%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP174-1 : 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 : n008.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 6.99s 3.38s
% Output : CNFRefutation 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 35 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > inverse > identity > 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(identity,type,
identity: $i ).
tff(f_119,axiom,
identity != a,
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
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(identity,inverse(a)) = inverse(a),
file(unknown,unknown) ).
tff(f_102,axiom,
! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_116,axiom,
greatest_lower_bound(identity,a) = a,
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,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(c_36,plain,
identity != a,
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_220,plain,
! [X_46,Y_47,Z_48] : ( multiply(multiply(X_46,Y_47),Z_48) = multiply(X_46,multiply(Y_47,Z_48)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_235,plain,
! [X_2,Z_48] : ( multiply(inverse(X_2),multiply(X_2,Z_48)) = multiply(identity,Z_48) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_220]) ).
tff(c_655,plain,
! [X_62,Z_63] : ( multiply(inverse(X_62),multiply(X_62,Z_63)) = Z_63 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_235]) ).
tff(c_243,plain,
! [X_2,Z_48] : ( multiply(inverse(X_2),multiply(X_2,Z_48)) = Z_48 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_235]) ).
tff(c_2899,plain,
! [X_104,Z_105] : ( multiply(inverse(inverse(X_104)),Z_105) = multiply(X_104,Z_105) ),
inference(superposition,[status(thm),theory(equality)],[c_655,c_243]) ).
tff(c_682,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_655]) ).
tff(c_2928,plain,
! [X_104] : ( multiply(X_104,identity) = X_104 ),
inference(superposition,[status(thm),theory(equality)],[c_2899,c_682]) ).
tff(c_34,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_183,plain,
! [X_44,Y_45] : ( least_upper_bound(X_44,greatest_lower_bound(X_44,Y_45)) = X_44 ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_198,plain,
least_upper_bound(identity,inverse(a)) = identity,
inference(superposition,[status(thm),theory(equality)],[c_34,c_183]) ).
tff(c_2968,plain,
! [X_104] : ( multiply(X_104,inverse(X_104)) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_2899]) ).
tff(c_32,plain,
greatest_lower_bound(identity,a) = a,
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_210,plain,
least_upper_bound(identity,a) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32,c_183]) ).
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_92]) ).
tff(c_251,plain,
least_upper_bound(a,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_210,c_10]) ).
tff(c_827,plain,
! [Y_67,X_68,Z_69] : ( least_upper_bound(multiply(Y_67,X_68),multiply(Z_69,X_68)) = multiply(least_upper_bound(Y_67,Z_69),X_68) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_5291,plain,
! [Y_130,X_131] : ( multiply(least_upper_bound(Y_130,identity),X_131) = least_upper_bound(multiply(Y_130,X_131),X_131) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_827]) ).
tff(c_5420,plain,
! [X_131] : ( least_upper_bound(multiply(a,X_131),X_131) = multiply(identity,X_131) ),
inference(superposition,[status(thm),theory(equality)],[c_251,c_5291]) ).
tff(c_5479,plain,
! [X_132] : ( least_upper_bound(multiply(a,X_132),X_132) = X_132 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_5420]) ).
tff(c_5557,plain,
least_upper_bound(identity,inverse(a)) = inverse(a),
inference(superposition,[status(thm),theory(equality)],[c_2968,c_5479]) ).
tff(c_5590,plain,
inverse(a) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_198,c_5557]) ).
tff(c_5609,plain,
multiply(a,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_5590,c_2968]) ).
tff(c_5622,plain,
identity = a,
inference(demodulation,[status(thm),theory(equality)],[c_2928,c_5609]) ).
tff(c_5624,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_5622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP174-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n008.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 7 21:31:32 EDT 2025
% 0.10/0.30 % CPUTime :
% 6.99/3.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.99/3.39
% 6.99/3.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------