%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP190-2 : 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 : n025.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 06:25:31 PM UTC 2025
% Result : Unsatisfiable 19.91s 8.09s
% Output : CNFRefutation 19.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > inverse > identity > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(greatest_lower_bound,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(least_upper_bound,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(f_119,axiom,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_65,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_117,axiom,
least_upper_bound(a,b) = a,
file(unknown,unknown) ).
tff(f_93,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X,Y,Z] : ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_114,axiom,
! [Y,Z,X] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
file(unknown,unknown) ).
tff(c_34,plain,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_311,plain,
! [X_50,Y_51,Z_52] : ( multiply(multiply(X_50,Y_51),Z_52) = multiply(X_50,multiply(Y_51,Z_52)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_326,plain,
! [X_2,Z_52] : ( multiply(inverse(X_2),multiply(X_2,Z_52)) = multiply(identity,Z_52) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_311]) ).
tff(c_334,plain,
! [X_2,Z_52] : ( multiply(inverse(X_2),multiply(X_2,Z_52)) = Z_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_326]) ).
tff(c_422,plain,
! [X_56,Z_57] : ( multiply(inverse(X_56),multiply(X_56,Z_57)) = Z_57 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_326]) ).
tff(c_2159,plain,
! [X_98,Z_99] : ( multiply(inverse(inverse(X_98)),Z_99) = multiply(X_98,Z_99) ),
inference(superposition,[status(thm),theory(equality)],[c_334,c_422]) ).
tff(c_443,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_422]) ).
tff(c_2194,plain,
! [X_98] : ( multiply(X_98,identity) = X_98 ),
inference(superposition,[status(thm),theory(equality)],[c_2159,c_443]) ).
tff(c_2208,plain,
! [X_98] : ( multiply(X_98,inverse(X_98)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_2159,c_4]) ).
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_65]) ).
tff(c_32,plain,
least_upper_bound(a,b) = a,
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_10,plain,
! [Y_9,X_8] : ( least_upper_bound(Y_9,X_8) = least_upper_bound(X_8,Y_9) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_158,plain,
! [X_44,Y_45] : ( greatest_lower_bound(X_44,least_upper_bound(X_44,Y_45)) = X_44 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_227,plain,
! [X_48,Y_49] : ( greatest_lower_bound(X_48,least_upper_bound(Y_49,X_48)) = X_48 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_158]) ).
tff(c_265,plain,
greatest_lower_bound(b,a) = b,
inference(superposition,[status(thm),theory(equality)],[c_32,c_227]) ).
tff(c_907,plain,
! [X_71,Y_72,Z_73] : ( greatest_lower_bound(multiply(X_71,Y_72),multiply(X_71,Z_73)) = multiply(X_71,greatest_lower_bound(Y_72,Z_73)) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_25530,plain,
! [X_259,Z_260] : ( multiply(inverse(X_259),greatest_lower_bound(X_259,Z_260)) = greatest_lower_bound(identity,multiply(inverse(X_259),Z_260)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_907]) ).
tff(c_25746,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),b),
inference(superposition,[status(thm),theory(equality)],[c_265,c_25530]) ).
tff(c_25789,plain,
greatest_lower_bound(identity,multiply(inverse(b),a)) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_25746]) ).
tff(c_1537,plain,
! [Y_86,X_87,Z_88] : ( greatest_lower_bound(multiply(Y_86,X_87),multiply(Z_88,X_87)) = multiply(greatest_lower_bound(Y_86,Z_88),X_87) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_1615,plain,
! [Z_88,X_1] : ( multiply(greatest_lower_bound(identity,Z_88),X_1) = greatest_lower_bound(X_1,multiply(Z_88,X_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1537]) ).
tff(c_25805,plain,
! [X_1] : ( greatest_lower_bound(X_1,multiply(multiply(inverse(b),a),X_1)) = multiply(identity,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_25789,c_1615]) ).
tff(c_54846,plain,
! [X_401] : ( greatest_lower_bound(X_401,multiply(inverse(b),multiply(a,X_401))) = X_401 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_25805]) ).
tff(c_55099,plain,
greatest_lower_bound(inverse(a),multiply(inverse(b),identity)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_2208,c_54846]) ).
tff(c_55167,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(demodulation,[status(thm),theory(equality)],[c_2194,c_55099]) ).
tff(c_55169,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_55167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP190-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % 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
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 21:35:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 19.91/8.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.91/8.10
% 19.91/8.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------