%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP169-1 : 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 : n022.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 06:25:25 PM UTC 2025
% Result : Unsatisfiable 20.54s 10.02s
% Output : CNFRefutation 20.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 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 : 63 ( 63 !; 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_120,axiom,
least_upper_bound(a,b) != a,
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_118,axiom,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file(unknown,unknown) ).
tff(f_109,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_106,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_115,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_104,axiom,
! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(c_34,plain,
least_upper_bound(a,b) != a,
inference(cnfTransformation,[status(thm)],[f_120]) ).
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_92]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_287,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_66]) ).
tff(c_302,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_287]) ).
tff(c_310,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_302]) ).
tff(c_312,plain,
! [X_53,Z_54] : ( multiply(inverse(X_53),multiply(X_53,Z_54)) = Z_54 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_302]) ).
tff(c_1079,plain,
! [X_77,Z_78] : ( multiply(inverse(inverse(X_77)),Z_78) = multiply(X_77,Z_78) ),
inference(superposition,[status(thm),theory(equality)],[c_310,c_312]) ).
tff(c_333,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_312]) ).
tff(c_1096,plain,
! [X_77] : ( multiply(X_77,identity) = X_77 ),
inference(superposition,[status(thm),theory(equality)],[c_1079,c_333]) ).
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_66]) ).
tff(c_1139,plain,
! [X_79] : ( multiply(X_79,identity) = X_79 ),
inference(superposition,[status(thm),theory(equality)],[c_1079,c_333]) ).
tff(c_324,plain,
! [X_2,Z_52] : ( multiply(inverse(inverse(X_2)),Z_52) = multiply(X_2,Z_52) ),
inference(superposition,[status(thm),theory(equality)],[c_310,c_312]) ).
tff(c_1146,plain,
! [X_2] : ( inverse(inverse(X_2)) = multiply(X_2,identity) ),
inference(superposition,[status(thm),theory(equality)],[c_1139,c_324]) ).
tff(c_1205,plain,
! [X_2] : ( inverse(inverse(X_2)) = X_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_1096,c_1146]) ).
tff(c_32,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_1219,plain,
! [X_80,Y_81,Z_82] : ( least_upper_bound(multiply(X_80,Y_81),multiply(X_80,Z_82)) = multiply(X_80,least_upper_bound(Y_81,Z_82)) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
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_106]) ).
tff(c_22891,plain,
! [X_268,Y_269,Z_270] : ( greatest_lower_bound(multiply(X_268,Y_269),multiply(X_268,least_upper_bound(Y_269,Z_270))) = multiply(X_268,Y_269) ),
inference(superposition,[status(thm),theory(equality)],[c_1219,c_22]) ).
tff(c_23257,plain,
! [X_2,Z_270] : ( greatest_lower_bound(identity,multiply(inverse(X_2),least_upper_bound(X_2,Z_270))) = multiply(inverse(X_2),X_2) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_22891]) ).
tff(c_26051,plain,
! [X_286,Z_287] : ( greatest_lower_bound(identity,multiply(inverse(X_286),least_upper_bound(X_286,Z_287))) = identity ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_23257]) ).
tff(c_26309,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(a)),inverse(b))) = identity,
inference(superposition,[status(thm),theory(equality)],[c_32,c_26051]) ).
tff(c_26381,plain,
greatest_lower_bound(identity,multiply(a,inverse(b))) = identity,
inference(demodulation,[status(thm),theory(equality)],[c_1205,c_26309]) ).
tff(c_1360,plain,
! [Y_84,X_85,Z_86] : ( greatest_lower_bound(multiply(Y_84,X_85),multiply(Z_86,X_85)) = multiply(greatest_lower_bound(Y_84,Z_86),X_85) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1432,plain,
! [Z_86,X_1] : ( multiply(greatest_lower_bound(identity,Z_86),X_1) = greatest_lower_bound(X_1,multiply(Z_86,X_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1360]) ).
tff(c_26403,plain,
! [X_1] : ( greatest_lower_bound(X_1,multiply(multiply(a,inverse(b)),X_1)) = multiply(identity,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_26381,c_1432]) ).
tff(c_48566,plain,
! [X_388] : ( greatest_lower_bound(X_388,multiply(a,multiply(inverse(b),X_388))) = X_388 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_26403]) ).
tff(c_48822,plain,
greatest_lower_bound(b,multiply(a,identity)) = b,
inference(superposition,[status(thm),theory(equality)],[c_4,c_48566]) ).
tff(c_48875,plain,
greatest_lower_bound(a,b) = b,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1096,c_48822]) ).
tff(c_20,plain,
! [X_18,Y_19] : ( least_upper_bound(X_18,greatest_lower_bound(X_18,Y_19)) = X_18 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_49479,plain,
least_upper_bound(a,b) = a,
inference(superposition,[status(thm),theory(equality)],[c_48875,c_20]) ).
tff(c_49511,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_49479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP169-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.12 % 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
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 21:30:36 EDT 2025
% 0.13/0.33 % CPUTime :
% 20.54/10.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.64/10.03
% 20.64/10.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------