TSTP Solution File: GRP370-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP370-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n013.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 10:41:06 EDT 2023
% Result : Unsatisfiable 43.25s 30.22s
% Output : CNFRefutation 43.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 41
% Syntax : Number of formulae : 334 ( 240 unt; 12 typ; 0 def)
% Number of atoms : 477 ( 460 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 312 ( 157 ~; 155 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Maximal term depth : 5 ( 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 203 (; 203 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > sk_c9 > sk_c8 > 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(sk_c8,type,
sk_c8: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(sk_c9,type,
sk_c9: $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_125,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c5) = sk_c9 ) ),
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_95,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_137,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_68,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_179,axiom,
! [X5,X6,X3,X1,X2,X4] :
( ( multiply(sk_c7,sk_c8) != sk_c9 )
| ( multiply(X3,X4) != sk_c8 )
| ( inverse(X3) != X4 )
| ( multiply(X4,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c9) != sk_c8 )
| ( inverse(X1) != sk_c9 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( inverse(X2) != sk_c7 )
| ( multiply(sk_c9,X5) != sk_c7 )
| ( multiply(X6,sk_c9) != X5 )
| ( inverse(X6) != sk_c9 ) ),
file(unknown,unknown) ).
tff(f_92,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_101,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_104,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_89,axiom,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_140,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_143,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_146,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( inverse(sk_c5) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_131,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
( ( multiply(sk_c2,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_80,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_83,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( inverse(sk_c5) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_74,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_71,axiom,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_119,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_122,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c3) = sk_c9 ) ),
file(unknown,unknown) ).
tff(f_107,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
file(unknown,unknown) ).
tff(f_116,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c4) = sk_c7 ) ),
file(unknown,unknown) ).
tff(f_113,axiom,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_48,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_81,plain,
inverse(sk_c1) = sk_c2,
inference(splitLeft,[status(thm)],[c_48]) ).
tff(c_85,plain,
multiply(sk_c2,sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_81,c_4]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_132,plain,
! [X_14,Y_15,Z_16] : ( multiply(multiply(X_14,Y_15),Z_16) = multiply(X_14,multiply(Y_15,Z_16)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_159,plain,
! [X_2,Z_16] : ( multiply(inverse(X_2),multiply(X_2,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_132]) ).
tff(c_193,plain,
! [X_18,Z_19] : ( multiply(inverse(X_18),multiply(X_18,Z_19)) = Z_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_229,plain,
multiply(inverse(sk_c2),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_85,c_193]) ).
tff(c_168,plain,
! [X_2,Z_16] : ( multiply(inverse(X_2),multiply(X_2,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_414,plain,
multiply(inverse(inverse(sk_c2)),sk_c1) = identity,
inference(superposition,[status(thm),theory(equality)],[c_229,c_168]) ).
tff(c_6745,plain,
multiply(inverse(inverse(inverse(sk_c2))),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_414,c_168]) ).
tff(c_235,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_193]) ).
tff(c_6873,plain,
inverse(sk_c2) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_6745,c_235]) ).
tff(c_28,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_105,plain,
multiply(sk_c1,sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_156,plain,
! [Z_16] : ( multiply(sk_c2,multiply(sk_c1,Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_85,c_132]) ).
tff(c_170,plain,
! [Z_17] : ( multiply(sk_c2,multiply(sk_c1,Z_17)) = Z_17 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_156]) ).
tff(c_182,plain,
multiply(sk_c2,sk_c8) = sk_c2,
inference(superposition,[status(thm),theory(equality)],[c_105,c_170]) ).
tff(c_211,plain,
multiply(inverse(sk_c2),sk_c2) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_182,c_193]) ).
tff(c_242,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_211]) ).
tff(c_56,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_100,plain,
multiply(sk_c2,sk_c7) = sk_c8,
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_223,plain,
multiply(inverse(sk_c2),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_100,c_193]) ).
tff(c_422,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_229,c_242,c_223]) ).
tff(c_10,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_95,plain,
multiply(sk_c7,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_320,plain,
multiply(sk_c7,identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_242,c_95]) ).
tff(c_424,plain,
multiply(sk_c1,identity) = sk_c9,
inference(demodulation,[status(thm),theory(equality)],[c_422,c_320]) ).
tff(c_167,plain,
! [Z_16] : ( multiply(sk_c2,multiply(sk_c1,Z_16)) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_156]) ).
tff(c_436,plain,
multiply(sk_c2,sk_c9) = identity,
inference(superposition,[status(thm),theory(equality)],[c_424,c_167]) ).
tff(c_6640,plain,
multiply(inverse(sk_c2),identity) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_436,c_168]) ).
tff(c_6646,plain,
sk_c9 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_229,c_6640]) ).
tff(c_575,plain,
multiply(inverse(inverse(inverse(sk_c2))),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_414,c_168]) ).
tff(c_704,plain,
inverse(sk_c2) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_575,c_235]) ).
tff(c_746,plain,
! [X_27,Z_28] : ( multiply(inverse(inverse(X_27)),Z_28) = multiply(X_27,Z_28) ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_168]) ).
tff(c_790,plain,
! [X_27,Z_16] : ( multiply(X_27,multiply(inverse(X_27),Z_16)) = Z_16 ),
inference(superposition,[status(thm),theory(equality)],[c_168,c_746]) ).
tff(c_433,plain,
multiply(inverse(sk_c1),sk_c9) = identity,
inference(superposition,[status(thm),theory(equality)],[c_424,c_168]) ).
tff(c_442,plain,
multiply(sk_c2,sk_c9) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_81,c_433]) ).
tff(c_450,plain,
multiply(inverse(sk_c2),identity) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_442,c_168]) ).
tff(c_456,plain,
sk_c9 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_229,c_450]) ).
tff(c_249,plain,
multiply(sk_c1,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_242,c_105]) ).
tff(c_250,plain,
multiply(sk_c2,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_242,c_100]) ).
tff(c_64,plain,
! [X6_7,X2_10,X1_9,X3_8] :
( ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_246,plain,
! [X6_7,X2_10,X1_9,X3_8] :
( ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_64]) ).
tff(c_247,plain,
! [X3_8] :
( ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_246]) ).
tff(c_307,plain,
! [X3_20] :
( ( multiply(inverse(X3_20),sk_c7) != identity )
| ( multiply(X3_20,inverse(X3_20)) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_242,c_242,c_247]) ).
tff(c_309,plain,
( ( multiply(sk_c2,sk_c7) != identity )
| ( multiply(sk_c1,inverse(sk_c1)) != identity ) ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_307]) ).
tff(c_315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_249,c_81,c_250,c_309]) ).
tff(c_316,plain,
! [X1_9,X2_10,X6_7] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_246]) ).
tff(c_445,plain,
! [X1_9,X2_10,X6_7] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != identity )
| ( inverse(X2_10) != sk_c1 )
| ( multiply(X2_10,sk_c1) != identity )
| ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_422,c_422,c_242,c_422,c_242,c_316]) ).
tff(c_446,plain,
! [X6_7] :
( ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c1 ) ),
inference(splitLeft,[status(thm)],[c_445]) ).
tff(c_6553,plain,
! [X6_86] :
( ( inverse(X6_86) != sk_c1 )
| ( multiply(sk_c1,multiply(X6_86,sk_c1)) != sk_c1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_456,c_456,c_456,c_446]) ).
tff(c_6586,plain,
inverse(inverse(sk_c1)) != sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_790,c_6553]) ).
tff(c_6615,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_704,c_81,c_6586]) ).
tff(c_6616,plain,
! [X2_10,X1_9] :
( ( inverse(X2_10) != sk_c1 )
| ( multiply(X2_10,sk_c1) != identity )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != identity ) ),
inference(splitRight,[status(thm)],[c_445]) ).
tff(c_46802,plain,
! [X2_10,X1_9] :
( ( inverse(X2_10) != sk_c1 )
| ( multiply(X2_10,sk_c1) != identity )
| ( inverse(X1_9) != sk_c1 )
| ( multiply(X1_9,sk_c1) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6646,c_6646,c_6616]) ).
tff(c_46804,plain,
! [X1_292] :
( ( inverse(X1_292) != sk_c1 )
| ( multiply(X1_292,sk_c1) != identity ) ),
inference(splitLeft,[status(thm)],[c_46802]) ).
tff(c_46883,plain,
inverse(sk_c2) != sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_85,c_46804]) ).
tff(c_46911,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6873,c_46883]) ).
tff(c_46913,plain,
! [X2_293] :
( ( inverse(X2_293) != sk_c1 )
| ( multiply(X2_293,sk_c1) != identity ) ),
inference(splitRight,[status(thm)],[c_46802]) ).
tff(c_46992,plain,
inverse(sk_c2) != sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_85,c_46913]) ).
tff(c_47020,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6873,c_46992]) ).
tff(c_47021,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_47022,plain,
multiply(sk_c1,sk_c2) != sk_c8,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_26,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_47079,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_47022,c_26]) ).
tff(c_47102,plain,
! [X_294,Y_295,Z_296] : ( multiply(multiply(X_294,Y_295),Z_296) = multiply(X_294,multiply(Y_295,Z_296)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_47147,plain,
! [X_2,Z_296] : ( multiply(inverse(X_2),multiply(X_2,Z_296)) = multiply(identity,Z_296) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_47102]) ).
tff(c_47269,plain,
! [X_299,Z_300] : ( multiply(inverse(X_299),multiply(X_299,Z_300)) = Z_300 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_47147]) ).
tff(c_47308,plain,
multiply(inverse(sk_c4),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_47079,c_47269]) ).
tff(c_47335,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_47021,c_47308]) ).
tff(c_47159,plain,
! [X_2,Z_296] : ( multiply(inverse(X_2),multiply(X_2,Z_296)) = Z_296 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_47147]) ).
tff(c_47345,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_47335,c_47159]) ).
tff(c_47351,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_47345]) ).
tff(c_47356,plain,
multiply(sk_c1,sk_c2) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_47351,c_47022]) ).
tff(c_47850,plain,
! [X_307,Z_308] : ( multiply(inverse(inverse(X_307)),Z_308) = multiply(X_307,Z_308) ),
inference(superposition,[status(thm),theory(equality)],[c_47269,c_47159]) ).
tff(c_47326,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_47269]) ).
tff(c_47860,plain,
! [X_307] : ( multiply(X_307,identity) = X_307 ),
inference(superposition,[status(thm),theory(equality)],[c_47850,c_47326]) ).
tff(c_30,plain,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_47088,plain,
multiply(sk_c9,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_47022,c_30]) ).
tff(c_32,plain,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_47074,plain,
multiply(sk_c5,sk_c9) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_47022,c_32]) ).
tff(c_34,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_47060,plain,
inverse(sk_c5) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_47022,c_34]) ).
tff(c_47064,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_47060,c_4]) ).
tff(c_47129,plain,
! [Z_296] : ( multiply(sk_c9,multiply(sk_c5,Z_296)) = multiply(identity,Z_296) ),
inference(superposition,[status(thm),theory(equality)],[c_47064,c_47102]) ).
tff(c_47174,plain,
! [Z_298] : ( multiply(sk_c9,multiply(sk_c5,Z_298)) = Z_298 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_47129]) ).
tff(c_47186,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_47074,c_47174]) ).
tff(c_47190,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_47088,c_47186]) ).
tff(c_24,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_47030,plain,
multiply(sk_c1,sk_c2) = sk_c8,
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_47036,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_47030,c_47022]) ).
tff(c_47037,plain,
inverse(sk_c3) = sk_c9,
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_47042,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_47037,c_4]) ).
tff(c_47197,plain,
multiply(sk_c7,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_47190,c_47042]) ).
tff(c_47138,plain,
! [Z_296] : ( multiply(sk_c2,multiply(sk_c7,Z_296)) = multiply(sk_c8,Z_296) ),
inference(superposition,[status(thm),theory(equality)],[c_100,c_47102]) ).
tff(c_47423,plain,
! [Z_301] : ( multiply(sk_c2,multiply(sk_c7,Z_301)) = Z_301 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_47351,c_47138]) ).
tff(c_47444,plain,
multiply(sk_c2,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_47197,c_47423]) ).
tff(c_47910,plain,
sk_c3 = sk_c2,
inference(demodulation,[status(thm),theory(equality)],[c_47860,c_47444]) ).
tff(c_47320,plain,
multiply(inverse(sk_c2),identity) = sk_c1,
inference(superposition,[status(thm),theory(equality)],[c_85,c_47269]) ).
tff(c_47317,plain,
multiply(inverse(sk_c2),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_100,c_47269]) ).
tff(c_47552,plain,
multiply(inverse(sk_c2),identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_47351,c_47317]) ).
tff(c_47564,plain,
sk_c7 = sk_c1,
inference(demodulation,[status(thm),theory(equality)],[c_47320,c_47552]) ).
tff(c_47580,plain,
multiply(sk_c1,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_47564,c_47197]) ).
tff(c_47998,plain,
multiply(sk_c1,sk_c2) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_47910,c_47580]) ).
tff(c_48006,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_47356,c_47998]) ).
tff(c_48008,plain,
multiply(sk_c2,sk_c7) != sk_c8,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_58,plain,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_48066,plain,
multiply(sk_c9,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_48008,c_58]) ).
tff(c_60,plain,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_48060,plain,
multiply(sk_c5,sk_c9) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_48008,c_60]) ).
tff(c_62,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_48028,plain,
inverse(sk_c5) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_48008,c_62]) ).
tff(c_48032,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_48028,c_4]) ).
tff(c_48085,plain,
! [X_310,Y_311,Z_312] : ( multiply(multiply(X_310,Y_311),Z_312) = multiply(X_310,multiply(Y_311,Z_312)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_48115,plain,
! [Z_312] : ( multiply(sk_c9,multiply(sk_c5,Z_312)) = multiply(identity,Z_312) ),
inference(superposition,[status(thm),theory(equality)],[c_48032,c_48085]) ).
tff(c_49011,plain,
! [Z_327] : ( multiply(sk_c9,multiply(sk_c5,Z_327)) = Z_327 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48115]) ).
tff(c_49023,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_48060,c_49011]) ).
tff(c_49027,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_48066,c_49023]) ).
tff(c_52,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_48043,plain,
inverse(sk_c3) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_48008,c_52]) ).
tff(c_49033,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_49027,c_48043]) ).
tff(c_49036,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_49027,c_95]) ).
tff(c_48130,plain,
! [X_2,Z_312] : ( multiply(inverse(X_2),multiply(X_2,Z_312)) = multiply(identity,Z_312) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_48085]) ).
tff(c_51741,plain,
! [X_363,Z_364] : ( multiply(inverse(X_363),multiply(X_363,Z_364)) = Z_364 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48130]) ).
tff(c_51774,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_49036,c_51741]) ).
tff(c_51822,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_51774]) ).
tff(c_50,plain,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_48080,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_48008,c_50]) ).
tff(c_49029,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_49027,c_48080]) ).
tff(c_51829,plain,
multiply(sk_c3,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_51822,c_49029]) ).
tff(c_49120,plain,
! [X_329,Z_330] : ( multiply(inverse(X_329),multiply(X_329,Z_330)) = Z_330 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48130]) ).
tff(c_49343,plain,
! [X_332] : ( multiply(inverse(inverse(X_332)),identity) = X_332 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_49120]) ).
tff(c_49361,plain,
multiply(inverse(sk_c7),identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_49033,c_49343]) ).
tff(c_48142,plain,
! [X_2,Z_312] : ( multiply(inverse(X_2),multiply(X_2,Z_312)) = Z_312 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48130]) ).
tff(c_49658,plain,
! [X_337,Z_338] : ( multiply(inverse(inverse(X_337)),Z_338) = multiply(X_337,Z_338) ),
inference(superposition,[status(thm),theory(equality)],[c_48142,c_49120]) ).
tff(c_49192,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_49120]) ).
tff(c_49727,plain,
! [X_339] : ( multiply(X_339,identity) = X_339 ),
inference(superposition,[status(thm),theory(equality)],[c_49658,c_49192]) ).
tff(c_49787,plain,
inverse(sk_c7) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_49361,c_49727]) ).
tff(c_49704,plain,
! [X_337,Z_312] : ( multiply(X_337,multiply(inverse(X_337),Z_312)) = Z_312 ),
inference(superposition,[status(thm),theory(equality)],[c_48142,c_49658]) ).
tff(c_48278,plain,
! [X_316,Z_317] : ( multiply(inverse(X_316),multiply(X_316,Z_317)) = Z_317 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48130]) ).
tff(c_48811,plain,
! [X_324,Z_325] : ( multiply(inverse(inverse(X_324)),Z_325) = multiply(X_324,Z_325) ),
inference(superposition,[status(thm),theory(equality)],[c_48278,c_48142]) ).
tff(c_48838,plain,
! [X_324] : ( multiply(X_324,inverse(X_324)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_48811,c_4]) ).
tff(c_48170,plain,
! [Z_314] : ( multiply(sk_c9,multiply(sk_c5,Z_314)) = Z_314 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_48115]) ).
tff(c_48182,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_48060,c_48170]) ).
tff(c_48186,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_48066,c_48182]) ).
tff(c_48195,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_48186,c_95]) ).
tff(c_48296,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_48195,c_48278]) ).
tff(c_48354,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_48296]) ).
tff(c_48161,plain,
! [X6_7,X2_10,X1_9,X3_8] :
( ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_64]) ).
tff(c_48214,plain,
! [X3_315] :
( ( multiply(inverse(X3_315),sk_c7) != sk_c8 )
| ( multiply(X3_315,inverse(X3_315)) != sk_c8 ) ),
inference(splitLeft,[status(thm)],[c_48161]) ).
tff(c_48225,plain,
( ( sk_c8 != identity )
| ( multiply(sk_c7,inverse(sk_c7)) != sk_c8 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_48214]) ).
tff(c_48466,plain,
multiply(sk_c7,inverse(sk_c7)) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_48354,c_48354,c_48225]) ).
tff(c_49002,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48838,c_48466]) ).
tff(c_49003,plain,
! [X1_9,X2_10,X6_7] :
( ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_48161]) ).
tff(c_49055,plain,
! [X1_9,X2_10,X6_7] :
( ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(sk_c7,multiply(X6_7,sk_c7)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_49027,c_49027,c_49027,c_49027,c_49027,c_49003]) ).
tff(c_51616,plain,
! [X6_361] :
( ( inverse(X6_361) != sk_c7 )
| ( multiply(sk_c7,multiply(X6_361,sk_c7)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_49055]) ).
tff(c_51647,plain,
inverse(inverse(sk_c7)) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_49704,c_51616]) ).
tff(c_51676,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49033,c_49787,c_51647]) ).
tff(c_51677,plain,
! [X2_10,X1_9] :
( ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_49055]) ).
tff(c_56640,plain,
! [X2_10,X1_9] :
( ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != identity )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_51822,c_51822,c_51677]) ).
tff(c_56642,plain,
! [X1_409] :
( ( inverse(X1_409) != sk_c7 )
| ( multiply(X1_409,sk_c7) != identity ) ),
inference(splitLeft,[status(thm)],[c_56640]) ).
tff(c_56676,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_51829,c_56642]) ).
tff(c_56699,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49033,c_56676]) ).
tff(c_56701,plain,
! [X2_410] :
( ( inverse(X2_410) != sk_c7 )
| ( multiply(X2_410,sk_c7) != identity ) ),
inference(splitRight,[status(thm)],[c_56640]) ).
tff(c_56735,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_51829,c_56701]) ).
tff(c_56758,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49033,c_56735]) ).
tff(c_56760,plain,
multiply(sk_c7,sk_c8) != sk_c9,
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_16,plain,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_56832,plain,
multiply(sk_c9,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_56760,c_16]) ).
tff(c_18,plain,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_56840,plain,
multiply(sk_c5,sk_c9) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_56760,c_18]) ).
tff(c_20,plain,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_56791,plain,
inverse(sk_c5) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_56760,c_20]) ).
tff(c_56795,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_56791,c_4]) ).
tff(c_56845,plain,
! [X_411,Y_412,Z_413] : ( multiply(multiply(X_411,Y_412),Z_413) = multiply(X_411,multiply(Y_412,Z_413)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_56878,plain,
! [Z_413] : ( multiply(sk_c9,multiply(sk_c5,Z_413)) = multiply(identity,Z_413) ),
inference(superposition,[status(thm),theory(equality)],[c_56795,c_56845]) ).
tff(c_56904,plain,
! [Z_414] : ( multiply(sk_c9,multiply(sk_c5,Z_414)) = Z_414 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_56878]) ).
tff(c_56916,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_56840,c_56904]) ).
tff(c_56920,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_56832,c_56916]) ).
tff(c_56928,plain,
multiply(sk_c7,sk_c8) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_56920,c_56760]) ).
tff(c_14,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_56768,plain,
multiply(sk_c7,sk_c8) = sk_c9,
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_56769,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56760,c_56768]) ).
tff(c_56770,plain,
inverse(sk_c4) = sk_c7,
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_12,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_56820,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_56760,c_12]) ).
tff(c_56890,plain,
! [X_2,Z_413] : ( multiply(inverse(X_2),multiply(X_2,Z_413)) = multiply(identity,Z_413) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_56845]) ).
tff(c_56979,plain,
! [X_415,Z_416] : ( multiply(inverse(X_415),multiply(X_415,Z_416)) = Z_416 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_56890]) ).
tff(c_57018,plain,
multiply(inverse(sk_c4),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_56820,c_56979]) ).
tff(c_57048,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_56770,c_57018]) ).
tff(c_57050,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56928,c_57048]) ).
tff(c_57052,plain,
inverse(sk_c1) != sk_c2,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_44,plain,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_57100,plain,
multiply(sk_c9,sk_c6) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_57052,c_44]) ).
tff(c_46,plain,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_57106,plain,
multiply(sk_c5,sk_c9) = sk_c6,
inference(negUnitSimplification,[status(thm)],[c_57052,c_46]) ).
tff(c_57051,plain,
inverse(sk_c5) = sk_c9,
inference(splitRight,[status(thm)],[c_48]) ).
tff(c_57056,plain,
multiply(sk_c9,sk_c5) = identity,
inference(superposition,[status(thm),theory(equality)],[c_57051,c_4]) ).
tff(c_57129,plain,
! [X_417,Y_418,Z_419] : ( multiply(multiply(X_417,Y_418),Z_419) = multiply(X_417,multiply(Y_418,Z_419)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_57162,plain,
! [Z_419] : ( multiply(sk_c9,multiply(sk_c5,Z_419)) = multiply(identity,Z_419) ),
inference(superposition,[status(thm),theory(equality)],[c_57056,c_57129]) ).
tff(c_57428,plain,
! [Z_425] : ( multiply(sk_c9,multiply(sk_c5,Z_425)) = Z_425 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57162]) ).
tff(c_57440,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_57106,c_57428]) ).
tff(c_57444,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57100,c_57440]) ).
tff(c_38,plain,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_57076,plain,
inverse(sk_c3) = sk_c9,
inference(negUnitSimplification,[status(thm)],[c_57052,c_38]) ).
tff(c_57453,plain,
inverse(sk_c3) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57444,c_57076]) ).
tff(c_36,plain,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_57111,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_57052,c_36]) ).
tff(c_57080,plain,
multiply(sk_c9,sk_c3) = identity,
inference(superposition,[status(thm),theory(equality)],[c_57076,c_4]) ).
tff(c_57156,plain,
! [Z_419] : ( multiply(sk_c9,multiply(sk_c3,Z_419)) = multiply(identity,Z_419) ),
inference(superposition,[status(thm),theory(equality)],[c_57080,c_57129]) ).
tff(c_57405,plain,
! [Z_424] : ( multiply(sk_c9,multiply(sk_c3,Z_424)) = Z_424 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57156]) ).
tff(c_57417,plain,
multiply(sk_c9,sk_c8) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_57111,c_57405]) ).
tff(c_57446,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57444,c_57444,c_57417]) ).
tff(c_57165,plain,
! [X_2,Z_419] : ( multiply(inverse(X_2),multiply(X_2,Z_419)) = multiply(identity,Z_419) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_57129]) ).
tff(c_60067,plain,
! [X_461,Z_462] : ( multiply(inverse(X_461),multiply(X_461,Z_462)) = Z_462 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57165]) ).
tff(c_60100,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_57446,c_60067]) ).
tff(c_60131,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_60100]) ).
tff(c_57449,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(demodulation,[status(thm),theory(equality)],[c_57444,c_57111]) ).
tff(c_60139,plain,
multiply(sk_c3,sk_c7) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_60131,c_57449]) ).
tff(c_60147,plain,
! [X_463] : ( multiply(inverse(identity),X_463) = X_463 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_60067]) ).
tff(c_57176,plain,
! [X_2,Z_419] : ( multiply(inverse(X_2),multiply(X_2,Z_419)) = Z_419 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57165]) ).
tff(c_60374,plain,
! [X_467] : ( multiply(inverse(inverse(identity)),X_467) = X_467 ),
inference(superposition,[status(thm),theory(equality)],[c_60147,c_57176]) ).
tff(c_60395,plain,
inverse(identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_60374,c_4]) ).
tff(c_60449,plain,
! [X_468,Z_469] : ( multiply(inverse(inverse(X_468)),Z_469) = multiply(X_468,Z_469) ),
inference(superposition,[status(thm),theory(equality)],[c_60067,c_57176]) ).
tff(c_60470,plain,
! [X_468] : ( multiply(X_468,inverse(X_468)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_60449,c_4]) ).
tff(c_60121,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_60067]) ).
tff(c_60456,plain,
! [X_468] : ( multiply(X_468,identity) = X_468 ),
inference(superposition,[status(thm),theory(equality)],[c_60449,c_60121]) ).
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_60807,plain,
! [X_475,Y_476,Z_477] : ( multiply(inverse(multiply(X_475,Y_476)),multiply(X_475,multiply(Y_476,Z_477))) = Z_477 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_60067]) ).
tff(c_60855,plain,
! [X_475,X_468] : ( multiply(inverse(multiply(X_475,X_468)),multiply(X_475,identity)) = inverse(X_468) ),
inference(superposition,[status(thm),theory(equality)],[c_60470,c_60807]) ).
tff(c_60941,plain,
! [X_475,X_468] : ( multiply(inverse(multiply(X_475,X_468)),X_475) = inverse(X_468) ),
inference(demodulation,[status(thm),theory(equality)],[c_60456,c_60855]) ).
tff(c_57452,plain,
multiply(sk_c7,sk_c3) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_57444,c_57080]) ).
tff(c_60900,plain,
! [X_475] : ( multiply(inverse(multiply(X_475,sk_c7)),multiply(X_475,identity)) = sk_c3 ),
inference(superposition,[status(thm),theory(equality)],[c_57452,c_60807]) ).
tff(c_60953,plain,
! [X_475] : ( multiply(inverse(multiply(X_475,sk_c7)),X_475) = sk_c3 ),
inference(demodulation,[status(thm),theory(equality)],[c_60456,c_60900]) ).
tff(c_60916,plain,
! [X_475,X_2] : ( multiply(inverse(multiply(X_475,inverse(X_2))),multiply(X_475,identity)) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_60807]) ).
tff(c_61194,plain,
! [X_481,X_482] : ( multiply(inverse(multiply(X_481,inverse(X_482))),X_481) = X_482 ),
inference(demodulation,[status(thm),theory(equality)],[c_60456,c_60916]) ).
tff(c_60463,plain,
! [X_468,Z_419] : ( multiply(X_468,multiply(inverse(X_468),Z_419)) = Z_419 ),
inference(superposition,[status(thm),theory(equality)],[c_60449,c_57176]) ).
tff(c_61376,plain,
! [X_484,X_485] : ( multiply(multiply(X_484,inverse(X_485)),X_485) = X_484 ),
inference(superposition,[status(thm),theory(equality)],[c_61194,c_60463]) ).
tff(c_62302,plain,
! [X_493] : ( inverse(multiply(inverse(X_493),sk_c7)) = multiply(sk_c3,X_493) ),
inference(superposition,[status(thm),theory(equality)],[c_60953,c_61376]) ).
tff(c_60957,plain,
! [X_475,X_2] : ( multiply(inverse(multiply(X_475,inverse(X_2))),X_475) = X_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_60456,c_60916]) ).
tff(c_62320,plain,
! [X_475,X_493] : ( multiply(inverse(multiply(X_475,multiply(sk_c3,X_493))),X_475) = multiply(inverse(X_493),sk_c7) ),
inference(superposition,[status(thm),theory(equality)],[c_62302,c_60957]) ).
tff(c_62389,plain,
! [X_493] : ( multiply(inverse(X_493),sk_c7) = inverse(multiply(sk_c3,X_493)) ),
inference(demodulation,[status(thm),theory(equality)],[c_60941,c_62320]) ).
tff(c_57522,plain,
! [X_426,Z_427] : ( multiply(inverse(X_426),multiply(X_426,Z_427)) = Z_427 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57165]) ).
tff(c_57904,plain,
! [X_433,Z_434] : ( multiply(inverse(inverse(X_433)),Z_434) = multiply(X_433,Z_434) ),
inference(superposition,[status(thm),theory(equality)],[c_57522,c_57176]) ).
tff(c_57576,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_57522]) ).
tff(c_57952,plain,
! [X_435] : ( multiply(X_435,identity) = X_435 ),
inference(superposition,[status(thm),theory(equality)],[c_57904,c_57576]) ).
tff(c_57555,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_57446,c_57522]) ).
tff(c_57586,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_57555]) ).
tff(c_57144,plain,
! [Z_419] : ( multiply(sk_c3,multiply(sk_c9,Z_419)) = multiply(sk_c8,Z_419) ),
inference(superposition,[status(thm),theory(equality)],[c_57111,c_57129]) ).
tff(c_57688,plain,
! [Z_429] : ( multiply(sk_c3,multiply(sk_c7,Z_429)) = Z_429 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57586,c_57444,c_57144]) ).
tff(c_57706,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_57452,c_57688]) ).
tff(c_42,plain,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_57064,plain,
inverse(sk_c4) = sk_c7,
inference(negUnitSimplification,[status(thm)],[c_57052,c_42]) ).
tff(c_57068,plain,
multiply(sk_c7,sk_c4) = identity,
inference(superposition,[status(thm),theory(equality)],[c_57064,c_4]) ).
tff(c_57712,plain,
multiply(sk_c3,identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_57068,c_57688]) ).
tff(c_57764,plain,
sk_c4 = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_57706,c_57712]) ).
tff(c_57570,plain,
multiply(inverse(sk_c7),identity) = sk_c4,
inference(superposition,[status(thm),theory(equality)],[c_57068,c_57522]) ).
tff(c_57777,plain,
multiply(inverse(sk_c7),identity) = sk_c3,
inference(demodulation,[status(thm),theory(equality)],[c_57764,c_57570]) ).
tff(c_57966,plain,
inverse(sk_c7) = sk_c3,
inference(superposition,[status(thm),theory(equality)],[c_57952,c_57777]) ).
tff(c_57918,plain,
! [X_433,Z_419] : ( multiply(X_433,multiply(inverse(X_433),Z_419)) = Z_419 ),
inference(superposition,[status(thm),theory(equality)],[c_57904,c_57176]) ).
tff(c_40,plain,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_57090,plain,
multiply(sk_c4,sk_c7) = sk_c8,
inference(negUnitSimplification,[status(thm)],[c_57052,c_40]) ).
tff(c_57223,plain,
! [X_421,Z_422] : ( multiply(inverse(X_421),multiply(X_421,Z_422)) = Z_422 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57165]) ).
tff(c_57250,plain,
multiply(inverse(sk_c4),sk_c8) = sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_57090,c_57223]) ).
tff(c_57266,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57064,c_57250]) ).
tff(c_57270,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c8,
inference(superposition,[status(thm),theory(equality)],[c_57266,c_57176]) ).
tff(c_57276,plain,
sk_c8 = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_57270]) ).
tff(c_57278,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57276,c_57266]) ).
tff(c_57179,plain,
! [Z_420] : ( multiply(sk_c9,multiply(sk_c5,Z_420)) = Z_420 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_57162]) ).
tff(c_57191,plain,
multiply(sk_c9,sk_c6) = sk_c9,
inference(superposition,[status(thm),theory(equality)],[c_57106,c_57179]) ).
tff(c_57195,plain,
sk_c9 = sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57100,c_57191]) ).
tff(c_57178,plain,
multiply(sk_c7,sk_c8) != sk_c9,
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_57197,plain,
multiply(sk_c7,sk_c8) != sk_c7,
inference(demodulation,[status(thm),theory(equality)],[c_57195,c_57178]) ).
tff(c_57395,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57278,c_57276,c_57197]) ).
tff(c_57396,plain,
! [X3_8,X1_9,X2_10,X6_7] :
( ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 )
| ( inverse(X1_9) != sk_c9 )
| ( multiply(X1_9,sk_c9) != sk_c8 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c9 )
| ( multiply(sk_c9,multiply(X6_7,sk_c9)) != sk_c7 ) ),
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_57467,plain,
! [X3_8,X1_9,X2_10,X6_7] :
( ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X6_7) != sk_c7 )
| ( multiply(sk_c7,multiply(X6_7,sk_c7)) != sk_c7 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_57444,c_57444,c_57444,c_57444,c_57444,c_57396]) ).
tff(c_59957,plain,
! [X6_460] :
( ( inverse(X6_460) != sk_c7 )
| ( multiply(sk_c7,multiply(X6_460,sk_c7)) != sk_c7 ) ),
inference(splitLeft,[status(thm)],[c_57467]) ).
tff(c_59984,plain,
inverse(inverse(sk_c7)) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_57918,c_59957]) ).
tff(c_60012,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_57966,c_59984]) ).
tff(c_60013,plain,
! [X2_10,X1_9,X3_8] :
( ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != sk_c8 )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != sk_c8 )
| ( multiply(inverse(X3_8),sk_c7) != sk_c8 )
| ( multiply(X3_8,inverse(X3_8)) != sk_c8 ) ),
inference(splitRight,[status(thm)],[c_57467]) ).
tff(c_66568,plain,
! [X2_10,X1_9,X3_8] :
( ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != identity )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != identity )
| ( inverse(multiply(sk_c3,X3_8)) != identity ) ),
inference(demodulation,[status(thm),theory(equality)],[c_60470,c_60131,c_62389,c_60131,c_60131,c_60131,c_60013]) ).
tff(c_66570,plain,
! [X3_532] : ( inverse(multiply(sk_c3,X3_532)) != identity ),
inference(splitLeft,[status(thm)],[c_66568]) ).
tff(c_66593,plain,
inverse(identity) != identity,
inference(superposition,[status(thm),theory(equality)],[c_60470,c_66570]) ).
tff(c_66609,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60395,c_66593]) ).
tff(c_66610,plain,
! [X2_10,X1_9] :
( ( inverse(X2_10) != sk_c7 )
| ( multiply(X2_10,sk_c7) != identity )
| ( inverse(X1_9) != sk_c7 )
| ( multiply(X1_9,sk_c7) != identity ) ),
inference(splitRight,[status(thm)],[c_66568]) ).
tff(c_210179,plain,
! [X1_888] :
( ( inverse(X1_888) != sk_c7 )
| ( multiply(X1_888,sk_c7) != identity ) ),
inference(splitLeft,[status(thm)],[c_66610]) ).
tff(c_210265,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_60139,c_210179]) ).
tff(c_210299,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_210265]) ).
tff(c_212456,plain,
! [X2_892] :
( ( inverse(X2_892) != sk_c7 )
| ( multiply(X2_892,sk_c7) != identity ) ),
inference(splitRight,[status(thm)],[c_66610]) ).
tff(c_212546,plain,
inverse(sk_c3) != sk_c7,
inference(superposition,[status(thm),theory(equality)],[c_60139,c_212456]) ).
tff(c_212581,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_212546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP370-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % 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 22:09:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 43.25/30.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.25/30.25
% 43.25/30.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.68/30.31
% 43.68/30.31 Inference rules
% 43.68/30.31 ----------------------
% 43.68/30.31 #Ref : 0
% 43.68/30.31 #Sup : 50256
% 43.68/30.31 #Fact : 0
% 43.68/30.31 #Define : 0
% 43.68/30.31 #Split : 20
% 43.68/30.31 #Chain : 0
% 43.68/30.31 #Close : 0
% 43.68/30.31
% 43.68/30.31 Ordering : KBO
% 43.68/30.31
% 43.68/30.31 Simplification rules
% 43.68/30.31 ----------------------
% 43.68/30.31 #Subsume : 8
% 43.68/30.31 #Demod : 189975
% 43.68/30.31 #Tautology : 41033
% 43.68/30.31 #SimpNegUnit : 26
% 43.68/30.31 #BackRed : 285
% 43.68/30.31
% 43.68/30.31 #Partial instantiations: 0
% 43.68/30.31 #Strategies tried : 1
% 43.68/30.31
% 43.68/30.31 Timing (in seconds)
% 43.68/30.31 ----------------------
% 43.68/30.31 Preprocessing : 0.53
% 43.68/30.31 Parsing : 0.22
% 43.68/30.31 CNF conversion : 0.02
% 43.68/30.31 Main loop : 28.57
% 43.68/30.31 Inferencing : 3.26
% 43.68/30.31 Reduction : 22.00
% 43.68/30.31 Demodulation : 21.27
% 43.68/30.31 BG Simplification : 0.24
% 43.68/30.31 Subsumption : 2.26
% 43.68/30.31 Abstraction : 0.77
% 43.68/30.31 MUC search : 0.00
% 43.68/30.31 Cooper : 0.00
% 43.68/30.31 Total : 29.20
% 43.68/30.31 Index Insertion : 0.00
% 43.68/30.31 Index Deletion : 0.00
% 43.68/30.31 Index Matching : 0.00
% 43.68/30.31 BG Taut test : 0.00
%------------------------------------------------------------------------------