%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP206-1 : TPTP v9.0.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/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 06:25:33 PM UTC 2025
% Result : Unsatisfiable 3.09s 1.88s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ right_division > multiply > left_division > #nlpp > right_inverse > left_inverse > identity > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(right_inverse,type,
right_inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(left_division,type,
left_division: ( $i * $i ) > $i ).
tff(right_division,type,
right_division: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(left_inverse,type,
left_inverse: $i > $i ).
tff(c,type,
c: $i ).
tff(f_26,axiom,
! [X] : ( multiply(X,identity) = X ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X,Y,Z] : ( multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)) ),
file(unknown,unknown) ).
tff(f_44,axiom,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_2] : ( multiply(X_2,identity) = X_2 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_2,plain,
! [X_1] : ( multiply(identity,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_305,plain,
! [X_33,Y_34,Z_35] : ( multiply(multiply(X_33,Y_34),multiply(Z_35,X_33)) = multiply(X_33,multiply(multiply(Y_34,Z_35),X_33)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_359,plain,
! [X_1,Y_34] : ( multiply(X_1,multiply(multiply(Y_34,identity),X_1)) = multiply(multiply(X_1,Y_34),X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_305]) ).
tff(c_373,plain,
! [X_1,Y_34] : ( multiply(multiply(X_1,Y_34),X_1) = multiply(X_1,multiply(Y_34,X_1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_359]) ).
tff(c_18,plain,
! [X_13,Y_14,Z_15] : ( multiply(multiply(X_13,Y_14),multiply(Z_15,X_13)) = multiply(X_13,multiply(multiply(Y_14,Z_15),X_13)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_20,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_21,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(a,multiply(multiply(b,c),a)),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_20]) ).
tff(c_619,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_373,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP206-1 : TPTP v9.0.0. Released v2.3.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.33 % Computer : n021.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 21:36:43 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.09/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.09/1.88
% 3.09/1.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------