%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 : n026.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 : Wed Apr 9 06:24:42 PM UTC 2025
% Result : Unsatisfiable 7.56s 2.80s
% Output : CNFRefutation 7.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 54 ( 54 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > k > j > identity > h > d > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(j,type,
j: $i ).
tff(h,type,
h: $i ).
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(k,type,
k: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(c,type,
c: $i ).
tff(f_70,axiom,
! [X] : ( multiply(X,inverse(X)) = identity ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_76,axiom,
multiply(d,inverse(b)) = h,
file(unknown,unknown) ).
tff(f_74,axiom,
multiply(a,b) = c,
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] : ( multiply(X,multiply(X,X)) = identity ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_75,axiom,
multiply(c,inverse(a)) = d,
file(unknown,unknown) ).
tff(f_77,axiom,
multiply(h,b) = j,
file(unknown,unknown) ).
tff(f_78,axiom,
multiply(j,inverse(h)) = k,
file(unknown,unknown) ).
tff(f_80,axiom,
multiply(k,inverse(b)) != identity,
file(unknown,unknown) ).
tff(c_10,plain,
! [X_7] : ( multiply(X_7,inverse(X_7)) = identity ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_145,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_63]) ).
tff(c_189,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_145]) ).
tff(c_224,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_189]) ).
tff(c_18,plain,
multiply(d,inverse(b)) = h,
inference(cnfTransformation,[status(thm)],[f_76]) ).
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_63]) ).
tff(c_14,plain,
multiply(a,b) = c,
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_12,plain,
! [X_8] : ( multiply(X_8,multiply(X_8,X_8)) = identity ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_176,plain,
! [X_8,Z_16] : ( multiply(X_8,multiply(multiply(X_8,X_8),Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_145]) ).
tff(c_566,plain,
! [X_24,Z_25] : ( multiply(X_24,multiply(X_24,multiply(X_24,Z_25))) = Z_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_176]) ).
tff(c_669,plain,
multiply(a,multiply(a,c)) = b,
inference(superposition,[status(thm),theory(equality)],[c_14,c_566]) ).
tff(c_705,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(superposition,[status(thm),theory(equality)],[c_669,c_224]) ).
tff(c_8,plain,
! [X_6] : ( multiply(X_6,identity) = X_6 ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_192,plain,
! [X_7,Z_16] : ( multiply(X_7,multiply(inverse(X_7),Z_16)) = multiply(identity,Z_16) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_145]) ).
tff(c_289,plain,
! [X_19,Z_20] : ( multiply(X_19,multiply(inverse(X_19),Z_20)) = Z_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_192]) ).
tff(c_338,plain,
! [X_19] : ( inverse(inverse(X_19)) = multiply(X_19,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_289]) ).
tff(c_356,plain,
! [X_19] : ( inverse(inverse(X_19)) = X_19 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_338]) ).
tff(c_229,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_189]) ).
tff(c_250,plain,
! [X_8] : ( multiply(inverse(X_8),identity) = multiply(X_8,X_8) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_229]) ).
tff(c_284,plain,
! [X_8] : ( multiply(X_8,X_8) = inverse(X_8) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_250]) ).
tff(c_16,plain,
multiply(c,inverse(a)) = d,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_643,plain,
multiply(c,multiply(c,d)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_16,c_566]) ).
tff(c_274,plain,
multiply(inverse(a),c) = b,
inference(superposition,[status(thm),theory(equality)],[c_14,c_229]) ).
tff(c_6036,plain,
! [Z_51] : ( multiply(inverse(a),multiply(c,Z_51)) = multiply(b,Z_51) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_6]) ).
tff(c_6130,plain,
multiply(inverse(a),inverse(a)) = multiply(b,multiply(c,d)),
inference(superposition,[status(thm),theory(equality)],[c_643,c_6036]) ).
tff(c_6176,plain,
multiply(b,multiply(c,d)) = a,
inference(demodulation,[status(thm),theory(equality)],[c_356,c_284,c_6130]) ).
tff(c_1084,plain,
! [X_29,Y_30] : ( multiply(X_29,multiply(Y_30,inverse(multiply(X_29,Y_30)))) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_145,c_10]) ).
tff(c_1131,plain,
! [Y_30,X_29] : ( multiply(Y_30,inverse(multiply(X_29,Y_30))) = multiply(inverse(X_29),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_1084,c_224]) ).
tff(c_3851,plain,
! [Y_40,X_41] : ( multiply(Y_40,inverse(multiply(X_41,Y_40))) = inverse(X_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1131]) ).
tff(c_4086,plain,
! [X_2,Z_16] : ( multiply(multiply(X_2,Z_16),inverse(Z_16)) = inverse(inverse(X_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_224,c_3851]) ).
tff(c_4161,plain,
! [X_2,Z_16] : ( multiply(multiply(X_2,Z_16),inverse(Z_16)) = X_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_4086]) ).
tff(c_6185,plain,
multiply(a,inverse(multiply(c,d))) = b,
inference(superposition,[status(thm),theory(equality)],[c_6176,c_4161]) ).
tff(c_6248,plain,
multiply(inverse(a),b) = inverse(multiply(c,d)),
inference(superposition,[status(thm),theory(equality)],[c_6185,c_224]) ).
tff(c_6259,plain,
inverse(multiply(c,d)) = multiply(a,c),
inference(demodulation,[status(thm),theory(equality)],[c_705,c_6248]) ).
tff(c_6478,plain,
inverse(multiply(a,c)) = multiply(c,d),
inference(superposition,[status(thm),theory(equality)],[c_6259,c_356]) ).
tff(c_4062,plain,
multiply(multiply(a,c),inverse(b)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_669,c_3851]) ).
tff(c_443,plain,
! [X_22] : ( multiply(X_22,X_22) = inverse(X_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_250]) ).
tff(c_456,plain,
! [X_22,Z_5] : ( multiply(inverse(X_22),Z_5) = multiply(X_22,multiply(X_22,Z_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_443,c_6]) ).
tff(c_7435,plain,
multiply(inverse(multiply(a,c)),inverse(b)) = multiply(multiply(a,c),inverse(a)),
inference(superposition,[status(thm),theory(equality)],[c_4062,c_456]) ).
tff(c_7469,plain,
multiply(c,h) = multiply(a,d),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_6,c_6478,c_16,c_6,c_7435]) ).
tff(c_405,plain,
! [Z_5] : ( multiply(inverse(a),multiply(c,Z_5)) = multiply(b,Z_5) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_6]) ).
tff(c_7484,plain,
multiply(inverse(a),multiply(a,d)) = multiply(b,h),
inference(superposition,[status(thm),theory(equality)],[c_7469,c_405]) ).
tff(c_7511,plain,
multiply(b,h) = d,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_7484]) ).
tff(c_7522,plain,
multiply(d,inverse(h)) = b,
inference(superposition,[status(thm),theory(equality)],[c_7511,c_4161]) ).
tff(c_20,plain,
multiply(h,b) = j,
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_268,plain,
multiply(inverse(d),h) = inverse(b),
inference(superposition,[status(thm),theory(equality)],[c_18,c_229]) ).
tff(c_1220,plain,
multiply(inverse(d),multiply(h,inverse(inverse(b)))) = identity,
inference(superposition,[status(thm),theory(equality)],[c_268,c_1084]) ).
tff(c_1333,plain,
multiply(inverse(d),j) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_356,c_1220]) ).
tff(c_222,plain,
! [X_8,Z_16] : ( multiply(X_8,multiply(X_8,multiply(X_8,Z_16))) = Z_16 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_176]) ).
tff(c_1357,plain,
multiply(inverse(d),multiply(inverse(d),identity)) = j,
inference(superposition,[status(thm),theory(equality)],[c_1333,c_222]) ).
tff(c_1370,plain,
j = d,
inference(demodulation,[status(thm),theory(equality)],[c_356,c_284,c_8,c_1357]) ).
tff(c_22,plain,
multiply(j,inverse(h)) = k,
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1384,plain,
multiply(d,inverse(h)) = k,
inference(demodulation,[status(thm),theory(equality)],[c_1370,c_22]) ).
tff(c_7558,plain,
k = b,
inference(demodulation,[status(thm),theory(equality)],[c_7522,c_1384]) ).
tff(c_24,plain,
multiply(k,inverse(b)) != identity,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_7624,plain,
multiply(b,inverse(b)) != identity,
inference(demodulation,[status(thm),theory(equality)],[c_7558,c_24]) ).
tff(c_7628,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_7624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRP002-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.13/0.13 % 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
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 21:09:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.56/2.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.56/2.81
% 7.56/2.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------