%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP033-3 : TPTP v9.0.0. Bugfixed v4.0.0.
% 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 : n019.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 06:24:49 PM UTC 2025
% Result : Unsatisfiable 3.91s 2.02s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > equalish > subgroup_member > multiply > #nlpp > j > inverse > identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(identity,type,
identity: $i ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(subgroup_member,type,
subgroup_member: $i > $o ).
tff(j,type,
j: $i > $i ).
tff(f_31,axiom,
! [X] : equalish(X,X),
file(unknown,unknown) ).
tff(f_99,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_105,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_150,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_157,axiom,
subgroup_member(a),
file(unknown,unknown) ).
tff(f_101,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y,W,Z] :
( ~ equalish(X,Y)
| ~ product(X,W,Z)
| product(Y,W,Z) ),
file(unknown,unknown) ).
tff(f_171,axiom,
! [A] :
( ~ product(j(A),A,j(A))
| ~ product(A,j(A),j(A))
| ~ subgroup_member(A) ),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : equalish(X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_22,plain,
! [X_29] : product(identity,X_29,X_29),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_28,plain,
! [X_32] : product(X_32,inverse(X_32),identity),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_134,plain,
! [C_91,A_92,B_93] :
( subgroup_member(C_91)
| ~ product(A_92,inverse(B_93),C_91)
| ~ subgroup_member(B_93)
| ~ subgroup_member(A_92) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_151,plain,
! [X_32] :
( subgroup_member(identity)
| ~ subgroup_member(X_32) ),
inference(resolution,[status(thm)],[c_28,c_134]) ).
tff(c_154,plain,
! [X_32] : ~ subgroup_member(X_32),
inference(splitLeft,[status(thm)],[c_151]) ).
tff(c_40,plain,
subgroup_member(a),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_161,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_154,c_40]) ).
tff(c_162,plain,
subgroup_member(identity),
inference(splitRight,[status(thm)],[c_151]) ).
tff(c_24,plain,
! [X_30] : product(X_30,identity,X_30),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_315,plain,
! [Y_112,W_113,Z_114,X_115] :
( product(Y_112,W_113,Z_114)
| ~ product(X_115,W_113,Z_114)
| ~ equalish(X_115,Y_112) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_339,plain,
! [Y_112,X_30] :
( product(Y_112,identity,X_30)
| ~ equalish(X_30,Y_112) ),
inference(resolution,[status(thm)],[c_24,c_315]) ).
tff(c_481,plain,
! [A_131] :
( ~ subgroup_member(A_131)
| ~ product(A_131,j(A_131),j(A_131))
| ~ product(j(A_131),A_131,j(A_131)) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_485,plain,
( ~ subgroup_member(identity)
| ~ product(identity,j(identity),j(identity))
| ~ equalish(j(identity),j(identity)) ),
inference(resolution,[status(thm)],[c_339,c_481]) ).
tff(c_497,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_22,c_162,c_485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP033-3 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.03/0.13 % 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 : n019.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 21:12:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.91/2.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/2.02
% 3.91/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------