%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP175-3 : 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 06:25:27 PM UTC 2025
% Result : Unsatisfiable 50.94s 34.90s
% Output : CNFRefutation 50.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 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 : 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 : 49 ( 49 !; 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_116,axiom,
least_upper_bound(identity,b) = b,
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_111,axiom,
! [Y,Z,X] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_100,axiom,
! [X] : ( greatest_lower_bound(X,X) = X ),
file(unknown,unknown) ).
tff(f_94,axiom,
! [X,Y,Z] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
file(unknown,unknown) ).
tff(f_109,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_118,axiom,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file(unknown,unknown) ).
tff(c_32,plain,
least_upper_bound(identity,b) = b,
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1575,plain,
! [Y_86,X_87,Z_88] : ( least_upper_bound(multiply(Y_86,X_87),multiply(Z_88,X_87)) = multiply(least_upper_bound(Y_86,Z_88),X_87) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_1811,plain,
! [Z_91,X_92] : ( multiply(least_upper_bound(identity,Z_91),X_92) = least_upper_bound(X_92,multiply(Z_91,X_92)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1575]) ).
tff(c_2457,plain,
! [X_100] : ( least_upper_bound(X_100,multiply(b,X_100)) = multiply(b,X_100) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_1811]) ).
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_104]) ).
tff(c_2502,plain,
! [X_100] : ( greatest_lower_bound(X_100,multiply(b,X_100)) = X_100 ),
inference(superposition,[status(thm),theory(equality)],[c_2457,c_22]) ).
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_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_18,plain,
! [X_17] : ( greatest_lower_bound(X_17,X_17) = X_17 ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_598,plain,
! [X_62,Y_63,Z_64] : ( greatest_lower_bound(greatest_lower_bound(X_62,Y_63),Z_64) = greatest_lower_bound(X_62,greatest_lower_bound(Y_63,Z_64)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_671,plain,
! [X_17,Z_64] : ( greatest_lower_bound(X_17,greatest_lower_bound(X_17,Z_64)) = greatest_lower_bound(X_17,Z_64) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_598]) ).
tff(c_1047,plain,
! [X_74,Y_75,Z_76] : ( greatest_lower_bound(multiply(X_74,Y_75),multiply(X_74,Z_76)) = multiply(X_74,greatest_lower_bound(Y_75,Z_76)) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_1111,plain,
! [X_2,Y_75] : ( multiply(inverse(X_2),greatest_lower_bound(Y_75,X_2)) = greatest_lower_bound(multiply(inverse(X_2),Y_75),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_1047]) ).
tff(c_35348,plain,
! [X_301,Y_302] : ( multiply(inverse(X_301),greatest_lower_bound(Y_302,X_301)) = greatest_lower_bound(identity,multiply(inverse(X_301),Y_302)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1111]) ).
tff(c_35614,plain,
! [X_17,Z_64] : ( multiply(inverse(greatest_lower_bound(X_17,Z_64)),greatest_lower_bound(X_17,Z_64)) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_17,Z_64)),X_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_671,c_35348]) ).
tff(c_69434,plain,
! [X_438,Z_439] : ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X_438,Z_439)),X_438)) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_35614]) ).
tff(c_133151,plain,
! [Y_576,X_577] : ( greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(Y_576,X_577)),X_577)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_69434]) ).
tff(c_133789,plain,
! [X_100] : ( greatest_lower_bound(identity,multiply(inverse(X_100),multiply(b,X_100))) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_2502,c_133151]) ).
tff(c_34,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_158839,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_133789,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP175-3 : 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 21:31:58 EDT 2025
% 0.14/0.34 % CPUTime :
% 50.94/34.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.94/34.91
% 50.94/34.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------