%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP037-3 : 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/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 : n032.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 06:24:50 PM UTC 2025
% Result : Unsatisfiable 2.98s 1.63s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > subgroup_member > multiply > #nlpp > inverse > another_inverse > identity > another_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(another_inverse,type,
another_inverse: $i > $i ).
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(another_identity,type,
another_identity: $i ).
tff(identity,type,
identity: $i ).
tff(subgroup_member,type,
subgroup_member: $i > $o ).
tff(f_174,axiom,
inverse(a) != another_inverse(a),
file(unknown,unknown) ).
tff(f_171,axiom,
subgroup_member(a),
file(unknown,unknown) ).
tff(f_149,axiom,
! [A] :
( ~ subgroup_member(A)
| product(another_inverse(A),A,another_identity) ),
file(unknown,unknown) ).
tff(f_172,axiom,
subgroup_member(another_identity),
file(unknown,unknown) ).
tff(f_139,axiom,
! [A] :
( ~ subgroup_member(A)
| product(A,another_identity,A) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_170,axiom,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| ( D = A ) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X] : product(inverse(X),X,identity),
file(unknown,unknown) ).
tff(c_38,plain,
inverse(a) != another_inverse(a),
inference(cnfTransformation,[status(thm)],[f_174]) ).
tff(c_34,plain,
subgroup_member(a),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_26,plain,
! [A_29] :
( product(another_inverse(A_29),A_29,another_identity)
| ~ subgroup_member(A_29) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_36,plain,
subgroup_member(another_identity),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_22,plain,
! [A_27] :
( product(A_27,another_identity,A_27)
| ~ subgroup_member(A_27) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_49,plain,
! [D_50,A_51,B_52,C_53] :
( ( D_50 = A_51 )
| ~ product(D_50,B_52,C_53)
| ~ product(A_51,B_52,C_53) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_77,plain,
! [A_54,X_55] :
( ( identity = A_54 )
| ~ product(A_54,X_55,X_55) ),
inference(resolution,[status(thm)],[c_2,c_49]) ).
tff(c_85,plain,
( ( identity = another_identity )
| ~ subgroup_member(another_identity) ),
inference(resolution,[status(thm)],[c_22,c_77]) ).
tff(c_105,plain,
identity = another_identity,
inference(demodulation,[status(thm),theory(equality)],[c_36,c_85]) ).
tff(c_6,plain,
! [X_3] : product(inverse(X_3),X_3,identity),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_74,plain,
! [X_3,A_51] :
( ( inverse(X_3) = A_51 )
| ~ product(A_51,X_3,identity) ),
inference(resolution,[status(thm)],[c_6,c_49]) ).
tff(c_536,plain,
! [X_97,A_98] :
( ( inverse(X_97) = A_98 )
| ~ product(A_98,X_97,another_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_105,c_74]) ).
tff(c_615,plain,
! [A_101] :
( ( inverse(A_101) = another_inverse(A_101) )
| ~ subgroup_member(A_101) ),
inference(resolution,[status(thm)],[c_26,c_536]) ).
tff(c_624,plain,
inverse(a) = another_inverse(a),
inference(resolution,[status(thm)],[c_34,c_615]) ).
tff(c_634,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : GRP037-3 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.08 % 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
% 0.08/0.26 % Computer : n032.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Apr 7 21:12:31 EDT 2025
% 0.08/0.27 % CPUTime :
% 2.98/1.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.63
% 2.98/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------