TSTP Solution File: GRP303-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP303-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:40:51 EDT 2023
% Result : Unsatisfiable 9.57s 3.66s
% Output : CNFRefutation 10.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 33
% Syntax : Number of formulae : 475 ( 390 unt; 10 typ; 0 def)
% Number of atoms : 642 ( 613 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 408 ( 231 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 236 (; 236 !; 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_75,axiom,
multiply(sk_c6,sk_c7) = sk_c5,
file(unknown,unknown) ).
tff(f_102,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_120,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_90,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_84,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_108,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_153,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( multiply(X4,sk_c6) != sk_c7 )
| ( inverse(X4) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( inverse(X2) != sk_c6 )
| ( multiply(X2,sk_c5) != sk_c6 ) ),
file(unknown,unknown) ).
tff(f_111,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_78,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_81,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_105,axiom,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_87,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c6) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_99,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_96,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_93,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_123,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_117,axiom,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_114,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_20225,plain,
! [X_260,Y_261,Z_262] : ( multiply(multiply(X_260,Y_261),Z_262) = multiply(X_260,multiply(Y_261,Z_262)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_20255,plain,
! [X_2,Z_262] : ( multiply(inverse(X_2),multiply(X_2,Z_262)) = multiply(identity,Z_262) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20225]) ).
tff(c_20425,plain,
! [X_269,Z_270] : ( multiply(inverse(X_269),multiply(X_269,Z_270)) = Z_270 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20255]) ).
tff(c_20269,plain,
! [X_2,Z_262] : ( multiply(inverse(X_2),multiply(X_2,Z_262)) = Z_262 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20255]) ).
tff(c_21381,plain,
! [X_286,Z_287] : ( multiply(inverse(inverse(X_286)),Z_287) = multiply(X_286,Z_287) ),
inference(superposition,[status(thm),theory(equality)],[c_20425,c_20269]) ).
tff(c_20488,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_20425]) ).
tff(c_21388,plain,
! [X_286] : ( multiply(X_286,identity) = X_286 ),
inference(superposition,[status(thm),theory(equality)],[c_21381,c_20488]) ).
tff(c_18110,plain,
! [X_216,Y_217,Z_218] : ( multiply(multiply(X_216,Y_217),Z_218) = multiply(X_216,multiply(Y_217,Z_218)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_18140,plain,
! [X_2,Z_218] : ( multiply(inverse(X_2),multiply(X_2,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_18110]) ).
tff(c_18154,plain,
! [X_2,Z_218] : ( multiply(inverse(X_2),multiply(X_2,Z_218)) = Z_218 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18140]) ).
tff(c_19671,plain,
! [X_249,Z_250] : ( multiply(inverse(X_249),multiply(X_249,Z_250)) = Z_250 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18140]) ).
tff(c_19895,plain,
! [X_253,Z_254] : ( multiply(inverse(inverse(X_253)),Z_254) = multiply(X_253,Z_254) ),
inference(superposition,[status(thm),theory(equality)],[c_18154,c_19671]) ).
tff(c_19725,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19671]) ).
tff(c_19902,plain,
! [X_253] : ( multiply(X_253,identity) = X_253 ),
inference(superposition,[status(thm),theory(equality)],[c_19895,c_19725]) ).
tff(c_16,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_34,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_15764,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_46,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_73,plain,
inverse(sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_46]) ).
tff(c_77,plain,
multiply(sk_c6,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_73,c_4]) ).
tff(c_15806,plain,
! [X_168,Y_169,Z_170] : ( multiply(multiply(X_168,Y_169),Z_170) = multiply(X_168,multiply(Y_169,Z_170)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_15842,plain,
! [Z_170] : ( multiply(sk_c6,multiply(sk_c2,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_15806]) ).
tff(c_15875,plain,
! [Z_172] : ( multiply(sk_c6,multiply(sk_c2,Z_172)) = Z_172 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15842]) ).
tff(c_15887,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15764,c_15875]) ).
tff(c_15891,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15887]) ).
tff(c_15902,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15891,c_16]) ).
tff(c_15845,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = multiply(identity,Z_170) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15806]) ).
tff(c_16104,plain,
! [X_175,Z_176] : ( multiply(inverse(X_175),multiply(X_175,Z_176)) = Z_176 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15845]) ).
tff(c_16134,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_15902,c_16104]) ).
tff(c_16170,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16134]) ).
tff(c_26,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_86,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_90,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_86,c_4]) ).
tff(c_16178,plain,
multiply(identity,sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16170,c_90]) ).
tff(c_15860,plain,
! [X_2,Z_170] : ( multiply(inverse(X_2),multiply(X_2,Z_170)) = Z_170 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15845]) ).
tff(c_16304,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_16178,c_15860]) ).
tff(c_16316,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16304]) ).
tff(c_22,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_99,plain,
multiply(sk_c1,sk_c7) = sk_c6,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_15057,plain,
! [X_155,Y_156,Z_157] : ( multiply(multiply(X_155,Y_156),Z_157) = multiply(X_155,multiply(Y_156,Z_157)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_15087,plain,
! [Z_157] : ( multiply(sk_c7,multiply(sk_c1,Z_157)) = multiply(identity,Z_157) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_15057]) ).
tff(c_15110,plain,
! [Z_158] : ( multiply(sk_c7,multiply(sk_c1,Z_158)) = Z_158 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15087]) ).
tff(c_15122,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_99,c_15110]) ).
tff(c_15093,plain,
! [X_2,Z_157] : ( multiply(inverse(X_2),multiply(X_2,Z_157)) = multiply(identity,Z_157) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_15057]) ).
tff(c_15250,plain,
! [X_163,Z_164] : ( multiply(inverse(X_163),multiply(X_163,Z_164)) = Z_164 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15093]) ).
tff(c_15295,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15122,c_15250]) ).
tff(c_15349,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15295]) ).
tff(c_14659,plain,
! [X_147,Y_148,Z_149] : ( multiply(multiply(X_147,Y_148),Z_149) = multiply(X_147,multiply(Y_148,Z_149)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14692,plain,
! [Z_149] : ( multiply(sk_c7,multiply(sk_c1,Z_149)) = multiply(identity,Z_149) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_14659]) ).
tff(c_14715,plain,
! [Z_150] : ( multiply(sk_c7,multiply(sk_c1,Z_150)) = Z_150 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14692]) ).
tff(c_14727,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_99,c_14715]) ).
tff(c_8,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_112,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_8]) ).
tff(c_127,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_151,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_127]) ).
tff(c_172,plain,
! [Z_15] : ( multiply(sk_c7,multiply(sk_c1,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_151]) ).
tff(c_184,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_99,c_172]) ).
tff(c_188,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_112,c_184]) ).
tff(c_190,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_188,c_112]) ).
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_127]) ).
tff(c_267,plain,
! [X_17,Z_18] : ( multiply(inverse(X_17),multiply(X_17,Z_18)) = Z_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_157]) ).
tff(c_297,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_190,c_267]) ).
tff(c_323,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_297]) ).
tff(c_170,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_532,plain,
! [X_21,Z_22] : ( multiply(inverse(inverse(X_21)),Z_22) = multiply(X_21,Z_22) ),
inference(superposition,[status(thm),theory(equality)],[c_267,c_170]) ).
tff(c_315,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_267]) ).
tff(c_539,plain,
! [X_21] : ( multiply(X_21,identity) = X_21 ),
inference(superposition,[status(thm),theory(equality)],[c_532,c_315]) ).
tff(c_195,plain,
multiply(sk_c6,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_188,c_16]) ).
tff(c_38,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_104,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_191,plain,
multiply(sk_c2,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_188,c_104]) ).
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_77,c_127]) ).
tff(c_250,plain,
! [Z_16] : ( multiply(sk_c6,multiply(sk_c2,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_154]) ).
tff(c_262,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_191,c_250]) ).
tff(c_266,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_195,c_262]) ).
tff(c_338,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_323,c_266]) ).
tff(c_50,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_52,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_50]) ).
tff(c_214,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( inverse(X3_6) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_188,c_188,c_188,c_188,c_188,c_188,c_52]) ).
tff(c_215,plain,
multiply(sk_c5,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_214]) ).
tff(c_216,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_215,c_190]) ).
tff(c_217,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c5 )
| ( multiply(X3_6,sk_c5) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c5 )
| ( multiply(X1_8,sk_c6) != sk_c5 )
| ( inverse(X1_8) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_214]) ).
tff(c_8893,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != identity )
| ( identity != X3_6 )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( identity != X2_9 )
| ( inverse(X2_9) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_323,c_539,c_338,c_323,c_338,c_539,c_338,c_323,c_539,c_338,c_323,c_323,c_539,c_338,c_323,c_338,c_217]) ).
tff(c_8895,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8893]) ).
tff(c_331,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_323,c_77]) ).
tff(c_425,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_331,c_170]) ).
tff(c_437,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_425]) ).
tff(c_332,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_323,c_73]) ).
tff(c_441,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_437,c_332]) ).
tff(c_8897,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8895,c_441]) ).
tff(c_8898,plain,
! [X1_8,X4_7,X3_6] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( inverse(X3_6) != identity )
| ( identity != X3_6 ) ),
inference(splitRight,[status(thm)],[c_8893]) ).
tff(c_13750,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8898]) ).
tff(c_13752,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13750,c_441]) ).
tff(c_13753,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity ) ),
inference(splitRight,[status(thm)],[c_8898]) ).
tff(c_13755,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_13753]) ).
tff(c_13757,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_13755,c_441]) ).
tff(c_14614,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_13753]) ).
tff(c_14616,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14614,c_441]) ).
tff(c_14618,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_14731,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14727,c_14618]) ).
tff(c_14695,plain,
! [Z_149] : ( multiply(sk_c6,multiply(sk_c2,Z_149)) = multiply(identity,Z_149) ),
inference(superposition,[status(thm),theory(equality)],[c_77,c_14659]) ).
tff(c_14772,plain,
! [Z_152] : ( multiply(sk_c6,multiply(sk_c2,Z_152)) = Z_152 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14695]) ).
tff(c_14784,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_104,c_14772]) ).
tff(c_14788,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_14784]) ).
tff(c_14801,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14788,c_16]) ).
tff(c_14698,plain,
! [X_2,Z_149] : ( multiply(inverse(X_2),multiply(X_2,Z_149)) = multiply(identity,Z_149) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_14659]) ).
tff(c_14877,plain,
! [X_153,Z_154] : ( multiply(inverse(X_153),multiply(X_153,Z_154)) = Z_154 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14698]) ).
tff(c_14913,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14801,c_14877]) ).
tff(c_14951,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_14913]) ).
tff(c_14820,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c5 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14788,c_14788,c_14788,c_14788,c_14788,c_14788,c_14788,c_52]) ).
tff(c_14821,plain,
multiply(sk_c7,sk_c5) != sk_c5,
inference(splitLeft,[status(thm)],[c_14820]) ).
tff(c_14957,plain,
multiply(identity,sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14951,c_14821]) ).
tff(c_14966,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14957]) ).
tff(c_14968,plain,
multiply(sk_c7,sk_c5) = sk_c5,
inference(splitRight,[status(thm)],[c_14820]) ).
tff(c_14798,plain,
multiply(sk_c1,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14788,c_99]) ).
tff(c_14711,plain,
! [Z_149] : ( multiply(sk_c7,multiply(sk_c1,Z_149)) = Z_149 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14692]) ).
tff(c_15002,plain,
multiply(sk_c7,sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_14798,c_14711]) ).
tff(c_15008,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_14968,c_15002]) ).
tff(c_15010,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14731,c_15008]) ).
tff(c_15012,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_15044,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_15012,c_40]) ).
tff(c_15011,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_15016,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15011,c_4]) ).
tff(c_15081,plain,
! [Z_157] : ( multiply(sk_c6,multiply(sk_c4,Z_157)) = multiply(identity,Z_157) ),
inference(superposition,[status(thm),theory(equality)],[c_15016,c_15057]) ).
tff(c_15218,plain,
! [Z_162] : ( multiply(sk_c6,multiply(sk_c4,Z_162)) = Z_162 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15081]) ).
tff(c_15230,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15044,c_15218]) ).
tff(c_15369,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15349,c_15349,c_15230]) ).
tff(c_15385,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15369]) ).
tff(c_15146,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( sk_c7 != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_15122,c_52]) ).
tff(c_15147,plain,
sk_c7 != sk_c5,
inference(splitLeft,[status(thm)],[c_15146]) ).
tff(c_15391,plain,
sk_c7 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15385,c_15147]) ).
tff(c_15384,plain,
multiply(identity,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15349,c_16]) ).
tff(c_15396,plain,
multiply(identity,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15385,c_15384]) ).
tff(c_15108,plain,
! [X_2,Z_157] : ( multiply(inverse(X_2),multiply(X_2,Z_157)) = Z_157 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15093]) ).
tff(c_15400,plain,
multiply(inverse(identity),identity) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_15396,c_15108]) ).
tff(c_15412,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15400]) ).
tff(c_15416,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15391,c_15412]) ).
tff(c_15418,plain,
sk_c7 = sk_c5,
inference(splitRight,[status(thm)],[c_15146]) ).
tff(c_15419,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15418,c_15418,c_15122]) ).
tff(c_15535,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_15419,c_15108]) ).
tff(c_15541,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15535]) ).
tff(c_15550,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_15541,c_77]) ).
tff(c_15735,plain,
sk_c2 = identity,
inference(superposition,[status(thm),theory(equality)],[c_15550,c_2]) ).
tff(c_15440,plain,
! [X_165,Z_166] : ( multiply(inverse(X_165),multiply(X_165,Z_166)) = Z_166 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15093]) ).
tff(c_15467,plain,
multiply(inverse(sk_c4),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_15044,c_15440]) ).
tff(c_15489,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15011,c_15467]) ).
tff(c_15545,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15541,c_15541,c_15489]) ).
tff(c_15553,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15545]) ).
tff(c_15424,plain,
multiply(sk_c2,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15418,c_15012]) ).
tff(c_15642,plain,
multiply(sk_c2,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15553,c_15541,c_15424]) ).
tff(c_15745,plain,
multiply(identity,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_15735,c_15642]) ).
tff(c_15750,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15745]) ).
tff(c_15752,plain,
multiply(sk_c1,sk_c7) != sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_18,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_15778,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_15752,c_18]) ).
tff(c_16177,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16170,c_15778]) ).
tff(c_20,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_15799,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_15752,c_20]) ).
tff(c_15893,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_15891,c_15799]) ).
tff(c_16218,plain,
multiply(sk_c3,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_16170,c_15893]) ).
tff(c_16222,plain,
multiply(inverse(sk_c3),identity) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_16218,c_15860]) ).
tff(c_16228,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16177,c_16222]) ).
tff(c_15898,plain,
multiply(sk_c1,sk_c7) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_15891,c_15752]) ).
tff(c_16217,plain,
multiply(sk_c1,identity) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16170,c_15898]) ).
tff(c_16232,plain,
multiply(sk_c1,identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_16228,c_16217]) ).
tff(c_16379,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16316,c_16232]) ).
tff(c_16381,plain,
multiply(sk_c2,sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_17725,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_16381,c_40]) ).
tff(c_15751,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_15756,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_15751,c_4]) ).
tff(c_17736,plain,
! [X_206,Y_207,Z_208] : ( multiply(multiply(X_206,Y_207),Z_208) = multiply(X_206,multiply(Y_207,Z_208)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17760,plain,
! [Z_208] : ( multiply(sk_c6,multiply(sk_c4,Z_208)) = multiply(identity,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_15756,c_17736]) ).
tff(c_17812,plain,
! [Z_211] : ( multiply(sk_c6,multiply(sk_c4,Z_211)) = Z_211 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17760]) ).
tff(c_17824,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17725,c_17812]) ).
tff(c_16380,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_36,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_16415,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_16381,c_36]) ).
tff(c_24,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_16408,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_15752,c_24]) ).
tff(c_10,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_16403,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_16490,plain,
! [X2_9,X1_8,X4_7,X3_6] :
( ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16403,c_52]) ).
tff(c_16607,plain,
! [X3_186] :
( ( inverse(X3_186) != sk_c7 )
| ( multiply(X3_186,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_16490]) ).
tff(c_16618,plain,
( ( inverse(inverse(sk_c7)) != sk_c7 )
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_16607]) ).
tff(c_16629,plain,
sk_c6 != identity,
inference(splitLeft,[status(thm)],[c_16618]) ).
tff(c_16423,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_16450,plain,
! [Z_180] : ( multiply(sk_c6,multiply(sk_c4,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_15756,c_16423]) ).
tff(c_16575,plain,
! [Z_185] : ( multiply(sk_c6,multiply(sk_c4,Z_185)) = Z_185 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16450]) ).
tff(c_16587,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_16408,c_16575]) ).
tff(c_16385,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_16380,c_4]) ).
tff(c_16447,plain,
! [Z_180] : ( multiply(sk_c7,multiply(sk_c3,Z_180)) = multiply(identity,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_16385,c_16423]) ).
tff(c_16505,plain,
! [Z_183] : ( multiply(sk_c7,multiply(sk_c3,Z_183)) = Z_183 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16447]) ).
tff(c_16517,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_16415,c_16505]) ).
tff(c_16528,plain,
! [Z_184] : ( multiply(sk_c6,multiply(sk_c7,Z_184)) = multiply(sk_c5,Z_184) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_16423]) ).
tff(c_16540,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_16517,c_16528]) ).
tff(c_16630,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16587,c_16540]) ).
tff(c_16459,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_16423]) ).
tff(c_16641,plain,
! [X_187,Z_188] : ( multiply(inverse(X_187),multiply(X_187,Z_188)) = Z_188 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16459]) ).
tff(c_16659,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16630,c_16641]) ).
tff(c_16738,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_16659]) ).
tff(c_16811,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16738,c_16738,c_16517]) ).
tff(c_16820,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16811]) ).
tff(c_16822,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16629,c_16820]) ).
tff(c_16824,plain,
sk_c6 = identity,
inference(splitRight,[status(thm)],[c_16618]) ).
tff(c_16625,plain,
( ( inverse(sk_c6) != sk_c7 )
| ( sk_c6 != sk_c5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_16607]) ).
tff(c_16628,plain,
sk_c6 != sk_c5,
inference(splitLeft,[status(thm)],[c_16625]) ).
tff(c_16825,plain,
sk_c5 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_16824,c_16628]) ).
tff(c_16828,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16824,c_16824,c_16587]) ).
tff(c_16845,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16828]) ).
tff(c_16880,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16825,c_16845]) ).
tff(c_16882,plain,
sk_c6 = sk_c5,
inference(splitRight,[status(thm)],[c_16625]) ).
tff(c_16985,plain,
( ( inverse(inverse(sk_c7)) != sk_c7 )
| ( sk_c5 != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_16882,c_16618]) ).
tff(c_16986,plain,
sk_c5 != identity,
inference(splitLeft,[status(thm)],[c_16985]) ).
tff(c_16885,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_16882,c_16882,c_16587]) ).
tff(c_16987,plain,
! [X_190,Z_191] : ( multiply(inverse(X_190),multiply(X_190,Z_191)) = Z_191 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16459]) ).
tff(c_17005,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_16885,c_16987]) ).
tff(c_17066,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17005]) ).
tff(c_17068,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16986,c_17066]) ).
tff(c_17070,plain,
sk_c5 = identity,
inference(splitRight,[status(thm)],[c_16985]) ).
tff(c_16881,plain,
inverse(sk_c6) != sk_c7,
inference(splitRight,[status(thm)],[c_16625]) ).
tff(c_16927,plain,
inverse(sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_16882,c_16881]) ).
tff(c_17080,plain,
inverse(identity) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17070,c_16927]) ).
tff(c_17085,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17070,c_16882]) ).
tff(c_16444,plain,
! [Z_180] : ( multiply(sk_c7,multiply(sk_c6,Z_180)) = multiply(sk_c5,Z_180) ),
inference(superposition,[status(thm),theory(equality)],[c_16403,c_16423]) ).
tff(c_17098,plain,
! [Z_192] : ( multiply(sk_c7,Z_192) = Z_192 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17085,c_2,c_17070,c_16444]) ).
tff(c_17116,plain,
sk_c1 = identity,
inference(superposition,[status(thm),theory(equality)],[c_17098,c_90]) ).
tff(c_17152,plain,
inverse(identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17116,c_86]) ).
tff(c_17198,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17080,c_17152]) ).
tff(c_17199,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_16490]) ).
tff(c_17324,plain,
! [X2_197] :
( ( multiply(X2_197,sk_c5) != sk_c6 )
| ( inverse(X2_197) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_17199]) ).
tff(c_17334,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_16408,c_17324]) ).
tff(c_17346,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15751,c_17334]) ).
tff(c_17347,plain,
! [X1_8,X4_7] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_17199]) ).
tff(c_17443,plain,
! [X4_200] :
( ( inverse(X4_200) != sk_c6 )
| ( multiply(X4_200,sk_c6) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_17347]) ).
tff(c_17460,plain,
( ( inverse(inverse(sk_c6)) != sk_c6 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17443]) ).
tff(c_17468,plain,
sk_c7 != identity,
inference(splitLeft,[status(thm)],[c_17460]) ).
tff(c_17356,plain,
! [Z_198] : ( multiply(sk_c6,multiply(sk_c4,Z_198)) = Z_198 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16450]) ).
tff(c_17368,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_16408,c_17356]) ).
tff(c_17213,plain,
! [Z_194] : ( multiply(sk_c7,multiply(sk_c3,Z_194)) = Z_194 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16447]) ).
tff(c_17225,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_16415,c_17213]) ).
tff(c_17379,plain,
! [Z_199] : ( multiply(sk_c6,multiply(sk_c7,Z_199)) = multiply(sk_c5,Z_199) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_16423]) ).
tff(c_17391,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_17225,c_17379]) ).
tff(c_17410,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17368,c_17391]) ).
tff(c_17469,plain,
! [X_201,Z_202] : ( multiply(inverse(X_201),multiply(X_201,Z_202)) = Z_202 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16459]) ).
tff(c_17496,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17410,c_17469]) ).
tff(c_17567,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17496]) ).
tff(c_17569,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17468,c_17567]) ).
tff(c_17571,plain,
sk_c7 = identity,
inference(splitRight,[status(thm)],[c_17460]) ).
tff(c_17453,plain,
inverse(sk_c3) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_16415,c_17443]) ).
tff(c_17466,plain,
sk_c7 != sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_16380,c_17453]) ).
tff(c_17573,plain,
sk_c6 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17571,c_17466]) ).
tff(c_17577,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_17571,c_17571,c_17225]) ).
tff(c_17590,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17577]) ).
tff(c_17595,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17573,c_17590]) ).
tff(c_17691,plain,
! [X1_205] :
( ( multiply(X1_205,sk_c6) != sk_c7 )
| ( inverse(X1_205) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_17347]) ).
tff(c_17701,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16415,c_17691]) ).
tff(c_17716,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16380,c_17701]) ).
tff(c_17717,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_17757,plain,
! [Z_208] : ( multiply(sk_c7,multiply(sk_c3,Z_208)) = multiply(identity,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_16385,c_17736]) ).
tff(c_17865,plain,
! [Z_213] : ( multiply(sk_c7,multiply(sk_c3,Z_213)) = Z_213 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17757]) ).
tff(c_17880,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_17717,c_17865]) ).
tff(c_17775,plain,
! [Z_208] : ( multiply(sk_c6,multiply(sk_c7,Z_208)) = multiply(sk_c5,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_17736]) ).
tff(c_17887,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_17880,c_17775]) ).
tff(c_17893,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17824,c_17887]) ).
tff(c_17769,plain,
! [X_2,Z_208] : ( multiply(inverse(X_2),multiply(X_2,Z_208)) = multiply(identity,Z_208) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17736]) ).
tff(c_17911,plain,
! [X_214,Z_215] : ( multiply(inverse(X_214),multiply(X_214,Z_215)) = Z_215 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17769]) ).
tff(c_17932,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_17893,c_17911]) ).
tff(c_18003,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17932]) ).
tff(c_18023,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18003,c_18003,c_17880]) ).
tff(c_18032,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18023]) ).
tff(c_18031,plain,
multiply(sk_c6,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18003,c_16]) ).
tff(c_18054,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18032,c_18031]) ).
tff(c_17718,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_18026,plain,
multiply(identity,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18003,c_17718]) ).
tff(c_18034,plain,
sk_c6 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18026]) ).
tff(c_18060,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18054,c_18032,c_18034]) ).
tff(c_18062,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_32,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_18090,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18062,c_32]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_18074,plain,
inverse(sk_c4) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_18062,c_30]) ).
tff(c_18078,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18074,c_4]) ).
tff(c_18131,plain,
! [Z_218] : ( multiply(sk_c6,multiply(sk_c4,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_18078,c_18110]) ).
tff(c_18156,plain,
! [Z_219] : ( multiply(sk_c6,multiply(sk_c4,Z_219)) = Z_219 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18131]) ).
tff(c_18168,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_18090,c_18156]) ).
tff(c_28,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_18097,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_18062,c_28]) ).
tff(c_18061,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_18066,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18061,c_4]) ).
tff(c_18134,plain,
! [Z_218] : ( multiply(sk_c7,multiply(sk_c3,Z_218)) = multiply(identity,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_18066,c_18110]) ).
tff(c_18442,plain,
! [Z_227] : ( multiply(sk_c7,multiply(sk_c3,Z_227)) = Z_227 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18134]) ).
tff(c_18457,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18097,c_18442]) ).
tff(c_18146,plain,
! [Z_218] : ( multiply(sk_c6,multiply(sk_c7,Z_218)) = multiply(sk_c5,Z_218) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_18110]) ).
tff(c_18464,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_18457,c_18146]) ).
tff(c_18470,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18168,c_18464]) ).
tff(c_19710,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18470,c_19671]) ).
tff(c_19734,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19710]) ).
tff(c_18180,plain,
! [Z_220] : ( multiply(sk_c7,multiply(sk_c3,Z_220)) = Z_220 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18134]) ).
tff(c_18192,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18097,c_18180]) ).
tff(c_18203,plain,
! [Z_221] : ( multiply(sk_c6,multiply(sk_c7,Z_221)) = multiply(sk_c5,Z_221) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_18110]) ).
tff(c_18215,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_18192,c_18203]) ).
tff(c_18225,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18168,c_18215]) ).
tff(c_18254,plain,
! [X_223,Z_224] : ( multiply(inverse(X_223),multiply(X_223,Z_224)) = Z_224 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18140]) ).
tff(c_18278,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18225,c_18254]) ).
tff(c_18333,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18278]) ).
tff(c_18341,plain,
multiply(identity,identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_18333,c_18333,c_18192]) ).
tff(c_18350,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18341]) ).
tff(c_18394,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18350,c_18350,c_18168]) ).
tff(c_18403,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18394]) ).
tff(c_18179,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_18343,plain,
multiply(identity,sk_c6) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18333,c_18179]) ).
tff(c_18351,plain,
sk_c6 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18343]) ).
tff(c_18413,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18403,c_18350,c_18351]) ).
tff(c_18415,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(splitRight,[status(thm)],[c_52]) ).
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_18533,plain,
! [Z_230] : ( multiply(sk_c7,multiply(sk_c6,Z_230)) = multiply(sk_c5,Z_230) ),
inference(superposition,[status(thm),theory(equality)],[c_18415,c_6]) ).
tff(c_18566,plain,
multiply(sk_c7,sk_c5) = multiply(sk_c5,sk_c7),
inference(superposition,[status(thm),theory(equality)],[c_16,c_18533]) ).
tff(c_18570,plain,
multiply(sk_c7,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18470,c_18566]) ).
tff(c_18554,plain,
multiply(sk_c7,sk_c5) = multiply(sk_c5,sk_c6),
inference(superposition,[status(thm),theory(equality)],[c_18168,c_18533]) ).
tff(c_18975,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18570,c_18554]) ).
tff(c_18995,plain,
! [Z_237] : ( multiply(sk_c4,multiply(sk_c5,Z_237)) = multiply(sk_c6,Z_237) ),
inference(superposition,[status(thm),theory(equality)],[c_18090,c_18110]) ).
tff(c_19010,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_18975,c_18995]) ).
tff(c_19020,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18090,c_18168,c_19010]) ).
tff(c_19029,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19020,c_18457]) ).
tff(c_19743,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19734,c_19734,c_19029]) ).
tff(c_19751,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19743]) ).
tff(c_19118,plain,
! [X_238,Z_239] : ( multiply(inverse(X_238),multiply(X_238,Z_239)) = Z_239 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18140]) ).
tff(c_19163,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18470,c_19118]) ).
tff(c_19188,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_19163]) ).
tff(c_19388,plain,
! [X_242,Z_243] : ( multiply(inverse(inverse(X_242)),Z_243) = multiply(X_242,Z_243) ),
inference(superposition,[status(thm),theory(equality)],[c_18154,c_19118]) ).
tff(c_19178,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_19118]) ).
tff(c_19395,plain,
! [X_242] : ( multiply(X_242,identity) = X_242 ),
inference(superposition,[status(thm),theory(equality)],[c_19388,c_19178]) ).
tff(c_19191,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19188,c_19188,c_19029]) ).
tff(c_19198,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19191]) ).
tff(c_18805,plain,
! [X_234,Z_235] : ( multiply(inverse(X_234),multiply(X_234,Z_235)) = Z_235 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18140]) ).
tff(c_18853,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18470,c_18805]) ).
tff(c_18878,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_18853]) ).
tff(c_18629,plain,
multiply(sk_c5,sk_c6) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18570,c_18554]) ).
tff(c_18656,plain,
! [Z_232] : ( multiply(sk_c4,multiply(sk_c5,Z_232)) = multiply(sk_c6,Z_232) ),
inference(superposition,[status(thm),theory(equality)],[c_18090,c_18110]) ).
tff(c_18674,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_18629,c_18656]) ).
tff(c_18685,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18090,c_18168,c_18674]) ).
tff(c_18694,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18685,c_18457]) ).
tff(c_18883,plain,
multiply(identity,identity) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18878,c_18878,c_18694]) ).
tff(c_18893,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18883]) ).
tff(c_18704,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_18685,c_73]) ).
tff(c_18727,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_18704,c_4]) ).
tff(c_18915,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_18893,c_18727]) ).
tff(c_18902,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18893,c_18704]) ).
tff(c_18931,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_18915,c_18902]) ).
tff(c_18414,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_18509,plain,
! [X2_229] :
( ( multiply(X2_229,sk_c5) != sk_c6 )
| ( inverse(X2_229) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_18414]) ).
tff(c_18519,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_18090,c_18509]) ).
tff(c_18531,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18074,c_18519]) ).
tff(c_18532,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_18414]) ).
tff(c_18628,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_18532]) ).
tff(c_18731,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_18685,c_18628]) ).
tff(c_18758,plain,
inverse(sk_c7) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_18694,c_18731]) ).
tff(c_18882,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_18878,c_18878,c_18758]) ).
tff(c_18973,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18931,c_18882]) ).
tff(c_18974,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_18532]) ).
tff(c_19069,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 )
| ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_19020,c_19020,c_19020,c_18974]) ).
tff(c_19070,plain,
! [X1_8] :
( ( multiply(X1_8,sk_c5) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_19069]) ).
tff(c_19660,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19188,c_19395,c_19198,c_19188,c_19070]) ).
tff(c_19039,plain,
inverse(sk_c2) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_19020,c_73]) ).
tff(c_19058,plain,
multiply(sk_c5,sk_c2) = identity,
inference(superposition,[status(thm),theory(equality)],[c_19039,c_4]) ).
tff(c_19220,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19198,c_19058]) ).
tff(c_19208,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19198,c_19039]) ).
tff(c_19226,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19220,c_19208]) ).
tff(c_19662,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19660,c_19226]) ).
tff(c_19663,plain,
! [X4_7] :
( ( inverse(X4_7) != sk_c5 )
| ( multiply(X4_7,sk_c5) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_19069]) ).
tff(c_20160,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_19902,c_19751,c_19734,c_19751,c_19663]) ).
tff(c_19766,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19751,c_19058]) ).
tff(c_19759,plain,
inverse(sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19751,c_19039]) ).
tff(c_19781,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_19766,c_19759]) ).
tff(c_20162,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20160,c_19781]) ).
tff(c_20164,plain,
inverse(sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_48,plain,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_20214,plain,
multiply(sk_c4,sk_c5) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_20164,c_48]) ).
tff(c_20163,plain,
inverse(sk_c4) = sk_c6,
inference(splitRight,[status(thm)],[c_46]) ).
tff(c_20168,plain,
multiply(sk_c6,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20163,c_4]) ).
tff(c_20252,plain,
! [Z_262] : ( multiply(sk_c6,multiply(sk_c4,Z_262)) = multiply(identity,Z_262) ),
inference(superposition,[status(thm),theory(equality)],[c_20168,c_20225]) ).
tff(c_20367,plain,
! [Z_266] : ( multiply(sk_c6,multiply(sk_c4,Z_266)) = Z_266 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20252]) ).
tff(c_20379,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_20214,c_20367]) ).
tff(c_20446,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_20379,c_20425]) ).
tff(c_20494,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_16,c_20425]) ).
tff(c_20784,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20446,c_20494]) ).
tff(c_44,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_20191,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20164,c_44]) ).
tff(c_42,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_20172,plain,
inverse(sk_c3) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_20164,c_42]) ).
tff(c_20176,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_20172,c_4]) ).
tff(c_20249,plain,
! [Z_262] : ( multiply(sk_c7,multiply(sk_c3,Z_262)) = multiply(identity,Z_262) ),
inference(superposition,[status(thm),theory(equality)],[c_20176,c_20225]) ).
tff(c_20271,plain,
! [Z_263] : ( multiply(sk_c7,multiply(sk_c3,Z_263)) = Z_263 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20249]) ).
tff(c_20283,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_20191,c_20271]) ).
tff(c_20455,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_20283,c_20425]) ).
tff(c_20795,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20784,c_20784,c_20455]) ).
tff(c_20805,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20795]) ).
tff(c_20814,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20805,c_20784]) ).
tff(c_20980,plain,
! [X_277,Z_278] : ( multiply(inverse(inverse(X_277)),Z_278) = multiply(X_277,Z_278) ),
inference(superposition,[status(thm),theory(equality)],[c_20269,c_20425]) ).
tff(c_20991,plain,
! [X_277] : ( multiply(X_277,identity) = X_277 ),
inference(superposition,[status(thm),theory(equality)],[c_20980,c_20488]) ).
tff(c_20630,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20446,c_20494]) ).
tff(c_20665,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20630,c_20630,c_20455]) ).
tff(c_20675,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20665]) ).
tff(c_20479,plain,
multiply(inverse(sk_c6),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_20168,c_20425]) ).
tff(c_20686,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_20675,c_20479]) ).
tff(c_20693,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_20686]) ).
tff(c_20692,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20675,c_20163]) ).
tff(c_20737,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20693,c_20692]) ).
tff(c_20684,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20675,c_20630]) ).
tff(c_20294,plain,
multiply(sk_c7,sk_c6) != sk_c5,
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_20318,plain,
! [Z_265] : ( multiply(sk_c3,multiply(sk_c6,Z_265)) = multiply(sk_c7,Z_265) ),
inference(superposition,[status(thm),theory(equality)],[c_20191,c_20225]) ).
tff(c_20342,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_16,c_20318]) ).
tff(c_20346,plain,
multiply(sk_c3,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_20283,c_20342]) ).
tff(c_20267,plain,
! [Z_262] : ( multiply(sk_c7,multiply(sk_c3,Z_262)) = Z_262 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_20249]) ).
tff(c_20350,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_20346,c_20267]) ).
tff(c_20357,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20294,c_20350]) ).
tff(c_20358,plain,
! [X3_6,X4_7,X1_8,X2_9] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( inverse(X2_9) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_20404,plain,
! [X2_268] :
( ( multiply(X2_268,sk_c5) != sk_c6 )
| ( inverse(X2_268) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_20358]) ).
tff(c_20411,plain,
inverse(sk_c4) != sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_20214,c_20404]) ).
tff(c_20423,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20163,c_20411]) ).
tff(c_20424,plain,
! [X1_8,X4_7,X3_6] :
( ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_20358]) ).
tff(c_20604,plain,
! [X3_6] :
( ( inverse(X3_6) != sk_c7 )
| ( multiply(X3_6,sk_c7) != sk_c6 ) ),
inference(splitLeft,[status(thm)],[c_20424]) ).
tff(c_20713,plain,
! [X3_273] :
( ( inverse(X3_273) != identity )
| ( multiply(X3_273,identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_20684,c_20675,c_20684,c_20604]) ).
tff(c_20735,plain,
inverse(identity) != identity,
inference(superposition,[status(thm),theory(equality)],[c_2,c_20713]) ).
tff(c_20757,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20737,c_20735]) ).
tff(c_20758,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != sk_c6 )
| ( multiply(X4_7,sk_c6) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_20424]) ).
tff(c_20829,plain,
! [X4_7,X1_8] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 )
| ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_20805,c_20805,c_20805,c_20758]) ).
tff(c_20830,plain,
! [X1_8] :
( ( multiply(X1_8,identity) != sk_c7 )
| ( inverse(X1_8) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_20829]) ).
tff(c_21262,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_20814,c_20991,c_20814,c_20830]) ).
tff(c_20491,plain,
! [X_1] : ( multiply(inverse(identity),X_1) = X_1 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_20425]) ).
tff(c_20816,plain,
multiply(inverse(identity),identity) = sk_c4,
inference(demodulation,[status(thm),theory(equality)],[c_20805,c_20479]) ).
tff(c_20823,plain,
sk_c4 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20491,c_20816]) ).
tff(c_20822,plain,
inverse(sk_c4) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20805,c_20163]) ).
tff(c_20861,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20823,c_20822]) ).
tff(c_21264,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21262,c_20861]) ).
tff(c_21265,plain,
! [X4_7] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_20829]) ).
tff(c_21765,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_21388,c_20814,c_21265]) ).
tff(c_21315,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20823,c_20822]) ).
tff(c_21767,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21765,c_21315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP303-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:37:37 EDT 2023
% 0.15/0.35 % CPUTime :
% 9.57/3.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.40/3.70
% 10.40/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.77/3.77
% 10.77/3.77 Inference rules
% 10.77/3.77 ----------------------
% 10.77/3.77 #Ref : 0
% 10.77/3.77 #Sup : 5409
% 10.77/3.77 #Fact : 0
% 10.77/3.77 #Define : 0
% 10.77/3.77 #Split : 33
% 10.77/3.77 #Chain : 0
% 10.77/3.77 #Close : 0
% 10.77/3.77
% 10.77/3.77 Ordering : KBO
% 10.77/3.77
% 10.77/3.77 Simplification rules
% 10.77/3.77 ----------------------
% 10.77/3.77 #Subsume : 6
% 10.77/3.77 #Demod : 12429
% 10.77/3.77 #Tautology : 4318
% 10.77/3.77 #SimpNegUnit : 44
% 10.77/3.77 #BackRed : 464
% 10.77/3.77
% 10.77/3.77 #Partial instantiations: 0
% 10.77/3.77 #Strategies tried : 1
% 10.77/3.77
% 10.77/3.77 Timing (in seconds)
% 10.77/3.77 ----------------------
% 10.77/3.77 Preprocessing : 0.44
% 10.77/3.77 Parsing : 0.19
% 10.77/3.77 CNF conversion : 0.02
% 10.77/3.77 Main loop : 2.22
% 10.77/3.77 Inferencing : 0.66
% 10.77/3.77 Reduction : 1.12
% 10.77/3.77 Demodulation : 1.00
% 10.77/3.78 BG Simplification : 0.07
% 10.77/3.78 Subsumption : 0.24
% 10.77/3.78 Abstraction : 0.11
% 10.77/3.78 MUC search : 0.00
% 10.77/3.78 Cooper : 0.00
% 10.77/3.78 Total : 2.78
% 10.77/3.78 Index Insertion : 0.00
% 10.77/3.78 Index Deletion : 0.00
% 10.77/3.78 Index Matching : 0.00
% 10.77/3.78 BG Taut test : 0.00
%------------------------------------------------------------------------------