TSTP Solution File: GRP253-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP253-1 : 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 : n004.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 10:40:39 EDT 2023
% Result : Unsatisfiable 7.65s 2.94s
% Output : CNFRefutation 8.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 431 ( 337 unt; 10 typ; 0 def)
% Number of atoms : 603 ( 568 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 439 ( 257 ~; 182 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 231 (; 231 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c5 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
! [X2,X3,X4,X1] :
( ( multiply(X2,sk_c7) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( inverse(X3) != sk_c6 )
| ( 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 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( multiply(sk_c3,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_12220,plain,
! [X_214,Y_215,Z_216] : ( multiply(multiply(X_214,Y_215),Z_216) = multiply(X_214,multiply(Y_215,Z_216)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12250,plain,
! [X_2,Z_216] : ( multiply(inverse(X_2),multiply(X_2,Z_216)) = multiply(identity,Z_216) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12220]) ).
tff(c_12262,plain,
! [X_2,Z_216] : ( multiply(inverse(X_2),multiply(X_2,Z_216)) = Z_216 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12250]) ).
tff(c_12489,plain,
! [X_228,Z_229] : ( multiply(inverse(X_228),multiply(X_228,Z_229)) = Z_229 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12250]) ).
tff(c_13975,plain,
! [X_249,Z_250] : ( multiply(inverse(inverse(X_249)),Z_250) = multiply(X_249,Z_250) ),
inference(superposition,[status(thm),theory(equality)],[c_12262,c_12489]) ).
tff(c_12564,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_12489]) ).
tff(c_13982,plain,
! [X_249] : ( multiply(X_249,identity) = X_249 ),
inference(superposition,[status(thm),theory(equality)],[c_13975,c_12564]) ).
tff(c_10,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_102,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_18,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_85,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_90,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_8729,plain,
! [X_115,Y_116,Z_117] : ( multiply(multiply(X_115,Y_116),Z_117) = multiply(X_115,multiply(Y_116,Z_117)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8756,plain,
! [Z_117] : ( multiply(sk_c7,multiply(sk_c1,Z_117)) = multiply(identity,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_8729]) ).
tff(c_8780,plain,
! [Z_118] : ( multiply(sk_c7,multiply(sk_c1,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8756]) ).
tff(c_8792,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_102,c_8780]) ).
tff(c_8765,plain,
! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = multiply(identity,Z_117) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8729]) ).
tff(c_9084,plain,
! [X_131,Z_132] : ( multiply(inverse(X_131),multiply(X_131,Z_132)) = Z_132 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8765]) ).
tff(c_9126,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_8792,c_9084]) ).
tff(c_9180,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9126]) ).
tff(c_36,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_73,plain,
inverse(sk_c3) = sk_c6,
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_77,plain,
multiply(sk_c6,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73,c_4]) ).
tff(c_9201,plain,
multiply(identity,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9180,c_77]) ).
tff(c_8778,plain,
! [X_2,Z_117] : ( multiply(inverse(X_2),multiply(X_2,Z_117)) = Z_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8765]) ).
tff(c_9369,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_9201,c_8778]) ).
tff(c_9381,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9369]) ).
tff(c_42,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_108,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_8291,plain,
! [X_103,Y_104,Z_105] : ( multiply(multiply(X_103,Y_104),Z_105) = multiply(X_103,multiply(Y_104,Z_105)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8324,plain,
! [Z_105] : ( multiply(sk_c6,multiply(sk_c3,Z_105)) = multiply(identity,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_8291]) ).
tff(c_8368,plain,
! [Z_107] : ( multiply(sk_c6,multiply(sk_c3,Z_107)) = Z_107 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8324]) ).
tff(c_8380,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_108,c_8368]) ).
tff(c_8321,plain,
! [Z_105] : ( multiply(sk_c7,multiply(sk_c1,Z_105)) = multiply(identity,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_8291]) ).
tff(c_8345,plain,
! [Z_106] : ( multiply(sk_c7,multiply(sk_c1,Z_106)) = Z_106 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8321]) ).
tff(c_8357,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_102,c_8345]) ).
tff(c_8461,plain,
! [Z_112] : ( multiply(sk_c1,multiply(sk_c7,Z_112)) = multiply(sk_c6,Z_112) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_8291]) ).
tff(c_8476,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_8357,c_8461]) ).
tff(c_8489,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_8380,c_8476]) ).
tff(c_124,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_148,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_124]) ).
tff(c_170,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_148]) ).
tff(c_182,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_102,c_170]) ).
tff(c_157,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_124]) ).
tff(c_240,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_157]) ).
tff(c_270,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_182,c_240]) ).
tff(c_314,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_270]) ).
tff(c_24,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_115,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_28,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_61,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_65,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_61,c_4]) ).
tff(c_154,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_65,c_124]) ).
tff(c_216,plain,
! [Z_17] : ( multiply(sk_c6,multiply(sk_c2,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154]) ).
tff(c_228,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_115,c_216]) ).
tff(c_258,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_228,c_240]) ).
tff(c_313,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_258]) ).
tff(c_44,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(sk_c5) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_232,plain,
inverse(sk_c5) != sk_c6,
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_358,plain,
inverse(identity) != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_313,c_232]) ).
tff(c_378,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_314,c_358]) ).
tff(c_371,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_314,c_73]) ).
tff(c_385,plain,
multiply(identity,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_371,c_4]) ).
tff(c_168,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_157]) ).
tff(c_449,plain,
multiply(inverse(identity),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_385,c_168]) ).
tff(c_461,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_449]) ).
tff(c_465,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_461,c_371]) ).
tff(c_468,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_378,c_465]) ).
tff(c_470,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_474,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_470,c_4]) ).
tff(c_486,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_474,c_228]) ).
tff(c_495,plain,
multiply(sk_c1,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_102]) ).
tff(c_900,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_157]) ).
tff(c_1156,plain,
! [X_33,Z_34] : ( multiply(inverse(inverse(X_33)),Z_34) = multiply(X_33,Z_34) ),
inference(superposition,[status(thm),theory(equality)],[c_900,c_168]) ).
tff(c_939,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_900]) ).
tff(c_1166,plain,
! [X_33] : ( multiply(X_33,identity) = X_33 ),
inference(superposition,[status(thm),theory(equality)],[c_1156,c_939]) ).
tff(c_151,plain,
! [Z_14] : ( multiply(sk_c6,multiply(sk_c3,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_124]) ).
tff(c_193,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c3,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_151]) ).
tff(c_205,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_108,c_193]) ).
tff(c_490,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_486,c_205]) ).
tff(c_500,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_490]) ).
tff(c_469,plain,
! [X2_6,X3_7,X4_8,X1_9] :
( ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_509,plain,
! [X2_6,X3_7,X4_8,X1_9] :
( ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != identity )
| ( multiply(X4_8,identity) != identity )
| ( inverse(X4_8) != identity )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_486,c_486,c_500,c_486,c_500,c_486,c_486,c_486,c_469]) ).
tff(c_845,plain,
! [X1_28] :
( ( inverse(X1_28) != sk_c7 )
| ( multiply(X1_28,sk_c7) != identity ) ),
inference(splitLeft,[status(thm)],[c_509]) ).
tff(c_856,plain,
inverse(sk_c1) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_495,c_845]) ).
tff(c_875,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_85,c_856]) ).
tff(c_876,plain,
! [X4_8,X3_7,X2_6] :
( ( multiply(X4_8,identity) != identity )
| ( inverse(X4_8) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != identity )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != identity ) ),
inference(splitRight,[status(thm)],[c_509]) ).
tff(c_8197,plain,
! [X4_8,X3_7,X2_6] :
( ( identity != X4_8 )
| ( inverse(X4_8) != identity )
| ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1166,c_1166,c_876]) ).
tff(c_8199,plain,
! [X2_102] :
( ( inverse(X2_102) != sk_c7 )
| ( multiply(X2_102,sk_c7) != identity ) ),
inference(splitLeft,[status(thm)],[c_8197]) ).
tff(c_8227,plain,
inverse(sk_c1) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_495,c_8199]) ).
tff(c_8248,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_85,c_8227]) ).
tff(c_8249,plain,
! [X3_7,X4_8] :
( ( inverse(X3_7) != identity )
| ( identity != X3_7 )
| ( identity != X4_8 )
| ( inverse(X4_8) != identity ) ),
inference(splitRight,[status(thm)],[c_8197]) ).
tff(c_8251,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8249]) ).
tff(c_488,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_470]) ).
tff(c_877,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_500,c_488]) ).
tff(c_8253,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8251,c_877]) ).
tff(c_8256,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_8249]) ).
tff(c_8258,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8256,c_877]) ).
tff(c_8259,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_8264,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8259,c_4]) ).
tff(c_8496,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8489,c_8264]) ).
tff(c_8492,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8489,c_8489,c_8380]) ).
tff(c_8580,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8496,c_8492]) ).
tff(c_8504,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8489,c_61]) ).
tff(c_8526,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8504,c_4]) ).
tff(c_8684,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8580,c_8526]) ).
tff(c_8260,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_8497,plain,
multiply(sk_c2,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8489,c_8260]) ).
tff(c_8693,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8684,c_8580,c_8580,c_8497]) ).
tff(c_8695,plain,
multiply(sk_c3,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_9198,plain,
multiply(sk_c3,sk_c5) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9180,c_8695]) ).
tff(c_9432,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9381,c_9198]) ).
tff(c_8694,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_8699,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8694,c_4]) ).
tff(c_9197,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9180,c_8699]) ).
tff(c_9437,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9197,c_8778]) ).
tff(c_9449,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9437]) ).
tff(c_9451,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9432,c_9449]) ).
tff(c_9453,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_9452,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_9466,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_8,plain,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_9487,plain,
multiply(sk_c4,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9453,c_8]) ).
tff(c_12,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_9472,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_9453,c_12]) ).
tff(c_9587,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9472,c_44]) ).
tff(c_9632,plain,
! [X2_143] :
( ( inverse(X2_143) != sk_c7 )
| ( multiply(X2_143,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_9587]) ).
tff(c_9639,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_9487,c_9632]) ).
tff(c_9651,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9452,c_9639]) ).
tff(c_9652,plain,
! [X3_7,X4_8,X1_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_9587]) ).
tff(c_9713,plain,
! [X1_147] :
( ( inverse(X1_147) != sk_c7 )
| ( multiply(X1_147,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_9652]) ).
tff(c_9720,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_9487,c_9713]) ).
tff(c_9732,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9452,c_9720]) ).
tff(c_9733,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_9652]) ).
tff(c_9778,plain,
! [X3_150] :
( ( inverse(X3_150) != sk_c6 )
| ( multiply(X3_150,sk_c6) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_9733]) ).
tff(c_9792,plain,
( ( inverse(inverse(sk_c6)) != sk_c6 )
| ( sk_c5 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9778]) ).
tff(c_9800,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_9792]) ).
tff(c_9457,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9452,c_4]) ).
tff(c_9493,plain,
! [X_135,Y_136,Z_137] : ( multiply(multiply(X_135,Y_136),Z_137) = multiply(X_135,multiply(Y_136,Z_137)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9517,plain,
! [Z_137] : ( multiply(sk_c7,multiply(sk_c4,Z_137)) = multiply(identity,Z_137) ),
inference(superposition,[status(thm),theory(equality)],[c_9457,c_9493]) ).
tff(c_9741,plain,
! [Z_148] : ( multiply(sk_c7,multiply(sk_c4,Z_148)) = Z_148 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9517]) ).
tff(c_9753,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_9487,c_9741]) ).
tff(c_9529,plain,
! [X_2,Z_137] : ( multiply(inverse(X_2),multiply(X_2,Z_137)) = multiply(identity,Z_137) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9493]) ).
tff(c_9801,plain,
! [X_151,Z_152] : ( multiply(inverse(X_151),multiply(X_151,Z_152)) = Z_152 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9529]) ).
tff(c_9822,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9753,c_9801]) ).
tff(c_9886,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9822]) ).
tff(c_9523,plain,
! [Z_137] : ( multiply(sk_c6,multiply(sk_c3,Z_137)) = multiply(identity,Z_137) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_9493]) ).
tff(c_9570,plain,
! [Z_140] : ( multiply(sk_c6,multiply(sk_c3,Z_140)) = Z_140 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9523]) ).
tff(c_9582,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9466,c_9570]) ).
tff(c_9899,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9886,c_9886,c_9582]) ).
tff(c_9911,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9899]) ).
tff(c_9913,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9800,c_9911]) ).
tff(c_9915,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_9792]) ).
tff(c_9796,plain,
( ( inverse(identity) != sk_c6 )
| ( sk_c6 != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_9778]) ).
tff(c_9798,plain,
sk_c6 != sk_c5,
inference(splitLeft,[status(thm)],[c_9796]) ).
tff(c_9917,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9915,c_9798]) ).
tff(c_9999,plain,
! [X_154,Z_155] : ( multiply(inverse(X_154),multiply(X_154,Z_155)) = Z_155 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9529]) ).
tff(c_10029,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9753,c_9999]) ).
tff(c_10083,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10029]) ).
tff(c_10085,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9917,c_10083]) ).
tff(c_10087,plain,
sk_c6 = sk_c5,
inference(splitRight,[status(thm)],[c_9796]) ).
tff(c_10097,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10087,c_9472]) ).
tff(c_9797,plain,
inverse(sk_c6) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9582,c_9778]) ).
tff(c_10088,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_10087,c_10087,c_9797]) ).
tff(c_10139,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10097,c_10088]) ).
tff(c_10154,plain,
! [X4_157] :
( ( multiply(X4_157,sk_c5) != sk_c6 )
| ( inverse(X4_157) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_9733]) ).
tff(c_10164,plain,
inverse(sk_c3) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_9466,c_10154]) ).
tff(c_10176,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_73,c_10164]) ).
tff(c_10178,plain,
multiply(sk_c3,sk_c5) != sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_38,plain,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c5) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_10196,plain,
multiply(sk_c4,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10178,c_38]) ).
tff(c_10177,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_10292,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10177,c_44]) ).
tff(c_10330,plain,
! [X2_166] :
( ( inverse(X2_166) != sk_c7 )
| ( multiply(X2_166,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_10292]) ).
tff(c_10337,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10196,c_10330]) ).
tff(c_10349,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9452,c_10337]) ).
tff(c_10350,plain,
! [X3_7,X4_8,X1_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_10292]) ).
tff(c_10388,plain,
! [X1_169] :
( ( inverse(X1_169) != sk_c7 )
| ( multiply(X1_169,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_10350]) ).
tff(c_10395,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10196,c_10388]) ).
tff(c_10407,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9452,c_10395]) ).
tff(c_10408,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_10350]) ).
tff(c_10488,plain,
! [X3_172] :
( ( inverse(X3_172) != sk_c6 )
| ( multiply(X3_172,sk_c6) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_10408]) ).
tff(c_10502,plain,
( ( inverse(inverse(sk_c6)) != sk_c6 )
| ( sk_c5 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10488]) ).
tff(c_10508,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_10502]) ).
tff(c_10204,plain,
! [X_158,Y_159,Z_160] : ( multiply(multiply(X_158,Y_159),Z_160) = multiply(X_158,multiply(Y_159,Z_160)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10225,plain,
! [Z_160] : ( multiply(sk_c7,multiply(sk_c4,Z_160)) = multiply(identity,Z_160) ),
inference(superposition,[status(thm),theory(equality)],[c_9457,c_10204]) ).
tff(c_10431,plain,
! [Z_171] : ( multiply(sk_c7,multiply(sk_c4,Z_171)) = Z_171 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10225]) ).
tff(c_10449,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10196,c_10431]) ).
tff(c_10237,plain,
! [X_2,Z_160] : ( multiply(inverse(X_2),multiply(X_2,Z_160)) = multiply(identity,Z_160) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10204]) ).
tff(c_10510,plain,
! [X_173,Z_174] : ( multiply(inverse(X_173),multiply(X_173,Z_174)) = Z_174 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10237]) ).
tff(c_10537,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_10449,c_10510]) ).
tff(c_10602,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10537]) ).
tff(c_10692,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10602,c_10177]) ).
tff(c_10713,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10692,c_4]) ).
tff(c_10250,plain,
! [X_2,Z_160] : ( multiply(inverse(X_2),multiply(X_2,Z_160)) = Z_160 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10237]) ).
tff(c_10720,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_10713,c_10250]) ).
tff(c_10732,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_10720]) ).
tff(c_10734,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10508,c_10732]) ).
tff(c_10736,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_10502]) ).
tff(c_10182,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10177,c_4]) ).
tff(c_10222,plain,
! [Z_160] : ( multiply(sk_c6,multiply(sk_c5,Z_160)) = multiply(identity,Z_160) ),
inference(superposition,[status(thm),theory(equality)],[c_10182,c_10204]) ).
tff(c_10245,plain,
! [Z_160] : ( multiply(sk_c6,multiply(sk_c5,Z_160)) = Z_160 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10222]) ).
tff(c_10739,plain,
! [Z_160] : ( multiply(sk_c6,multiply(identity,Z_160)) = Z_160 ),
inference(demodulation,[status(thm),theory(equality)],[c_10736,c_10245]) ).
tff(c_10743,plain,
! [Z_160] : ( multiply(sk_c6,Z_160) = Z_160 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10739]) ).
tff(c_10409,plain,
! [Z_170] : ( multiply(sk_c4,multiply(sk_c7,Z_170)) = multiply(sk_c6,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_10196,c_10204]) ).
tff(c_10427,plain,
multiply(sk_c6,sk_c1) = multiply(sk_c4,identity),
inference(superposition,[status(thm),theory(equality)],[c_90,c_10409]) ).
tff(c_10764,plain,
multiply(sk_c4,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10743,c_10427]) ).
tff(c_10424,plain,
multiply(sk_c6,sk_c4) = multiply(sk_c4,identity),
inference(superposition,[status(thm),theory(equality)],[c_9457,c_10409]) ).
tff(c_10765,plain,
multiply(sk_c4,identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_10743,c_10424]) ).
tff(c_10842,plain,
sk_c4 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_10764,c_10765]) ).
tff(c_10845,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_10842,c_10196]) ).
tff(c_10850,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9453,c_10845]) ).
tff(c_10852,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_14,plain,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_10879,plain,
multiply(sk_c4,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_10852,c_14]) ).
tff(c_16,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_10866,plain,
inverse(sk_c4) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_10852,c_16]) ).
tff(c_10870,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_10866,c_4]) ).
tff(c_10894,plain,
! [X_178,Y_179,Z_180] : ( multiply(multiply(X_178,Y_179),Z_180) = multiply(X_178,multiply(Y_179,Z_180)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10912,plain,
! [Z_180] : ( multiply(sk_c7,multiply(sk_c4,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_10870,c_10894]) ).
tff(c_11177,plain,
! [Z_192] : ( multiply(sk_c7,multiply(sk_c4,Z_192)) = Z_192 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10912]) ).
tff(c_11189,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10879,c_11177]) ).
tff(c_10924,plain,
! [X_2,Z_180] : ( multiply(inverse(X_2),multiply(X_2,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10894]) ).
tff(c_11776,plain,
! [X_206,Z_207] : ( multiply(inverse(X_206),multiply(X_206,Z_207)) = Z_207 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_11797,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11189,c_11776]) ).
tff(c_11846,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11797]) ).
tff(c_10851,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_10952,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10851,c_44]) ).
tff(c_11044,plain,
! [X2_186] :
( ( inverse(X2_186) != sk_c7 )
| ( multiply(X2_186,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_10952]) ).
tff(c_11051,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10879,c_11044]) ).
tff(c_11063,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10866,c_11051]) ).
tff(c_11064,plain,
! [X3_7,X4_8,X1_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_10952]) ).
tff(c_11156,plain,
! [X1_191] :
( ( inverse(X1_191) != sk_c7 )
| ( multiply(X1_191,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_11064]) ).
tff(c_11163,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_10879,c_11156]) ).
tff(c_11175,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10866,c_11163]) ).
tff(c_11176,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_11064]) ).
tff(c_11214,plain,
! [X3_194] :
( ( inverse(X3_194) != sk_c6 )
| ( multiply(X3_194,sk_c6) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_11176]) ).
tff(c_11225,plain,
( ( inverse(inverse(sk_c6)) != sk_c6 )
| ( sk_c5 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11214]) ).
tff(c_11231,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_11225]) ).
tff(c_11233,plain,
! [X_195,Z_196] : ( multiply(inverse(X_195),multiply(X_195,Z_196)) = Z_196 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_11254,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11189,c_11233]) ).
tff(c_11303,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11254]) ).
tff(c_11348,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11303,c_10851]) ).
tff(c_11364,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11348,c_4]) ).
tff(c_10936,plain,
! [X_2,Z_180] : ( multiply(inverse(X_2),multiply(X_2,Z_180)) = Z_180 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_11381,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11364,c_10936]) ).
tff(c_11393,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11381]) ).
tff(c_11395,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11231,c_11393]) ).
tff(c_11397,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_11225]) ).
tff(c_11229,plain,
( ( inverse(identity) != sk_c6 )
| ( sk_c6 != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_11214]) ).
tff(c_11230,plain,
sk_c6 != sk_c5,
inference(splitLeft,[status(thm)],[c_11229]) ).
tff(c_11398,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11397,c_11230]) ).
tff(c_11487,plain,
! [X_199,Z_200] : ( multiply(inverse(X_199),multiply(X_199,Z_200)) = Z_200 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_11511,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11189,c_11487]) ).
tff(c_11537,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11511]) ).
tff(c_11539,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11398,c_11537]) ).
tff(c_11541,plain,
sk_c6 = sk_c5,
inference(splitRight,[status(thm)],[c_11229]) ).
tff(c_11549,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11541,c_10851]) ).
tff(c_11625,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11549,c_11549,c_11541,c_11541,c_11225]) ).
tff(c_11547,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_11541,c_10879]) ).
tff(c_10932,plain,
! [Z_180] : ( multiply(sk_c7,multiply(sk_c4,Z_180)) = Z_180 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10912]) ).
tff(c_11608,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_11547,c_10932]) ).
tff(c_11671,plain,
! [X_202,Z_203] : ( multiply(inverse(X_202),multiply(X_202,Z_203)) = Z_203 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_11695,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_11608,c_11671]) ).
tff(c_11740,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11695]) ).
tff(c_11742,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11625,c_11740]) ).
tff(c_11757,plain,
! [X4_205] :
( ( multiply(X4_205,sk_c5) != sk_c6 )
| ( inverse(X4_205) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_11176]) ).
tff(c_11768,plain,
( ( sk_c6 != identity )
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_11757]) ).
tff(c_11773,plain,
( ( sk_c6 != identity )
| ( inverse(sk_c6) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10851,c_11768]) ).
tff(c_11774,plain,
inverse(sk_c6) != sk_c6,
inference(splitLeft,[status(thm)],[c_11773]) ).
tff(c_11853,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_11846,c_11774]) ).
tff(c_11865,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11846,c_61]) ).
tff(c_11915,plain,
multiply(identity,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_11865,c_4]) ).
tff(c_11932,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_11915,c_10936]) ).
tff(c_11944,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_11932]) ).
tff(c_11948,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_11944,c_11865]) ).
tff(c_12000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11853,c_11948]) ).
tff(c_12001,plain,
sk_c6 != identity,
inference(splitRight,[status(thm)],[c_11773]) ).
tff(c_12075,plain,
! [X_212,Z_213] : ( multiply(inverse(X_212),multiply(X_212,Z_213)) = Z_213 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10924]) ).
tff(c_12108,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_11189,c_12075]) ).
tff(c_12162,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12108]) ).
tff(c_12164,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12001,c_12162]) ).
tff(c_12166,plain,
inverse(sk_c3) != sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_32,plain,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_12208,plain,
multiply(sk_c4,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_12166,c_32]) ).
tff(c_34,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_12180,plain,
inverse(sk_c4) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_12166,c_34]) ).
tff(c_12184,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12180,c_4]) ).
tff(c_12241,plain,
! [Z_216] : ( multiply(sk_c7,multiply(sk_c4,Z_216)) = multiply(identity,Z_216) ),
inference(superposition,[status(thm),theory(equality)],[c_12184,c_12220]) ).
tff(c_12411,plain,
! [Z_226] : ( multiply(sk_c7,multiply(sk_c4,Z_226)) = Z_226 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12241]) ).
tff(c_12429,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12208,c_12411]) ).
tff(c_12516,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_12429,c_12489]) ).
tff(c_12572,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12516]) ).
tff(c_12165,plain,
inverse(sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_12170,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_12165,c_4]) ).
tff(c_12587,plain,
multiply(identity,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12572,c_12170]) ).
tff(c_12660,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_12587,c_12262]) ).
tff(c_12672,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_12660]) ).
tff(c_12912,plain,
! [X_233,Z_234] : ( multiply(inverse(inverse(X_233)),Z_234) = multiply(X_233,Z_234) ),
inference(superposition,[status(thm),theory(equality)],[c_12262,c_12489]) ).
tff(c_12919,plain,
! [X_233] : ( multiply(X_233,identity) = X_233 ),
inference(superposition,[status(thm),theory(equality)],[c_12912,c_12564]) ).
tff(c_12265,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12165,c_44]) ).
tff(c_12329,plain,
! [X2_221] :
( ( inverse(X2_221) != sk_c7 )
| ( multiply(X2_221,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_12265]) ).
tff(c_12336,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12208,c_12329]) ).
tff(c_12348,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12180,c_12336]) ).
tff(c_12349,plain,
! [X3_7,X4_8,X1_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_12265]) ).
tff(c_12468,plain,
! [X1_227] :
( ( inverse(X1_227) != sk_c7 )
| ( multiply(X1_227,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_12349]) ).
tff(c_12475,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_12208,c_12468]) ).
tff(c_12487,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12180,c_12475]) ).
tff(c_12488,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_12349]) ).
tff(c_12675,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != identity )
| ( inverse(X4_8) != identity )
| ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12572,c_12572,c_12572,c_12572,c_12488]) ).
tff(c_12676,plain,
! [X3_7] :
( ( inverse(X3_7) != identity )
| ( multiply(X3_7,identity) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_12675]) ).
tff(c_13736,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_12919,c_12672,c_12676]) ).
tff(c_12589,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12572,c_12165]) ).
tff(c_12678,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12672,c_12589]) ).
tff(c_13738,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13736,c_12678]) ).
tff(c_13739,plain,
! [X4_8] :
( ( multiply(X4_8,sk_c5) != identity )
| ( inverse(X4_8) != identity ) ),
inference(splitRight,[status(thm)],[c_12675]) ).
tff(c_14799,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_13982,c_12672,c_13739]) ).
tff(c_13741,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_12672,c_12589]) ).
tff(c_14801,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14799,c_13741]) ).
tff(c_14803,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_26,plain,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_14861,plain,
multiply(sk_c4,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14803,c_26]) ).
tff(c_14802,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_14807,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14802,c_4]) ).
tff(c_14869,plain,
! [X_263,Y_264,Z_265] : ( multiply(multiply(X_263,Y_264),Z_265) = multiply(X_263,multiply(Y_264,Z_265)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14896,plain,
! [Z_265] : ( multiply(sk_c7,multiply(sk_c4,Z_265)) = multiply(identity,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_14807,c_14869]) ).
tff(c_14926,plain,
! [Z_267] : ( multiply(sk_c7,multiply(sk_c4,Z_267)) = Z_267 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14896]) ).
tff(c_14938,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14861,c_14926]) ).
tff(c_14899,plain,
! [X_2,Z_265] : ( multiply(inverse(X_2),multiply(X_2,Z_265)) = multiply(identity,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14869]) ).
tff(c_15656,plain,
! [X_287,Z_288] : ( multiply(inverse(X_287),multiply(X_287,Z_288)) = Z_288 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14899]) ).
tff(c_15692,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14938,c_15656]) ).
tff(c_15740,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15692]) ).
tff(c_30,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_14827,plain,
inverse(sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_14803,c_30]) ).
tff(c_14943,plain,
! [X1_9,X4_8,X3_7,X2_6] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( inverse(X2_6) != sk_c7 )
| ( multiply(X2_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14827,c_44]) ).
tff(c_15033,plain,
! [X2_271] :
( ( inverse(X2_271) != sk_c7 )
| ( multiply(X2_271,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_14943]) ).
tff(c_15040,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14861,c_15033]) ).
tff(c_15052,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14802,c_15040]) ).
tff(c_15053,plain,
! [X3_7,X4_8,X1_9] :
( ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 )
| ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_14943]) ).
tff(c_15088,plain,
! [X1_274] :
( ( inverse(X1_274) != sk_c7 )
| ( multiply(X1_274,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_15053]) ).
tff(c_15095,plain,
inverse(sk_c4) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14861,c_15088]) ).
tff(c_15107,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14802,c_15095]) ).
tff(c_15108,plain,
! [X4_8,X3_7] :
( ( multiply(X4_8,sk_c5) != sk_c6 )
| ( inverse(X4_8) != sk_c6 )
| ( inverse(X3_7) != sk_c6 )
| ( multiply(X3_7,sk_c6) != sk_c5 ) ),
inference(splitRight,[status(thm)],[c_15053]) ).
tff(c_15191,plain,
! [X3_278] :
( ( inverse(X3_278) != sk_c6 )
| ( multiply(X3_278,sk_c6) != sk_c5 ) ),
inference(splitLeft,[status(thm)],[c_15108]) ).
tff(c_15205,plain,
( ( inverse(inverse(sk_c6)) != sk_c6 )
| ( sk_c5 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15191]) ).
tff(c_15211,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_15205]) ).
tff(c_15213,plain,
! [X_279,Z_280] : ( multiply(inverse(X_279),multiply(X_279,Z_280)) = Z_280 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14899]) ).
tff(c_15249,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14938,c_15213]) ).
tff(c_15297,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15249]) ).
tff(c_15378,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15297,c_14827]) ).
tff(c_15397,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15378,c_4]) ).
tff(c_14911,plain,
! [X_2,Z_265] : ( multiply(inverse(X_2),multiply(X_2,Z_265)) = Z_265 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14899]) ).
tff(c_15404,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15397,c_14911]) ).
tff(c_15416,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15404]) ).
tff(c_15418,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15211,c_15416]) ).
tff(c_15420,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_15205]) ).
tff(c_15209,plain,
( ( inverse(identity) != sk_c6 )
| ( sk_c6 != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15191]) ).
tff(c_15210,plain,
sk_c6 != sk_c5,
inference(splitLeft,[status(thm)],[c_15209]) ).
tff(c_15421,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15420,c_15210]) ).
tff(c_15109,plain,
! [Z_275] : ( multiply(sk_c4,multiply(sk_c7,Z_275)) = multiply(sk_c6,Z_275) ),
inference(superposition,[status(thm),theory(equality)],[c_14861,c_14869]) ).
tff(c_15124,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_14938,c_15109]) ).
tff(c_15137,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_14861,c_15124]) ).
tff(c_15446,plain,
! [X_283,Z_284] : ( multiply(inverse(X_283),multiply(X_283,Z_284)) = Z_284 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14899]) ).
tff(c_15482,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15137,c_15446]) ).
tff(c_15526,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15482]) ).
tff(c_15528,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15421,c_15526]) ).
tff(c_15530,plain,
sk_c6 = sk_c5,
inference(splitRight,[status(thm)],[c_15209]) ).
tff(c_15541,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15530,c_14827]) ).
tff(c_15592,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15541,c_15541,c_15530,c_15530,c_15205]) ).
tff(c_15539,plain,
multiply(sk_c4,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15530,c_14861]) ).
tff(c_15552,plain,
multiply(sk_c5,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15541,c_4]) ).
tff(c_14910,plain,
! [Z_265] : ( multiply(sk_c7,multiply(sk_c4,Z_265)) = Z_265 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14896]) ).
tff(c_15576,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_15539,c_14910]) ).
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_15602,plain,
! [Z_285] : ( multiply(sk_c4,multiply(sk_c7,Z_285)) = multiply(sk_c5,Z_285) ),
inference(superposition,[status(thm),theory(equality)],[c_15539,c_6]) ).
tff(c_15617,plain,
multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_15576,c_15602]) ).
tff(c_15633,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15539,c_15552,c_15617]) ).
tff(c_15635,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15592,c_15633]) ).
tff(c_15637,plain,
! [X4_286] :
( ( multiply(X4_286,sk_c5) != sk_c6 )
| ( inverse(X4_286) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_15108]) ).
tff(c_15652,plain,
( ( sk_c6 != sk_c5 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_15637]) ).
tff(c_15655,plain,
inverse(identity) != sk_c6,
inference(splitLeft,[status(thm)],[c_15652]) ).
tff(c_15746,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15740,c_15655]) ).
tff(c_15758,plain,
inverse(sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15740,c_14827]) ).
tff(c_15777,plain,
multiply(identity,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15758,c_4]) ).
tff(c_15784,plain,
multiply(inverse(identity),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15777,c_14911]) ).
tff(c_15796,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15784]) ).
tff(c_15800,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15796,c_15758]) ).
tff(c_15865,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15746,c_15800]) ).
tff(c_15867,plain,
inverse(identity) = sk_c6,
inference(splitRight,[status(thm)],[c_15652]) ).
tff(c_15912,plain,
multiply(sk_c6,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15867,c_4]) ).
tff(c_15922,plain,
! [Z_5] : ( multiply(sk_c6,multiply(identity,Z_5)) = multiply(identity,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_15912,c_6]) ).
tff(c_15934,plain,
! [Z_292] : ( multiply(sk_c6,Z_292) = Z_292 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_15922]) ).
tff(c_14831,plain,
multiply(sk_c6,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_14827,c_4]) ).
tff(c_15953,plain,
sk_c5 = identity,
inference(superposition,[status(thm),theory(equality)],[c_15934,c_14831]) ).
tff(c_15866,plain,
sk_c6 != sk_c5,
inference(splitRight,[status(thm)],[c_15652]) ).
tff(c_15975,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15953,c_15866]) ).
tff(c_15987,plain,
! [X_293,Z_294] : ( multiply(inverse(X_293),multiply(X_293,Z_294)) = Z_294 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14899]) ).
tff(c_16017,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_14938,c_15987]) ).
tff(c_16055,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16017]) ).
tff(c_16062,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15975,c_16055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP253-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 22:09:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.65/2.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.21/3.00
% 8.21/3.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.60/3.06
% 8.60/3.06 Inference rules
% 8.60/3.06 ----------------------
% 8.60/3.06 #Ref : 0
% 8.60/3.06 #Sup : 4044
% 8.60/3.06 #Fact : 0
% 8.60/3.06 #Define : 0
% 8.60/3.06 #Split : 52
% 8.60/3.06 #Chain : 0
% 8.60/3.06 #Close : 0
% 8.60/3.06
% 8.60/3.06 Ordering : KBO
% 8.60/3.06
% 8.60/3.06 Simplification rules
% 8.60/3.06 ----------------------
% 8.60/3.06 #Subsume : 34
% 8.60/3.06 #Demod : 5367
% 8.60/3.06 #Tautology : 2944
% 8.60/3.06 #SimpNegUnit : 36
% 8.60/3.06 #BackRed : 336
% 8.60/3.06
% 8.60/3.06 #Partial instantiations: 0
% 8.60/3.06 #Strategies tried : 1
% 8.60/3.06
% 8.60/3.06 Timing (in seconds)
% 8.60/3.06 ----------------------
% 8.60/3.06 Preprocessing : 0.43
% 8.60/3.06 Parsing : 0.19
% 8.60/3.06 CNF conversion : 0.02
% 8.60/3.06 Main loop : 1.51
% 8.60/3.06 Inferencing : 0.51
% 8.60/3.06 Reduction : 0.61
% 8.60/3.06 Demodulation : 0.49
% 8.60/3.06 BG Simplification : 0.05
% 8.60/3.06 Subsumption : 0.21
% 8.60/3.06 Abstraction : 0.06
% 8.60/3.06 MUC search : 0.00
% 8.60/3.06 Cooper : 0.00
% 8.60/3.06 Total : 2.07
% 8.60/3.06 Index Insertion : 0.00
% 8.60/3.06 Index Deletion : 0.00
% 8.60/3.06 Index Matching : 0.00
% 8.60/3.06 BG Taut test : 0.00
%------------------------------------------------------------------------------