff(c_9748,plain,
! [Z_136] : ( multiply(sk_c6,multiply(sk_c4,Z_136)) = Z_136 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9682]) ).
tff(c_9760,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9631,c_9748]) ).
tff(c_9764,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9611,c_9760]) ).
tff(c_9694,plain,
! [Z_133] : ( multiply(sk_c6,multiply(sk_c2,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_9649]) ).
tff(c_9725,plain,
! [Z_135] : ( multiply(sk_c6,multiply(sk_c2,Z_135)) = Z_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9694]) ).
tff(c_9737,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_129,c_9725]) ).
tff(c_9880,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9764,c_9764,c_9737]) ).
tff(c_9895,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9880]) ).
tff(c_46,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_9636,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9575,c_46]) ).
tff(c_9883,plain,
multiply(sk_c5,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9764,c_9636]) ).
tff(c_9949,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9895,c_9883]) ).
tff(c_9954,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9949,c_112]) ).
tff(c_9697,plain,
! [X_2,Z_133] : ( multiply(inverse(X_2),multiply(X_2,Z_133)) = multiply(identity,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9649]) ).
tff(c_9710,plain,
! [X_2,Z_133] : ( multiply(inverse(X_2),multiply(X_2,Z_133)) = Z_133 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9697]) ).
tff(c_10069,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_9954,c_9710]) ).
tff(c_10081,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10069]) ).
tff(c_9889,plain,
multiply(sk_c1,identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9764,c_9575]) ).
tff(c_10000,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9949,c_9889]) ).
tff(c_10085,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_10081,c_10000]) ).
tff(c_10090,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10085]) ).
tff(c_10092,plain,
multiply(sk_c2,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_10106,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10093,c_10092]) ).
tff(c_10107,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_10119,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10107,c_4]) ).
tff(c_70,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_10166,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_10092,c_70]) ).
tff(c_10091,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_10112,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10091,c_4]) ).
tff(c_10183,plain,
! [X_142,Y_143,Z_144] : ( multiply(multiply(X_142,Y_143),Z_144) = multiply(X_142,multiply(Y_143,Z_144)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10213,plain,
! [Z_144] : ( multiply(sk_c6,multiply(sk_c4,Z_144)) = multiply(identity,Z_144) ),
inference(superposition,[status(thm),theory(equality)],[c_10112,c_10183]) ).
tff(c_10295,plain,
! [Z_148] : ( multiply(sk_c6,multiply(sk_c4,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10213]) ).
tff(c_10307,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10166,c_10295]) ).
tff(c_10311,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10119,c_10307]) ).
tff(c_10326,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10311,c_95]) ).
tff(c_10362,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10326,c_4]) ).
tff(c_10228,plain,
! [X_2,Z_144] : ( multiply(inverse(X_2),multiply(X_2,Z_144)) = multiply(identity,Z_144) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10183]) ).
tff(c_10241,plain,
! [X_2,Z_144] : ( multiply(inverse(X_2),multiply(X_2,Z_144)) = Z_144 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10228]) ).
tff(c_10517,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_10362,c_10241]) ).
tff(c_10529,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10517]) ).
tff(c_10322,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10311,c_10107]) ).
tff(c_10324,plain,
multiply(identity,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10311,c_123]) ).
tff(c_10383,plain,
sk_c7 = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10324,c_2]) ).
tff(c_74,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_10160,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10092,c_74]) ).
tff(c_10317,plain,
multiply(sk_c5,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10311,c_10160]) ).
tff(c_10419,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10383,c_10317]) ).
tff(c_10437,plain,
! [X_150,Z_151] : ( multiply(inverse(X_150),multiply(X_150,Z_151)) = Z_151 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10228]) ).
tff(c_10458,plain,
multiply(inverse(sk_c5),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10419,c_10437]) ).
tff(c_10487,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10322,c_10458]) ).
tff(c_10321,plain,
multiply(sk_c2,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_10311,c_10092]) ).
tff(c_10595,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10529,c_10487,c_10321]) ).
tff(c_10597,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_12,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_10623,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10597,c_12]) ).
tff(c_10627,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10623,c_4]) ).
tff(c_16,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_10610,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10597,c_16]) ).
tff(c_14,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_10671,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_10597,c_14]) ).
tff(c_10683,plain,
! [X_152,Y_153,Z_154] : ( multiply(multiply(X_152,Y_153),Z_154) = multiply(X_152,multiply(Y_153,Z_154)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10731,plain,
! [X_2,Z_154] : ( multiply(inverse(X_2),multiply(X_2,Z_154)) = multiply(identity,Z_154) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10683]) ).
tff(c_10811,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_10731]) ).
tff(c_10850,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10671,c_10811]) ).
tff(c_10903,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10627,c_10610,c_10850]) ).
tff(c_10925,plain,
multiply(identity,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10903,c_10597]) ).
tff(c_10929,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10925]) ).
tff(c_10665,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_10728,plain,
! [Z_154] : ( multiply(sk_c6,multiply(sk_c2,Z_154)) = multiply(identity,Z_154) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_10683]) ).
tff(c_10748,plain,
! [Z_155] : ( multiply(sk_c6,multiply(sk_c2,Z_155)) = Z_155 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10728]) ).
tff(c_10760,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10665,c_10748]) ).
tff(c_18,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_10677,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10597,c_18]) ).
tff(c_10847,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10677,c_10811]) ).
tff(c_10902,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10760,c_10623,c_10847]) ).
tff(c_10971,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10929,c_10902]) ).
tff(c_10972,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_10614,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10610,c_4]) ).
tff(c_10990,plain,
! [X_161,Y_162,Z_163] : ( multiply(multiply(X_161,Y_162),Z_163) = multiply(X_161,multiply(Y_162,Z_163)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_11023,plain,
! [Z_163] : ( multiply(sk_c6,multiply(sk_c4,Z_163)) = multiply(identity,Z_163) ),
inference(superposition,[status(thm),theory(equality)],[c_10614,c_10990]) ).
tff(c_11088,plain,
! [Z_166] : ( multiply(sk_c6,multiply(sk_c4,Z_166)) = Z_166 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11023]) ).
tff(c_11100,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10972,c_11088]) ).
tff(c_11104,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10627,c_11100]) ).
tff(c_11117,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11104,c_10610]) ).
tff(c_11110,plain,
multiply(sk_c4,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11104,c_10972]) ).
tff(c_11035,plain,
! [X_2,Z_163] : ( multiply(inverse(X_2),multiply(X_2,Z_163)) = multiply(identity,Z_163) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10990]) ).
tff(c_11048,plain,
! [X_2,Z_163] : ( multiply(inverse(X_2),multiply(X_2,Z_163)) = Z_163 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11035]) ).
tff(c_11277,plain,
multiply(inverse(sk_c4),sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11110,c_11048]) ).
tff(c_11283,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11117,c_11277]) ).
tff(c_11118,plain,
multiply(identity,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11104,c_10597]) ).
tff(c_11121,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11118]) ).
tff(c_11288,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11283,c_11121]) ).
tff(c_20,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_10647,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_10597,c_20]) ).
tff(c_11113,plain,
multiply(sk_c5,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11104,c_10647]) ).
tff(c_11325,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11283,c_11113]) ).
tff(c_11326,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11288,c_11325]) ).
tff(c_11328,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_26,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_11341,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_11328,c_26]) ).
tff(c_11345,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11341,c_4]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_11353,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_11328,c_30]) ).
tff(c_28,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_11376,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_11328,c_28]) ).
tff(c_11410,plain,
! [X_170,Y_171,Z_172] : ( multiply(multiply(X_170,Y_171),Z_172) = multiply(X_170,multiply(Y_171,Z_172)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_11449,plain,
! [X_2,Z_172] : ( multiply(inverse(X_2),multiply(X_2,Z_172)) = multiply(identity,Z_172) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11410]) ).
tff(c_11579,plain,
! [X_177,Z_178] : ( multiply(inverse(X_177),multiply(X_177,Z_178)) = Z_178 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11449]) ).
tff(c_11612,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11376,c_11579]) ).
tff(c_11641,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11345,c_11353,c_11612]) ).
tff(c_32,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_11389,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_11328,c_32]) ).
tff(c_22,plain,
( ( multiply(sk_c3,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_11367,plain,
multiply(sk_c3,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_11328,c_22]) ).
tff(c_11327,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_11332,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11327,c_4]) ).
tff(c_11443,plain,
! [Z_172] : ( multiply(sk_c7,multiply(sk_c3,Z_172)) = multiply(identity,Z_172) ),
inference(superposition,[status(thm),theory(equality)],[c_11332,c_11410]) ).
tff(c_11479,plain,
! [Z_174] : ( multiply(sk_c7,multiply(sk_c3,Z_174)) = Z_174 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11443]) ).
tff(c_11491,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11367,c_11479]) ).
tff(c_11425,plain,
! [Z_172] : ( multiply(sk_c5,multiply(sk_c7,Z_172)) = multiply(sk_c6,Z_172) ),
inference(superposition,[status(thm),theory(equality)],[c_11389,c_11410]) ).
tff(c_11517,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_11491,c_11425]) ).
tff(c_11523,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11389,c_11517]) ).
tff(c_11440,plain,
! [Z_172] : ( multiply(sk_c6,multiply(sk_c5,Z_172)) = multiply(identity,Z_172) ),
inference(superposition,[status(thm),theory(equality)],[c_11345,c_11410]) ).
tff(c_11540,plain,
! [Z_176] : ( multiply(sk_c6,multiply(sk_c5,Z_176)) = Z_176 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11440]) ).
tff(c_11555,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11389,c_11540]) ).
tff(c_11562,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11523,c_11555]) ).
tff(c_34,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_11382,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_11328,c_34]) ).
tff(c_11464,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_11341,c_11389,c_11382,c_78]) ).
tff(c_11465,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitLeft,[status(thm)],[c_11464]) ).
tff(c_11566,plain,
multiply(sk_c6,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11562,c_11465]) ).
tff(c_11574,plain,
sk_c6 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11523,c_11566]) ).
tff(c_11666,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11641,c_11574]) ).
tff(c_11652,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11641,c_11345]) ).
tff(c_11461,plain,
! [X_2,Z_172] : ( multiply(inverse(X_2),multiply(X_2,Z_172)) = Z_172 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11449]) ).
tff(c_11767,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11652,c_11461]) ).
tff(c_11779,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11767]) ).
tff(c_11781,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11666,c_11779]) ).
tff(c_11783,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_11464]) ).
tff(c_11824,plain,
! [Z_182] : ( multiply(sk_c6,multiply(sk_c5,Z_182)) = Z_182 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11440]) ).
tff(c_11842,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11382,c_11824]) ).
tff(c_11846,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11783,c_11842]) ).
tff(c_11857,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11345]) ).
tff(c_11852,plain,
multiply(sk_c5,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11382]) ).
tff(c_11856,plain,
inverse(sk_c4) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11353]) ).
tff(c_11791,plain,
! [Z_181] : ( multiply(sk_c4,multiply(sk_c6,Z_181)) = multiply(sk_c5,Z_181) ),
inference(superposition,[status(thm),theory(equality)],[c_11376,c_11410]) ).
tff(c_11803,plain,
multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_11783,c_11791]) ).
tff(c_11816,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_11389,c_11803]) ).
tff(c_11848,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11816]) ).
tff(c_12600,plain,
! [X_196,Z_197] : ( multiply(inverse(X_196),multiply(X_196,Z_197)) = Z_197 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11449]) ).
tff(c_12624,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11848,c_12600]) ).
tff(c_12657,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11852,c_11856,c_12624]) ).
tff(c_11839,plain,
multiply(sk_c6,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11389,c_11824]) ).
tff(c_12703,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11857,c_12657,c_11846,c_11846,c_11839]) ).
tff(c_12708,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12703,c_12657]) ).
tff(c_12884,plain,
! [X_199,Z_200] : ( multiply(inverse(inverse(X_199)),Z_200) = multiply(X_199,Z_200) ),
inference(superposition,[status(thm),theory(equality)],[c_12600,c_11461]) ).
tff(c_12648,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12600]) ).
tff(c_12891,plain,
! [X_199] : ( multiply(X_199,identity) = X_199 ),
inference(superposition,[status(thm),theory(equality)],[c_12884,c_12648]) ).
tff(c_11936,plain,
! [X_183,Z_184] : ( multiply(inverse(X_183),multiply(X_183,Z_184)) = Z_184 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11449]) ).
tff(c_12177,plain,
! [X_186,Z_187] : ( multiply(inverse(inverse(X_186)),Z_187) = multiply(X_186,Z_187) ),
inference(superposition,[status(thm),theory(equality)],[c_11936,c_11461]) ).
tff(c_11978,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11936]) ).
tff(c_12184,plain,
! [X_186] : ( multiply(X_186,identity) = X_186 ),
inference(superposition,[status(thm),theory(equality)],[c_12177,c_11978]) ).
tff(c_11954,plain,
multiply(inverse(sk_c4),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11848,c_11936]) ).
tff(c_11985,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11857,c_11856,c_11954]) ).
tff(c_11782,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_11464]) ).
tff(c_11879,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11846,c_11846,c_11846,c_11846,c_11846,c_11782]) ).
tff(c_11880,plain,
! [X2_9] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_11879]) ).
tff(c_12559,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12184,c_11985,c_11985,c_11985,c_11880]) ).
tff(c_11858,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11341]) ).
tff(c_11994,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11985,c_11985,c_11858]) ).
tff(c_12561,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12559,c_11994]) ).
tff(c_12562,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c5 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_11879]) ).
tff(c_21325,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( identity != X3_6 )
| ( inverse(X3_6) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12708,c_12891,c_12708,c_12703,c_12703,c_12891,c_12703,c_12703,c_12891,c_12708,c_12703,c_12708,c_12562]) ).
tff(c_21327,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_21325]) ).
tff(c_12712,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12703,c_12703,c_11858]) ).
tff(c_21329,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21327,c_12712]) ).
tff(c_21330,plain,
! [X4_7,X1_8] :
( ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_21325]) ).
tff(c_21332,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_21330]) ).
tff(c_21334,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21332,c_12712]) ).
tff(c_21337,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_21330]) ).
tff(c_21339,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21337,c_12712]) ).
tff(c_21341,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_54,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_21353,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_21341,c_54]) ).
tff(c_21357,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21353,c_4]) ).
tff(c_56,plain,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_21396,plain,
multiply(sk_c4,sk_c6) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_21341,c_56]) ).
tff(c_21340,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_21345,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21340,c_4]) ).
tff(c_21436,plain,
! [X_292,Y_293,Z_294] : ( multiply(multiply(X_292,Y_293),Z_294) = multiply(X_292,multiply(Y_293,Z_294)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_21472,plain,
! [Z_294] : ( multiply(sk_c6,multiply(sk_c4,Z_294)) = multiply(identity,Z_294) ),
inference(superposition,[status(thm),theory(equality)],[c_21345,c_21436]) ).
tff(c_21753,plain,
! [Z_301] : ( multiply(sk_c6,multiply(sk_c4,Z_301)) = Z_301 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21472]) ).
tff(c_21765,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_21396,c_21753]) ).
tff(c_21769,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21357,c_21765]) ).
tff(c_21811,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21340]) ).
tff(c_60,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_21414,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_21341,c_60]) ).
tff(c_21515,plain,
! [Z_296] : ( multiply(sk_c6,multiply(sk_c4,Z_296)) = Z_296 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21472]) ).
tff(c_21527,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_21396,c_21515]) ).
tff(c_21531,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21357,c_21527]) ).
tff(c_21539,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21531,c_21357]) ).
tff(c_21583,plain,
sk_c5 = identity,
inference(superposition,[status(thm),theory(equality)],[c_21539,c_2]) ).
tff(c_62,plain,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_21405,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_21341,c_62]) ).
tff(c_21513,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_21353,c_21414,c_21405,c_78]) ).
tff(c_21514,plain,
multiply(sk_c6,sk_c7) != sk_c5,
inference(splitLeft,[status(thm)],[c_21513]) ).
tff(c_21533,plain,
multiply(identity,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_21531,c_21514]) ).
tff(c_21544,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21533]) ).
tff(c_21652,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_21583,c_21544]) ).
tff(c_21540,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21531,c_21353]) ).
tff(c_21651,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21583,c_21540]) ).
tff(c_21457,plain,
! [Z_294] : ( multiply(sk_c5,multiply(sk_c6,Z_294)) = multiply(sk_c7,Z_294) ),
inference(superposition,[status(thm),theory(equality)],[c_21405,c_21436]) ).
tff(c_21702,plain,
! [Z_300] : ( multiply(sk_c7,Z_300) = Z_300 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21583,c_2,c_21531,c_21457]) ).
tff(c_52,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_21374,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_21341,c_52]) ).
tff(c_21378,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21374,c_4]) ).
tff(c_21720,plain,
sk_c3 = identity,
inference(superposition,[status(thm),theory(equality)],[c_21702,c_21378]) ).
tff(c_21738,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_21720,c_21374]) ).
tff(c_21741,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21651,c_21738]) ).
tff(c_21743,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21652,c_21741]) ).
tff(c_21745,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(splitRight,[status(thm)],[c_21513]) ).
tff(c_21770,plain,
! [Z_302] : ( multiply(sk_c4,multiply(sk_c6,Z_302)) = multiply(sk_c5,Z_302) ),
inference(superposition,[status(thm),theory(equality)],[c_21396,c_21436]) ).
tff(c_21788,plain,
multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_21745,c_21770]) ).
tff(c_21798,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_21414,c_21788]) ).
tff(c_21831,plain,
multiply(sk_c4,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21798]) ).
tff(c_21475,plain,
! [X_2,Z_294] : ( multiply(inverse(X_2),multiply(X_2,Z_294)) = multiply(identity,Z_294) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_21436]) ).
tff(c_22365,plain,
! [X_313,Z_314] : ( multiply(inverse(X_313),multiply(X_313,Z_314)) = Z_314 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21475]) ).
tff(c_22386,plain,
multiply(inverse(sk_c4),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_21831,c_22365]) ).
tff(c_22420,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21811,c_22386]) ).
tff(c_21801,plain,
multiply(identity,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21745]) ).
tff(c_22358,plain,
sk_c7 = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_21801,c_2]) ).
tff(c_22434,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22420,c_22358]) ).
tff(c_21487,plain,
! [X_2,Z_294] : ( multiply(inverse(X_2),multiply(X_2,Z_294)) = Z_294 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21475]) ).
tff(c_22609,plain,
! [X_317,Z_318] : ( multiply(inverse(inverse(X_317)),Z_318) = multiply(X_317,Z_318) ),
inference(superposition,[status(thm),theory(equality)],[c_21487,c_22365]) ).
tff(c_22413,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22365]) ).
tff(c_22616,plain,
! [X_317] : ( multiply(X_317,identity) = X_317 ),
inference(superposition,[status(thm),theory(equality)],[c_22609,c_22413]) ).
tff(c_21912,plain,
! [X_303,Z_304] : ( multiply(inverse(X_303),multiply(X_303,Z_304)) = Z_304 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21475]) ).
tff(c_22086,plain,
! [X_306,Z_307] : ( multiply(inverse(inverse(X_306)),Z_307) = multiply(X_306,Z_307) ),
inference(superposition,[status(thm),theory(equality)],[c_21487,c_21912]) ).
tff(c_21945,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_21912]) ).
tff(c_22093,plain,
! [X_306] : ( multiply(X_306,identity) = X_306 ),
inference(superposition,[status(thm),theory(equality)],[c_22086,c_21945]) ).
tff(c_21807,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21357]) ).
tff(c_21958,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_21807,c_21487]) ).
tff(c_21970,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_21958]) ).
tff(c_21744,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(X3_6,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X2_9,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_21513]) ).
tff(c_21840,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( multiply(X3_6,identity) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X4_7,sk_c5) != identity )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != identity )
| ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21769,c_21769,c_21769,c_21769,c_21769,c_21744]) ).
tff(c_21841,plain,
! [X2_9] :
( ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_21840]) ).
tff(c_22348,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_22093,c_21970,c_21841]) ).
tff(c_21827,plain,
multiply(identity,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_21811,c_4]) ).
tff(c_21873,plain,
sk_c4 = identity,
inference(superposition,[status(thm),theory(equality)],[c_21827,c_2]) ).
tff(c_21883,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21873,c_21811]) ).
tff(c_22350,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22348,c_21883]) ).
tff(c_22351,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != sk_c7 )
| ( multiply(X1_8,sk_c7) != identity )
| ( multiply(X4_7,sk_c5) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X3_6,identity) != sk_c7 )
| ( inverse(X3_6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_21840]) ).
tff(c_29920,plain,
! [X1_8,X4_7,X3_6] :
( ( inverse(X1_8) != identity )
| ( identity != X1_8 )
| ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( identity != X3_6 )
| ( inverse(X3_6) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22434,c_22616,c_22434,c_22616,c_22420,c_22616,c_22434,c_22434,c_22351]) ).
tff(c_29922,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_29920]) ).
tff(c_21808,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_21769,c_21353]) ).
tff(c_22436,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_22420,c_21808]) ).
tff(c_29924,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29922,c_22436]) ).
tff(c_29925,plain,
! [X4_7,X1_8] :
( ( identity != X4_7 )
| ( inverse(X4_7) != identity )
| ( inverse(X1_8) != identity )
| ( identity != X1_8 ) ),
inference(splitRight,[status(thm)],[c_29920]) ).
tff(c_29927,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_29925]) ).
tff(c_29929,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29927,c_22436]) ).
tff(c_29932,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_29925]) ).
tff(c_29934,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_29932,c_22436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP341-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % 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
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 22:23:16 EDT 2023
% 0.15/0.37 % CPUTime :
% 12.75/4.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.82/4.29
% 12.82/4.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.20/4.37
% 13.20/4.37 Inference rules
% 13.20/4.37 ----------------------
% 13.20/4.37 #Ref : 0
% 13.20/4.37 #Sup : 7386
% 13.20/4.37 #Fact : 0
% 13.20/4.37 #Define : 0
% 13.20/4.37 #Split : 26
% 13.20/4.37 #Chain : 0
% 13.20/4.37 #Close : 0
% 13.20/4.37
% 13.20/4.37 Ordering : KBO
% 13.20/4.37
% 13.20/4.37 Simplification rules
% 13.20/4.37 ----------------------
% 13.20/4.37 #Subsume : 3
% 13.20/4.37 #Demod : 16857
% 13.20/4.37 #Tautology : 5967
% 13.20/4.37 #SimpNegUnit : 51
% 13.20/4.37 #BackRed : 399
% 13.20/4.37
% 13.20/4.37 #Partial instantiations: 0
% 13.20/4.37 #Strategies tried : 1
% 13.20/4.37
% 13.20/4.37 Timing (in seconds)
% 13.20/4.37 ----------------------
% 13.20/4.37 Preprocessing : 0.52
% 13.20/4.37 Parsing : 0.21
% 13.20/4.37 CNF conversion : 0.03
% 13.20/4.37 Main loop : 2.69
% 13.20/4.37 Inferencing : 0.81
% 13.20/4.37 Reduction : 1.30
% 13.20/4.37 Demodulation : 1.14
% 13.20/4.37 BG Simplification : 0.09
% 13.20/4.37 Subsumption : 0.31
% 13.20/4.37 Abstraction : 0.15
% 13.20/4.37 MUC search : 0.00
% 13.20/4.37 Cooper : 0.00
% 13.20/4.37 Total : 3.33
% 13.20/4.37 Index Insertion : 0.00
% 13.20/4.37 Index Deletion : 0.00
% 13.20/4.37 Index Matching : 0.00
% 13.20/4.37 BG Taut test : 0.00
%------------------------------------------------------------------------------