%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP033-4 : 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 : n013.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 2.85s 1.68s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > 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(subgroup_member,type,
subgroup_member: $i > $o ).
tff(j,type,
j: $i > $i ).
tff(f_49,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_125,axiom,
! [A,B,C] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file(unknown,unknown) ).
tff(f_130,axiom,
subgroup_member(a),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X] : product(X,identity,X),
file(unknown,unknown) ).
tff(f_144,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] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_8,plain,
! [X_4] : product(X_4,inverse(X_4),identity),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_69,plain,
! [C_41,A_42,B_43] :
( subgroup_member(C_41)
| ~ product(A_42,inverse(B_43),C_41)
| ~ subgroup_member(B_43)
| ~ subgroup_member(A_42) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_87,plain,
! [X_4] :
( subgroup_member(identity)
| ~ subgroup_member(X_4) ),
inference(resolution,[status(thm)],[c_8,c_69]) ).
tff(c_104,plain,
! [X_4] : ~ subgroup_member(X_4),
inference(splitLeft,[status(thm)],[c_87]) ).
tff(c_20,plain,
subgroup_member(a),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_108,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_104,c_20]) ).
tff(c_109,plain,
subgroup_member(identity),
inference(splitRight,[status(thm)],[c_87]) ).
tff(c_4,plain,
! [X_2] : product(X_2,identity,X_2),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_123,plain,
! [A_45] :
( ~ subgroup_member(A_45)
| ~ product(A_45,j(A_45),j(A_45))
| ~ product(j(A_45),A_45,j(A_45)) ),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_127,plain,
( ~ subgroup_member(identity)
| ~ product(identity,j(identity),j(identity)) ),
inference(resolution,[status(thm)],[c_4,c_123]) ).
tff(c_131,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_109,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP033-4 : TPTP v9.0.0. Released v1.0.0.
% 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
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Apr 7 21:12:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.85/1.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.85/1.68
% 2.85/1.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------