%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET012-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 : 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 08:37:26 PM UTC 2025
% Result : Unsatisfiable 7.22s 2.69s
% Output : CNFRefutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_sets > equal_elements > union > member_of_1_not_of_2 > intersection > #nlpp > complement > empty_set > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(member_of_1_not_of_2,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(equal_elements,type,
equal_elements: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(f_72,axiom,
! [X,Xs] :
( member(X,Xs)
| member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X,Xs] :
( ~ member(X,Xs)
| ~ member(X,complement(Xs)) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_134,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_142,axiom,
! [Xs,Ys] :
( ~ equal_sets(Xs,Ys)
| equal_sets(Ys,Xs) ),
file(unknown,unknown) ).
tff(f_169,axiom,
~ equal_sets(complement(complement(a)),a),
file(unknown,unknown) ).
tff(c_10,plain,
! [X_9,Xs_10] :
( member(X_9,complement(Xs_10))
| member(X_9,Xs_10) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_78,plain,
! [Subset_69,Superset_70] :
( member(member_of_1_not_of_2(Subset_69,Superset_70),Subset_69)
| subset(Subset_69,Superset_70) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_12,plain,
! [X_11,Xs_12] :
( ~ member(X_11,complement(Xs_12))
| ~ member(X_11,Xs_12) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_219,plain,
! [Xs_103,Superset_104] :
( ~ member(member_of_1_not_of_2(complement(Xs_103),Superset_104),Xs_103)
| subset(complement(Xs_103),Superset_104) ),
inference(resolution,[status(thm)],[c_78,c_12]) ).
tff(c_4812,plain,
! [Xs_402,Superset_403] :
( subset(complement(complement(Xs_402)),Superset_403)
| member(member_of_1_not_of_2(complement(complement(Xs_402)),Superset_403),Xs_402) ),
inference(resolution,[status(thm)],[c_10,c_219]) ).
tff(c_8,plain,
! [Subset_7,Superset_8] :
( subset(Subset_7,Superset_8)
| ~ member(member_of_1_not_of_2(Subset_7,Superset_8),Superset_8) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4889,plain,
! [Xs_402] : subset(complement(complement(Xs_402)),Xs_402),
inference(resolution,[status(thm)],[c_4812,c_8]) ).
tff(c_6,plain,
! [Subset_5,Superset_6] :
( member(member_of_1_not_of_2(Subset_5,Superset_6),Subset_5)
| subset(Subset_5,Superset_6) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_67,plain,
! [Subset_67,Superset_68] :
( subset(Subset_67,Superset_68)
| ~ member(member_of_1_not_of_2(Subset_67,Superset_68),Superset_68) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_240,plain,
! [Subset_105,Xs_106] :
( subset(Subset_105,complement(Xs_106))
| member(member_of_1_not_of_2(Subset_105,complement(Xs_106)),Xs_106) ),
inference(resolution,[status(thm)],[c_10,c_67]) ).
tff(c_5071,plain,
! [Subset_422,Xs_423] :
( ~ member(member_of_1_not_of_2(Subset_422,complement(complement(Xs_423))),Xs_423)
| subset(Subset_422,complement(complement(Xs_423))) ),
inference(resolution,[status(thm)],[c_240,c_12]) ).
tff(c_5173,plain,
! [Subset_424] : subset(Subset_424,complement(complement(Subset_424))),
inference(resolution,[status(thm)],[c_6,c_5071]) ).
tff(c_30,plain,
! [Set2_36,Set1_35] :
( equal_sets(Set2_36,Set1_35)
| ~ subset(Set2_36,Set1_35)
| ~ subset(Set1_35,Set2_36) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_5185,plain,
! [Subset_424] :
( equal_sets(Subset_424,complement(complement(Subset_424)))
| ~ subset(complement(complement(Subset_424)),Subset_424) ),
inference(resolution,[status(thm)],[c_5173,c_30]) ).
tff(c_5196,plain,
! [Subset_425] : equal_sets(Subset_425,complement(complement(Subset_425))),
inference(demodulation,[status(thm),theory(equality)],[c_4889,c_5185]) ).
tff(c_34,plain,
! [Ys_39,Xs_38] :
( equal_sets(Ys_39,Xs_38)
| ~ equal_sets(Xs_38,Ys_39) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_5243,plain,
! [Subset_425] : equal_sets(complement(complement(Subset_425)),Subset_425),
inference(resolution,[status(thm)],[c_5196,c_34]) ).
tff(c_44,plain,
~ equal_sets(complement(complement(a)),a),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_5247,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5243,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET012-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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
% 0.14/0.34 % Computer : n021.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 : Tue Apr 8 19:40:29 EDT 2025
% 0.14/0.34 % CPUTime :
% 7.22/2.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.22/2.69
% 7.22/2.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------