%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP166-4 : 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/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 : n027.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 7.80s 2.93s
% Output : CNFRefutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 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 : 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 : 26 ( 26 !; 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_90,axiom,
! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_117,axiom,
greatest_lower_bound(b,identity) = identity,
file(unknown,unknown) ).
tff(f_113,axiom,
! [Y,Z,X] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
file(unknown,unknown) ).
tff(f_119,axiom,
greatest_lower_bound(a,multiply(b,a)) != a,
file(unknown,unknown) ).
tff(c_8,plain,
! [Y_7,X_6] : ( greatest_lower_bound(Y_7,X_6) = greatest_lower_bound(X_6,Y_7) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
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_64]) ).
tff(c_34,plain,
greatest_lower_bound(b,identity) = identity,
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_1062,plain,
! [Y_73,X_74,Z_75] : ( greatest_lower_bound(multiply(Y_73,X_74),multiply(Z_75,X_74)) = multiply(greatest_lower_bound(Y_73,Z_75),X_74) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_12198,plain,
! [Y_172,X_173] : ( multiply(greatest_lower_bound(Y_172,identity),X_173) = greatest_lower_bound(multiply(Y_172,X_173),X_173) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1062]) ).
tff(c_12439,plain,
! [X_173] : ( greatest_lower_bound(multiply(b,X_173),X_173) = multiply(identity,X_173) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_12198]) ).
tff(c_12485,plain,
! [X_174] : ( greatest_lower_bound(multiply(b,X_174),X_174) = X_174 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12439]) ).
tff(c_1129,plain,
! [Y_73,X_1] : ( multiply(greatest_lower_bound(Y_73,identity),X_1) = greatest_lower_bound(multiply(Y_73,X_1),X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1062]) ).
tff(c_12492,plain,
! [X_1] : ( greatest_lower_bound(multiply(multiply(b,identity),X_1),X_1) = multiply(identity,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_12485,c_1129]) ).
tff(c_12642,plain,
! [X_1] : ( greatest_lower_bound(X_1,multiply(b,X_1)) = X_1 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2,c_6,c_2,c_12492]) ).
tff(c_36,plain,
greatest_lower_bound(a,multiply(b,a)) != a,
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_12672,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12642,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n027.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 21:30:06 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.80/2.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.80/2.93
% 7.80/2.93 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------