%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP012-4 : TPTP v9.0.0. Released v1.0.0.
% 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 : n016.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 06:24:45 PM UTC 2025
% Result : Unsatisfiable 3.64s 1.93s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > identity > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(f_65,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X] : ( multiply(X,inverse(X)) = identity ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(f_69,axiom,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file(unknown,unknown) ).
tff(c_8,plain,
! [X_6] : ( multiply(X_6,identity) = X_6 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_86,plain,
! [X_12,Y_13,Z_14] : ( multiply(multiply(X_12,Y_13),Z_14) = multiply(X_12,multiply(Y_13,Z_14)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_10,plain,
! [X_7] : ( multiply(X_7,inverse(X_7)) = identity ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_96,plain,
! [X_12,Y_13] : ( multiply(X_12,multiply(Y_13,inverse(multiply(X_12,Y_13)))) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_86,c_10]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4,plain,
! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_116,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = multiply(identity,Z_14) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_86]) ).
tff(c_312,plain,
! [X_20,Z_21] : ( multiply(inverse(X_20),multiply(X_20,Z_21)) = Z_21 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_116]) ).
tff(c_343,plain,
! [Y_13,X_12] : ( multiply(Y_13,inverse(multiply(X_12,Y_13))) = multiply(inverse(X_12),identity) ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_312]) ).
tff(c_637,plain,
! [Y_28,X_29] : ( multiply(Y_28,inverse(multiply(X_29,Y_28))) = inverse(X_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_343]) ).
tff(c_133,plain,
! [X_2,Z_14] : ( multiply(inverse(X_2),multiply(X_2,Z_14)) = Z_14 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_116]) ).
tff(c_660,plain,
! [Y_28,X_29] : ( multiply(inverse(Y_28),inverse(X_29)) = inverse(multiply(X_29,Y_28)) ),
inference(superposition,[status(thm),theory(equality)],[c_637,c_133]) ).
tff(c_12,plain,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_1362,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_660,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP012-4 : TPTP v9.0.0. Released v1.0.0.
% 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 : n016.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 21:10:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.64/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.93
% 3.64/1.93 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------