TSTP Solution File: GRP361-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP361-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:41:03 EDT 2023
% Result : Unsatisfiable 11.42s 3.93s
% Output : CNFRefutation 11.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 37
% Syntax : Number of formulae : 336 ( 253 unt; 10 typ; 0 def)
% Number of atoms : 467 ( 447 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 275 ( 134 ~; 141 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 137 (; 137 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c7 > sk_c6 > sk_c5 > sk_c4 > sk_c3 > sk_c2 > sk_c1 > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sk_c4,type,
sk_c4: $i ).
tff(sk_c7,type,
sk_c7: $i ).
tff(sk_c5,type,
sk_c5: $i ).
tff(sk_c2,type,
sk_c2: $i ).
tff(sk_c3,type,
sk_c3: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c6,type,
sk_c6: $i ).
tff(sk_c1,type,
sk_c1: $i ).
tff(identity,type,
identity: $i ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_125,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_152,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [X3,X4,X1,X2] :
( ( multiply(sk_c6,sk_c5) != sk_c7 )
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c7,X3) != sk_c6 )
| ( multiply(X4,sk_c7) != X3 )
| ( inverse(X4) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( inverse(X1) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c5) != sk_c7 )
| ( inverse(X2) != sk_c5 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_134,axiom,
( ( multiply(sk_c1,sk_c7) = sk_c2 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_65,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c6,sk_c5) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c7,sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_95,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( inverse(sk_c4) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_86,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( inverse(sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
file(unknown,unknown) ).
tff(f_149,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_17504,plain,
! [X_232,Y_233,Z_234] : ( multiply(multiply(X_232,Y_233),Z_234) = multiply(X_232,multiply(Y_233,Z_234)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17534,plain,
! [X_2,Z_234] : ( multiply(inverse(X_2),multiply(X_2,Z_234)) = multiply(identity,Z_234) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17504]) ).
tff(c_17546,plain,
! [X_2,Z_234] : ( multiply(inverse(X_2),multiply(X_2,Z_234)) = Z_234 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17534]) ).
tff(c_17646,plain,
! [X_236,Z_237] : ( multiply(inverse(X_236),multiply(X_236,Z_237)) = Z_237 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17534]) ).
tff(c_17784,plain,
! [X_240,Z_241] : ( multiply(inverse(inverse(X_240)),Z_241) = multiply(X_240,Z_241) ),
inference(superposition,[status(thm),theory(equality)],[c_17546,c_17646]) ).
tff(c_17673,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17646]) ).
tff(c_17795,plain,
! [X_240] : ( multiply(X_240,identity) = X_240 ),
inference(superposition,[status(thm),theory(equality)],[c_17784,c_17673]) ).
tff(c_9981,plain,
! [X_136,Y_137,Z_138] : ( multiply(multiply(X_136,Y_137),Z_138) = multiply(X_136,multiply(Y_137,Z_138)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10014,plain,
! [X_2,Z_138] : ( multiply(inverse(X_2),multiply(X_2,Z_138)) = multiply(identity,Z_138) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9981]) ).
tff(c_10128,plain,
! [X_140,Z_141] : ( multiply(inverse(X_140),multiply(X_140,Z_141)) = Z_141 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10014]) ).
tff(c_10027,plain,
! [X_2,Z_138] : ( multiply(inverse(X_2),multiply(X_2,Z_138)) = Z_138 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10014]) ).
tff(c_10296,plain,
! [X_144,Z_145] : ( multiply(inverse(inverse(X_144)),Z_145) = multiply(X_144,Z_145) ),
inference(superposition,[status(thm),theory(equality)],[c_10128,c_10027]) ).
tff(c_10155,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_10128]) ).
tff(c_10307,plain,
! [X_144] : ( multiply(X_144,identity) = X_144 ),
inference(superposition,[status(thm),theory(equality)],[c_10296,c_10155]) ).
tff(c_149,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_179,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_149]) ).
tff(c_189,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_179]) ).
tff(c_307,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_179]) ).
tff(c_510,plain,
! [X_20,Z_21] : ( multiply(inverse(inverse(X_20)),Z_21) = multiply(X_20,Z_21) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_307]) ).
tff(c_337,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_307]) ).
tff(c_517,plain,
! [X_20] : ( multiply(X_20,identity) = X_20 ),
inference(superposition,[status(thm),theory(equality)],[c_510,c_337]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_111,plain,
multiply(sk_c7,sk_c2) = sk_c6,
inference(splitLeft,[status(thm)],[c_42]) ).
tff(c_48,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_128,plain,
multiply(sk_c1,sk_c7) = sk_c2,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_66,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_85,plain,
inverse(sk_c1) = sk_c7,
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_89,plain,
multiply(sk_c7,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_85,c_4]) ).
tff(c_176,plain,
! [Z_14] : ( multiply(sk_c7,multiply(sk_c1,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_149]) ).
tff(c_225,plain,
! [Z_16] : ( multiply(sk_c7,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_176]) ).
tff(c_240,plain,
multiply(sk_c7,sk_c2) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_128,c_225]) ).
tff(c_244,plain,
sk_c7 = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_111,c_240]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_98,plain,
inverse(sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_102,plain,
multiply(sk_c5,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_98,c_4]) ).
tff(c_173,plain,
! [Z_14] : ( multiply(sk_c5,multiply(sk_c7,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_102,c_149]) ).
tff(c_191,plain,
! [Z_15] : ( multiply(sk_c5,multiply(sk_c7,Z_15)) = Z_15 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_173]) ).
tff(c_203,plain,
multiply(sk_c5,sk_c6) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_111,c_191]) ).
tff(c_68,plain,
! [X2_9,X1_8,X4_7] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c7 )
| ( multiply(X1_8,sk_c6) != sk_c7 )
| ( inverse(X1_8) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( inverse(X4_7) != sk_c7 )
| ( multiply(sk_c7,multiply(X4_7,sk_c7)) != sk_c6 )
| ( inverse(sk_c7) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_258,plain,
! [X2_9,X1_8,X4_7] :
( ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( sk_c6 != sk_c2 )
| ( multiply(sk_c6,sk_c6) != sk_c5 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(sk_c6,multiply(X4_7,sk_c6)) != sk_c6 )
| ( inverse(sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_244,c_244,c_244,c_244,c_244,c_203,c_244,c_244,c_244,c_244,c_68]) ).
tff(c_259,plain,
multiply(sk_c6,sk_c5) != sk_c6,
inference(splitLeft,[status(thm)],[c_258]) ).
tff(c_18,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_117,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_248,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_117]) ).
tff(c_297,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_259,c_248]) ).
tff(c_299,plain,
multiply(sk_c6,sk_c5) = sk_c6,
inference(splitRight,[status(thm)],[c_258]) ).
tff(c_399,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_299,c_189]) ).
tff(c_405,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_399]) ).
tff(c_250,plain,
multiply(sk_c5,sk_c6) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_102]) ).
tff(c_443,plain,
sk_c6 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_405,c_250]) ).
tff(c_249,plain,
multiply(sk_c6,sk_c2) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_111]) ).
tff(c_368,plain,
multiply(inverse(sk_c6),sk_c6) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_249,c_189]) ).
tff(c_374,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_368]) ).
tff(c_206,plain,
multiply(sk_c5,identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_89,c_191]) ).
tff(c_409,plain,
multiply(identity,identity) = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_206]) ).
tff(c_410,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_409]) ).
tff(c_253,plain,
inverse(sk_c1) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_244,c_85]) ).
tff(c_416,plain,
inverse(identity) = sk_c6,
inference(demodulation,[status(thm),theory(equality)],[c_410,c_253]) ).
tff(c_445,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_443,c_416]) ).
tff(c_298,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(sk_c6) != sk_c5 )
| ( multiply(sk_c6,sk_c6) != sk_c5 )
| ( sk_c6 != sk_c2 )
| ( inverse(X4_7) != sk_c6 )
| ( multiply(sk_c6,multiply(X4_7,sk_c6)) != sk_c6 )
| ( multiply(X1_8,sk_c6) != sk_c6 )
| ( inverse(X1_8) != sk_c6 )
| ( inverse(X2_9) != sk_c5 )
| ( multiply(X2_9,sk_c5) != sk_c6 ) ),
inference(splitRight,[status(thm)],[c_258]) ).
tff(c_8377,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_517,c_443,c_405,c_405,c_443,c_517,c_443,c_443,c_517,c_443,c_443,c_2,c_443,c_443,c_443,c_374,c_443,c_2,c_443,c_405,c_445,c_443,c_405,c_298]) ).
tff(c_8379,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8377]) ).
tff(c_8381,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8379,c_445]) ).
tff(c_8382,plain,
! [X1_8,X4_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 ) ),
inference(splitRight,[status(thm)],[c_8377]) ).
tff(c_8384,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_8382]) ).
tff(c_8386,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8384,c_445]) ).
tff(c_8389,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_8382]) ).
tff(c_8391,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8389,c_445]) ).
tff(c_8393,plain,
multiply(sk_c1,sk_c7) != sk_c2,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_46,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_8433,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_46]) ).
tff(c_8434,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_8393,c_8433]) ).
tff(c_44,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_8442,plain,
( ( sk_c7 = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8434,c_44]) ).
tff(c_8443,plain,
sk_c7 = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_8393,c_8442]) ).
tff(c_8448,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8443,c_102]) ).
tff(c_52,plain,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_8428,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_8393,c_52]) ).
tff(c_8444,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8443,c_8428]) ).
tff(c_54,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_8405,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_8393,c_54]) ).
tff(c_8409,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8405,c_4]) ).
tff(c_8568,plain,
! [X_112,Y_113,Z_114] : ( multiply(multiply(X_112,Y_113),Z_114) = multiply(X_112,multiply(Y_113,Z_114)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8592,plain,
! [Z_114] : ( multiply(sk_c5,multiply(sk_c4,Z_114)) = multiply(identity,Z_114) ),
inference(superposition,[status(thm),theory(equality)],[c_8409,c_8568]) ).
tff(c_8827,plain,
! [Z_118] : ( multiply(sk_c5,multiply(sk_c4,Z_118)) = Z_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8592]) ).
tff(c_8839,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_8444,c_8827]) ).
tff(c_8843,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8448,c_8839]) ).
tff(c_8451,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_8443,c_85]) ).
tff(c_8852,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8843,c_8451]) ).
tff(c_8948,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8852,c_4]) ).
tff(c_8595,plain,
! [X_2,Z_114] : ( multiply(inverse(X_2),multiply(X_2,Z_114)) = multiply(identity,Z_114) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_8568]) ).
tff(c_8606,plain,
! [X_2,Z_114] : ( multiply(inverse(X_2),multiply(X_2,Z_114)) = Z_114 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8595]) ).
tff(c_8983,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_8948,c_8606]) ).
tff(c_8995,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8983]) ).
tff(c_8446,plain,
multiply(sk_c1,sk_c5) != sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8443,c_8393]) ).
tff(c_8847,plain,
multiply(sk_c1,identity) != sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_8843,c_8446]) ).
tff(c_9039,plain,
sk_c2 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_8995,c_8847]) ).
tff(c_8436,plain,
multiply(sk_c7,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8434,c_111]) ).
tff(c_8478,plain,
multiply(sk_c5,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8443,c_8436]) ).
tff(c_8851,plain,
multiply(identity,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_8843,c_8478]) ).
tff(c_9045,plain,
multiply(inverse(identity),identity) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_8851,c_8606]) ).
tff(c_9057,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9045]) ).
tff(c_9059,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9039,c_9057]) ).
tff(c_9061,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_10,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_9095,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_10]) ).
tff(c_9096,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_9061,c_9095]) ).
tff(c_9097,plain,
multiply(identity,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9096,c_9061]) ).
tff(c_9099,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9097]) ).
tff(c_8,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_9133,plain,
( ( sk_c7 = sk_c5 )
| ( sk_c7 = sk_c5 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9096,c_2,c_9096,c_8]) ).
tff(c_9134,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9099,c_9099,c_9133]) ).
tff(c_9136,plain,
multiply(sk_c7,sk_c2) != sk_c6,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_34,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_9203,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_34]) ).
tff(c_9204,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_9136,c_9203]) ).
tff(c_12,plain,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_9150,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_9207,plain,
multiply(identity,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9204,c_9150]) ).
tff(c_9209,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9207]) ).
tff(c_9218,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_102]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_9198,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_9136,c_40]) ).
tff(c_9214,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_9198]) ).
tff(c_9135,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_42]) ).
tff(c_9140,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9135,c_4]) ).
tff(c_9260,plain,
! [X_121,Y_122,Z_123] : ( multiply(multiply(X_121,Y_122),Z_123) = multiply(X_121,multiply(Y_122,Z_123)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_9281,plain,
! [Z_123] : ( multiply(sk_c5,multiply(sk_c4,Z_123)) = multiply(identity,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_9140,c_9260]) ).
tff(c_9576,plain,
! [Z_130] : ( multiply(sk_c5,multiply(sk_c4,Z_130)) = Z_130 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9281]) ).
tff(c_9591,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9214,c_9576]) ).
tff(c_9595,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9218,c_9591]) ).
tff(c_9208,plain,
multiply(sk_c7,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9204,c_9136]) ).
tff(c_9247,plain,
multiply(sk_c5,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_9208]) ).
tff(c_9604,plain,
multiply(identity,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9595,c_9247]) ).
tff(c_9613,plain,
sk_c2 != identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9604]) ).
tff(c_9221,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_85]) ).
tff(c_9605,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9595,c_9221]) ).
tff(c_9625,plain,
multiply(identity,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_9605,c_4]) ).
tff(c_9284,plain,
! [X_2,Z_123] : ( multiply(inverse(X_2),multiply(X_2,Z_123)) = multiply(identity,Z_123) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_9260]) ).
tff(c_9294,plain,
! [X_2,Z_123] : ( multiply(inverse(X_2),multiply(X_2,Z_123)) = Z_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9284]) ).
tff(c_9695,plain,
multiply(inverse(identity),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_9625,c_9294]) ).
tff(c_9707,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_9695]) ).
tff(c_9248,plain,
( ( multiply(sk_c4,sk_c5) = sk_c5 )
| ( multiply(sk_c1,sk_c5) = sk_c2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_9209,c_52]) ).
tff(c_9249,plain,
multiply(sk_c1,sk_c5) = sk_c2,
inference(splitLeft,[status(thm)],[c_9248]) ).
tff(c_9603,plain,
multiply(sk_c1,identity) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_9595,c_9249]) ).
tff(c_9796,plain,
sk_c2 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9707,c_9603]) ).
tff(c_9797,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9613,c_9796]) ).
tff(c_9799,plain,
multiply(sk_c1,sk_c5) != sk_c2,
inference(splitRight,[status(thm)],[c_9248]) ).
tff(c_9185,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c1,sk_c7) = sk_c2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_46]) ).
tff(c_9186,plain,
multiply(sk_c1,sk_c7) = sk_c2,
inference(splitLeft,[status(thm)],[c_9185]) ).
tff(c_9215,plain,
multiply(sk_c1,sk_c5) = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_9209,c_9186]) ).
tff(c_9874,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9799,c_9215]) ).
tff(c_9875,plain,
sk_c6 = identity,
inference(splitRight,[status(thm)],[c_9185]) ).
tff(c_9884,plain,
multiply(identity,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_9875,c_9150]) ).
tff(c_9886,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9884]) ).
tff(c_9922,plain,
( ( multiply(sk_c4,sk_c5) = sk_c5 )
| ( multiply(sk_c5,sk_c2) = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9886,c_9875,c_9886,c_40]) ).
tff(c_9923,plain,
multiply(sk_c5,sk_c2) = identity,
inference(splitLeft,[status(thm)],[c_9922]) ).
tff(c_9885,plain,
multiply(sk_c7,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_9875,c_9136]) ).
tff(c_9942,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9923,c_9886,c_9885]) ).
tff(c_9944,plain,
multiply(sk_c5,sk_c2) != identity,
inference(splitRight,[status(thm)],[c_9922]) ).
tff(c_9954,plain,
( ( multiply(sk_c5,sk_c5) = identity )
| ( multiply(sk_c5,sk_c2) = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9875,c_9886,c_9875,c_9886,c_34]) ).
tff(c_9955,plain,
multiply(sk_c5,sk_c5) = identity,
inference(negUnitSimplification,[status(thm)],[c_9944,c_9954]) ).
tff(c_9943,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(splitRight,[status(thm)],[c_9922]) ).
tff(c_10011,plain,
! [Z_138] : ( multiply(sk_c5,multiply(sk_c4,Z_138)) = multiply(identity,Z_138) ),
inference(superposition,[status(thm),theory(equality)],[c_9140,c_9981]) ).
tff(c_10029,plain,
! [Z_139] : ( multiply(sk_c5,multiply(sk_c4,Z_139)) = Z_139 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_10011]) ).
tff(c_10041,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_9943,c_10029]) ).
tff(c_10045,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_9955,c_10041]) ).
tff(c_10057,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10045,c_9886]) ).
tff(c_10078,plain,
! [X2_9,X1_8,X4_7] :
( ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10057,c_10045,c_2,c_9875,c_10057,c_10045,c_10057,c_2,c_10057,c_9875,c_10057,c_10057,c_10045,c_2,c_9875,c_10057,c_2,c_10045,c_9875,c_10057,c_10057,c_9875,c_10057,c_10045,c_10045,c_68]) ).
tff(c_10079,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_10078]) ).
tff(c_9894,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_9886,c_98]) ).
tff(c_10054,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_10045,c_10045,c_9894]) ).
tff(c_10087,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10079,c_10054]) ).
tff(c_10088,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_10078]) ).
tff(c_16974,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10307,c_10307,c_10307,c_10088]) ).
tff(c_16976,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16974]) ).
tff(c_16978,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16976,c_10054]) ).
tff(c_16979,plain,
! [X1_8,X4_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 ) ),
inference(splitRight,[status(thm)],[c_16974]) ).
tff(c_16981,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_16979]) ).
tff(c_16983,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16981,c_10054]) ).
tff(c_16986,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_16979]) ).
tff(c_16988,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16986,c_10054]) ).
tff(c_16990,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_17018,plain,
( ( sk_c6 = identity )
| ( multiply(sk_c6,sk_c5) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_10]) ).
tff(c_17019,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_16990,c_17018]) ).
tff(c_17022,plain,
multiply(sk_c7,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17019,c_9136]) ).
tff(c_17021,plain,
multiply(identity,sk_c5) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17019,c_16990]) ).
tff(c_17023,plain,
sk_c7 != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17021]) ).
tff(c_32,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c2) = sk_c6 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_17034,plain,
( ( sk_c7 = sk_c5 )
| ( multiply(sk_c7,sk_c2) = identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17019,c_2,c_17019,c_32]) ).
tff(c_17035,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17022,c_17023,c_17034]) ).
tff(c_17037,plain,
inverse(sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_28,plain,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_17082,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17037,c_28]) ).
tff(c_30,plain,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_17049,plain,
inverse(sk_c4) = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_17037,c_30]) ).
tff(c_17053,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17049,c_4]) ).
tff(c_17103,plain,
! [X_224,Y_225,Z_226] : ( multiply(multiply(X_224,Y_225),Z_226) = multiply(X_224,multiply(Y_225,Z_226)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_17130,plain,
! [Z_226] : ( multiply(sk_c5,multiply(sk_c4,Z_226)) = multiply(identity,Z_226) ),
inference(superposition,[status(thm),theory(equality)],[c_17053,c_17103]) ).
tff(c_17152,plain,
! [Z_227] : ( multiply(sk_c5,multiply(sk_c4,Z_227)) = Z_227 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17130]) ).
tff(c_17164,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17082,c_17152]) ).
tff(c_22,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_17067,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_17037,c_22]) ).
tff(c_17168,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17164,c_17067]) ).
tff(c_26,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c7) = sk_c5 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_17077,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17037,c_26]) ).
tff(c_17178,plain,
multiply(sk_c3,sk_c5) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17168,c_17077]) ).
tff(c_17036,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_17041,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17036,c_4]) ).
tff(c_17133,plain,
! [Z_226] : ( multiply(sk_c7,multiply(sk_c3,Z_226)) = multiply(identity,Z_226) ),
inference(superposition,[status(thm),theory(equality)],[c_17041,c_17103]) ).
tff(c_17192,plain,
! [Z_228] : ( multiply(sk_c7,multiply(sk_c3,Z_228)) = Z_228 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17133]) ).
tff(c_17204,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17178,c_17192]) ).
tff(c_17121,plain,
! [Z_226] : ( multiply(sk_c3,multiply(sk_c6,Z_226)) = multiply(sk_c7,Z_226) ),
inference(superposition,[status(thm),theory(equality)],[c_17077,c_17103]) ).
tff(c_17209,plain,
! [Z_229] : ( multiply(sk_c3,multiply(sk_c5,Z_229)) = multiply(sk_c7,Z_229) ),
inference(demodulation,[status(thm),theory(equality)],[c_17168,c_17121]) ).
tff(c_17224,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_17164,c_17209]) ).
tff(c_17234,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_17178,c_17224]) ).
tff(c_17242,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17204,c_17234]) ).
tff(c_17243,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17242,c_17242,c_17204]) ).
tff(c_17139,plain,
! [X_2,Z_226] : ( multiply(inverse(X_2),multiply(X_2,Z_226)) = multiply(identity,Z_226) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_17103]) ).
tff(c_17150,plain,
! [X_2,Z_226] : ( multiply(inverse(X_2),multiply(X_2,Z_226)) = Z_226 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17139]) ).
tff(c_17330,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17243,c_17150]) ).
tff(c_17336,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_17330]) ).
tff(c_17250,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17242,c_17037]) ).
tff(c_17342,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_17336,c_17336,c_17250]) ).
tff(c_17253,plain,
inverse(sk_c1) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17242,c_85]) ).
tff(c_17268,plain,
multiply(sk_c5,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17253,c_4]) ).
tff(c_17353,plain,
sk_c1 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17336,c_17268]) ).
tff(c_17340,plain,
inverse(sk_c1) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17336,c_17253]) ).
tff(c_17376,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17353,c_17340]) ).
tff(c_17377,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17342,c_17376]) ).
tff(c_17379,plain,
inverse(sk_c1) != sk_c7,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_17391,plain,
inverse(sk_c7) = sk_c5,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_17396,plain,
multiply(sk_c5,sk_c7) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17391,c_4]) ).
tff(c_58,plain,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_17422,plain,
( ( sk_c6 = identity )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17396,c_58]) ).
tff(c_17423,plain,
sk_c6 = identity,
inference(negUnitSimplification,[status(thm)],[c_17379,c_17422]) ).
tff(c_56,plain,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_17447,plain,
( ( sk_c7 = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17423,c_56]) ).
tff(c_17448,plain,
sk_c7 = sk_c5,
inference(negUnitSimplification,[status(thm)],[c_17379,c_17447]) ).
tff(c_17453,plain,
multiply(sk_c5,sk_c5) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17448,c_17396]) ).
tff(c_64,plain,
( ( multiply(sk_c4,sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_17440,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17379,c_64]) ).
tff(c_17449,plain,
multiply(sk_c4,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17448,c_17440]) ).
tff(c_17378,plain,
inverse(sk_c4) = sk_c5,
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_17383,plain,
multiply(sk_c5,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_17378,c_4]) ).
tff(c_17531,plain,
! [Z_234] : ( multiply(sk_c5,multiply(sk_c4,Z_234)) = multiply(identity,Z_234) ),
inference(superposition,[status(thm),theory(equality)],[c_17383,c_17504]) ).
tff(c_17548,plain,
! [Z_235] : ( multiply(sk_c5,multiply(sk_c4,Z_235)) = Z_235 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_17531]) ).
tff(c_17560,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_17449,c_17548]) ).
tff(c_17564,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17453,c_17560]) ).
tff(c_17454,plain,
inverse(sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_17448,c_17391]) ).
tff(c_17571,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17564,c_17564,c_17454]) ).
tff(c_17573,plain,
sk_c7 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_17564,c_17448]) ).
tff(c_17593,plain,
! [X2_9,X1_8,X4_7] :
( ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( inverse(identity) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17573,c_17564,c_2,c_17423,c_17573,c_17564,c_17573,c_2,c_17573,c_17423,c_17573,c_17573,c_17564,c_2,c_17423,c_17573,c_2,c_17564,c_17423,c_17573,c_17573,c_17423,c_17573,c_17564,c_17564,c_68]) ).
tff(c_17594,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_17593]) ).
tff(c_17604,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_17571,c_17594]) ).
tff(c_17605,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( multiply(X4_7,identity) != identity )
| ( multiply(X1_8,identity) != identity )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( multiply(X2_9,identity) != identity ) ),
inference(splitRight,[status(thm)],[c_17593]) ).
tff(c_24462,plain,
! [X4_7,X1_8,X2_9] :
( ( inverse(X4_7) != identity )
| ( identity != X4_7 )
| ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X2_9) != identity )
| ( identity != X2_9 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_17795,c_17795,c_17795,c_17605]) ).
tff(c_24464,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_24462]) ).
tff(c_24466,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24464,c_17571]) ).
tff(c_24467,plain,
! [X1_8,X4_7] :
( ( identity != X1_8 )
| ( inverse(X1_8) != identity )
| ( inverse(X4_7) != identity )
| ( identity != X4_7 ) ),
inference(splitRight,[status(thm)],[c_24462]) ).
tff(c_24469,plain,
inverse(identity) != identity,
inference(splitLeft,[status(thm)],[c_24467]) ).
tff(c_24471,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24469,c_17571]) ).
tff(c_24474,plain,
inverse(identity) != identity,
inference(splitRight,[status(thm)],[c_24467]) ).
tff(c_24476,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24474,c_17571]) ).
tff(c_24478,plain,
inverse(sk_c7) != sk_c5,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_24508,plain,
multiply(sk_c4,sk_c5) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_24478,c_28]) ).
tff(c_24540,plain,
! [X_320,Y_321,Z_322] : ( multiply(multiply(X_320,Y_321),Z_322) = multiply(X_320,multiply(Y_321,Z_322)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_24570,plain,
! [Z_322] : ( multiply(sk_c5,multiply(sk_c4,Z_322)) = multiply(identity,Z_322) ),
inference(superposition,[status(thm),theory(equality)],[c_17383,c_24540]) ).
tff(c_24610,plain,
! [Z_324] : ( multiply(sk_c5,multiply(sk_c4,Z_324)) = Z_324 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24570]) ).
tff(c_24622,plain,
multiply(sk_c5,sk_c7) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_24508,c_24610]) ).
tff(c_24513,plain,
multiply(sk_c5,sk_c7) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_24478,c_22]) ).
tff(c_24626,plain,
sk_c6 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24622,c_24513]) ).
tff(c_62,plain,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_24497,plain,
multiply(sk_c3,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_17379,c_62]) ).
tff(c_24477,plain,
inverse(sk_c3) = sk_c7,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_24482,plain,
multiply(sk_c7,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_24477,c_4]) ).
tff(c_24567,plain,
! [Z_322] : ( multiply(sk_c7,multiply(sk_c3,Z_322)) = multiply(identity,Z_322) ),
inference(superposition,[status(thm),theory(equality)],[c_24482,c_24540]) ).
tff(c_24585,plain,
! [Z_323] : ( multiply(sk_c7,multiply(sk_c3,Z_323)) = Z_323 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24567]) ).
tff(c_24597,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(superposition,[status(thm),theory(equality)],[c_24497,c_24585]) ).
tff(c_24634,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24626,c_24597]) ).
tff(c_24642,plain,
! [Z_325] : ( multiply(sk_c4,multiply(sk_c5,Z_325)) = multiply(sk_c7,Z_325) ),
inference(superposition,[status(thm),theory(equality)],[c_24508,c_24540]) ).
tff(c_24657,plain,
multiply(sk_c7,sk_c7) = multiply(sk_c4,sk_c5),
inference(superposition,[status(thm),theory(equality)],[c_24622,c_24642]) ).
tff(c_24667,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_24508,c_24657]) ).
tff(c_24686,plain,
sk_c7 = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24634,c_24667]) ).
tff(c_24688,plain,
multiply(sk_c5,sk_c5) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24686,c_24686,c_24634]) ).
tff(c_24573,plain,
! [X_2,Z_322] : ( multiply(inverse(X_2),multiply(X_2,Z_322)) = multiply(identity,Z_322) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_24540]) ).
tff(c_24583,plain,
! [X_2,Z_322] : ( multiply(inverse(X_2),multiply(X_2,Z_322)) = Z_322 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24573]) ).
tff(c_24752,plain,
multiply(inverse(sk_c5),sk_c5) = sk_c5,
inference(superposition,[status(thm),theory(equality)],[c_24688,c_24583]) ).
tff(c_24758,plain,
sk_c5 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_24752]) ).
tff(c_24694,plain,
inverse(sk_c5) != sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24686,c_24478]) ).
tff(c_24763,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_24758,c_24758,c_24694]) ).
tff(c_24695,plain,
inverse(sk_c3) = sk_c5,
inference(demodulation,[status(thm),theory(equality)],[c_24686,c_24477]) ).
tff(c_24704,plain,
multiply(sk_c5,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_24695,c_4]) ).
tff(c_24774,plain,
sk_c3 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24758,c_24704]) ).
tff(c_24762,plain,
inverse(sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24758,c_24695]) ).
tff(c_24797,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_24774,c_24762]) ).
tff(c_24798,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24763,c_24797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP361-1 : TPTP v8.1.2. Released v2.5.0.
% 0.14/0.14 % 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
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 22:12:59 EDT 2023
% 0.14/0.36 % CPUTime :
% 11.42/3.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.61/3.97
% 11.61/3.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.81/4.02
% 11.81/4.02 Inference rules
% 11.81/4.02 ----------------------
% 11.81/4.02 #Ref : 0
% 11.81/4.02 #Sup : 6125
% 11.81/4.02 #Fact : 0
% 11.81/4.02 #Define : 0
% 11.81/4.02 #Split : 25
% 11.81/4.02 #Chain : 0
% 11.81/4.02 #Close : 0
% 11.81/4.02
% 11.81/4.02 Ordering : KBO
% 11.81/4.02
% 11.81/4.02 Simplification rules
% 11.81/4.02 ----------------------
% 11.81/4.02 #Subsume : 6
% 11.81/4.02 #Demod : 14116
% 11.81/4.02 #Tautology : 4954
% 11.81/4.02 #SimpNegUnit : 63
% 11.81/4.02 #BackRed : 254
% 11.81/4.02
% 11.81/4.02 #Partial instantiations: 0
% 11.81/4.02 #Strategies tried : 1
% 11.81/4.02
% 11.81/4.02 Timing (in seconds)
% 11.81/4.02 ----------------------
% 11.81/4.03 Preprocessing : 0.56
% 11.81/4.03 Parsing : 0.21
% 11.81/4.03 CNF conversion : 0.03
% 11.81/4.03 Main loop : 2.26
% 11.81/4.03 Inferencing : 0.70
% 11.81/4.03 Reduction : 1.05
% 11.81/4.03 Demodulation : 0.91
% 11.81/4.03 BG Simplification : 0.08
% 11.81/4.03 Subsumption : 0.28
% 11.81/4.03 Abstraction : 0.14
% 11.81/4.03 MUC search : 0.00
% 11.81/4.03 Cooper : 0.00
% 11.81/4.03 Total : 2.92
% 11.81/4.03 Index Insertion : 0.00
% 11.81/4.03 Index Deletion : 0.00
% 11.81/4.03 Index Matching : 0.00
% 11.81/4.03 BG Taut test : 0.00
%------------------------------------------------------------------------------