%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP166-2 : 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/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 : n021.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 06:25:24 PM UTC 2025
% Result : Unsatisfiable 17.42s 7.66s
% Output : CNFRefutation 17.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% 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 ( 3 avg)
% Maximal term depth : 4 ( 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 : 55 ( 55 !; 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_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_97,axiom,
! [X] : ( least_upper_bound(X,X) = X ),
file(unknown,unknown) ).
tff(f_116,axiom,
greatest_lower_bound(b,identity) = identity,
file(unknown,unknown) ).
tff(f_101,axiom,
! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y,Z] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_106,axiom,
! [X,Y,Z] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_118,axiom,
greatest_lower_bound(a,multiply(a,b)) != a,
file(unknown,unknown) ).
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_309,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_63]) ).
tff(c_324,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_309]) ).
tff(c_332,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_324]) ).
tff(c_480,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_324]) ).
tff(c_1690,plain,
! [X_88,Z_89] : ( multiply(inverse(inverse(X_88)),Z_89) = multiply(X_88,Z_89) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_480]) ).
tff(c_501,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_480]) ).
tff(c_1725,plain,
! [X_88] : ( multiply(X_88,identity) = X_88 ),
inference(superposition,[status(thm),theory(equality)],[c_1690,c_501]) ).
tff(c_16,plain,
! [X_16] : ( least_upper_bound(X_16,X_16) = X_16 ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_34,plain,
greatest_lower_bound(b,identity) = identity,
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_145,plain,
! [X_42,Y_43] : ( least_upper_bound(X_42,greatest_lower_bound(X_42,Y_43)) = X_42 ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_166,plain,
least_upper_bound(b,identity) = b,
inference(superposition,[status(thm),theory(equality)],[c_34,c_145]) ).
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_91]) ).
tff(c_604,plain,
! [X_61,Y_62,Z_63] : ( least_upper_bound(least_upper_bound(X_61,Y_62),Z_63) = least_upper_bound(X_61,least_upper_bound(Y_62,Z_63)) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4401,plain,
! [Y_123,X_124,Z_125] : ( least_upper_bound(least_upper_bound(Y_123,X_124),Z_125) = least_upper_bound(X_124,least_upper_bound(Y_123,Z_125)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_604]) ).
tff(c_5450,plain,
! [Z_133] : ( least_upper_bound(identity,least_upper_bound(b,Z_133)) = least_upper_bound(b,Z_133) ),
inference(superposition,[status(thm),theory(equality)],[c_166,c_4401]) ).
tff(c_5548,plain,
least_upper_bound(identity,b) = least_upper_bound(b,b),
inference(superposition,[status(thm),theory(equality)],[c_16,c_5450]) ).
tff(c_5575,plain,
least_upper_bound(identity,b) = b,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5548]) ).
tff(c_1594,plain,
! [X_85,Y_86,Z_87] : ( least_upper_bound(multiply(X_85,Y_86),multiply(X_85,Z_87)) = multiply(X_85,least_upper_bound(Y_86,Z_87)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_22,plain,
! [X_20,Y_21] : ( greatest_lower_bound(X_20,least_upper_bound(X_20,Y_21)) = X_20 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_60471,plain,
! [X_371,Y_372,Z_373] : ( greatest_lower_bound(multiply(X_371,Y_372),multiply(X_371,least_upper_bound(Y_372,Z_373))) = multiply(X_371,Y_372) ),
inference(superposition,[status(thm),theory(equality)],[c_1594,c_22]) ).
tff(c_61026,plain,
! [X_371] : ( greatest_lower_bound(multiply(X_371,identity),multiply(X_371,b)) = multiply(X_371,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_5575,c_60471]) ).
tff(c_61252,plain,
! [X_371] : ( greatest_lower_bound(X_371,multiply(X_371,b)) = X_371 ),
inference(demodulation,[status(thm),theory(equality)],[c_1725,c_1725,c_61026]) ).
tff(c_36,plain,
greatest_lower_bound(a,multiply(a,b)) != a,
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_61285,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_61252,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP166-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:30:43 EDT 2025
% 0.12/0.34 % CPUTime :
% 17.42/7.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.42/7.67
% 17.42/7.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------