%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP166-1 : 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 : 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 45.41s 33.69s
% Output : CNFRefutation 45.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 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 : 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 : 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_91,axiom,
! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
file(unknown,unknown) ).
tff(f_117,axiom,
least_upper_bound(b,identity) = b,
file(unknown,unknown) ).
tff(f_103,axiom,
! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_108,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_101,axiom,
! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
file(unknown,unknown) ).
tff(f_119,axiom,
least_upper_bound(a,multiply(a,b)) != multiply(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_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_630,plain,
! [X_58,Y_59,Z_60] : ( multiply(multiply(X_58,Y_59),Z_60) = multiply(X_58,multiply(Y_59,Z_60)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_645,plain,
! [X_2,Z_60] : ( multiply(inverse(X_2),multiply(X_2,Z_60)) = multiply(identity,Z_60) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_630]) ).
tff(c_653,plain,
! [X_2,Z_60] : ( multiply(inverse(X_2),multiply(X_2,Z_60)) = Z_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_645]) ).
tff(c_723,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_645]) ).
tff(c_2234,plain,
! [X_96,Z_97] : ( multiply(inverse(inverse(X_96)),Z_97) = multiply(X_96,Z_97) ),
inference(superposition,[status(thm),theory(equality)],[c_653,c_723]) ).
tff(c_744,plain,
! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_723]) ).
tff(c_2266,plain,
! [X_96] : ( multiply(X_96,identity) = X_96 ),
inference(superposition,[status(thm),theory(equality)],[c_2234,c_744]) ).
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_89]) ).
tff(c_34,plain,
least_upper_bound(b,identity) = b,
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_145,plain,
! [X_42,Y_43] : ( greatest_lower_bound(X_42,least_upper_bound(X_42,Y_43)) = X_42 ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_199,plain,
! [Y_46,X_47] : ( greatest_lower_bound(Y_46,least_upper_bound(X_47,Y_46)) = Y_46 ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_145]) ).
tff(c_234,plain,
greatest_lower_bound(identity,b) = identity,
inference(superposition,[status(thm),theory(equality)],[c_34,c_199]) ).
tff(c_276,plain,
greatest_lower_bound(b,identity) = identity,
inference(superposition,[status(thm),theory(equality)],[c_8,c_234]) ).
tff(c_1255,plain,
! [X_78,Y_79,Z_80] : ( greatest_lower_bound(multiply(X_78,Y_79),multiply(X_78,Z_80)) = multiply(X_78,greatest_lower_bound(Y_79,Z_80)) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
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_101]) ).
tff(c_43472,plain,
! [X_310,Y_311,Z_312] : ( least_upper_bound(multiply(X_310,Y_311),multiply(X_310,greatest_lower_bound(Y_311,Z_312))) = multiply(X_310,Y_311) ),
inference(superposition,[status(thm),theory(equality)],[c_1255,c_20]) ).
tff(c_43834,plain,
! [X_310] : ( least_upper_bound(multiply(X_310,b),multiply(X_310,identity)) = multiply(X_310,b) ),
inference(superposition,[status(thm),theory(equality)],[c_276,c_43472]) ).
tff(c_43953,plain,
! [X_310] : ( least_upper_bound(X_310,multiply(X_310,b)) = multiply(X_310,b) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2266,c_43834]) ).
tff(c_36,plain,
least_upper_bound(a,multiply(a,b)) != multiply(a,b),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_212061,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_43953,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP166-1 : 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 21:30:21 EDT 2025
% 0.13/0.34 % CPUTime :
% 45.41/33.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.41/33.70
% 45.41/33.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------