%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP186-4 : 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 : n023.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 06:25:30 PM UTC 2025
% Result : Unsatisfiable 37.63s 24.10s
% Output : CNFRefutation 37.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 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 : 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 : 19 ( 19 !; 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_91,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [X] : ( inverse(inverse(X)) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
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_121,axiom,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file(unknown,unknown) ).
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_34,plain,
! [X_34] : ( inverse(inverse(X_34)) = X_34 ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_92,plain,
! [X_41] : ( multiply(inverse(X_41),X_41) = identity ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_99,plain,
! [X_34] : ( multiply(X_34,inverse(X_34)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_92]) ).
tff(c_1621,plain,
! [X_93,Y_94,Z_95] : ( least_upper_bound(multiply(X_93,Y_94),multiply(X_93,Z_95)) = multiply(X_93,least_upper_bound(Y_94,Z_95)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_1712,plain,
! [X_34,Y_94] : ( multiply(X_34,least_upper_bound(Y_94,inverse(X_34))) = least_upper_bound(multiply(X_34,Y_94),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_99,c_1621]) ).
tff(c_1740,plain,
! [X_34,Y_94] : ( multiply(X_34,least_upper_bound(Y_94,inverse(X_34))) = least_upper_bound(identity,multiply(X_34,Y_94)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_1712]) ).
tff(c_38,plain,
multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),identity),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_39,plain,
multiply(a,least_upper_bound(b,inverse(a))) != least_upper_bound(identity,multiply(a,b)),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_10,c_38]) ).
tff(c_162646,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1740,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP186-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 21:34:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 37.63/24.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.69/24.10
% 37.69/24.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------