%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET015-1 : 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/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 : n016.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 08:37:29 PM UTC 2025
% Result : Unsatisfiable 12.27s 4.25s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_sets > equal_elements > union > member_of_1_not_of_2 > intersection > #nlpp > complement > empty_set > bs > as
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(member_of_1_not_of_2,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(bs,type,
bs: $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(as,type,
as: $i ).
tff(f_62,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_96,axiom,
! [X,Xs,Ys] :
( ~ member(X,union(Xs,Ys))
| member(X,Xs)
| member(X,Ys) ),
file(unknown,unknown) ).
tff(f_84,axiom,
! [X,Xs,Ys] :
( ~ member(X,Xs)
| member(X,union(Xs,Ys)) ),
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_89,axiom,
! [X,Ys,Xs] :
( ~ member(X,Ys)
| member(X,union(Xs,Ys)) ),
file(unknown,unknown) ).
tff(f_134,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_169,axiom,
~ equal_sets(union(as,bs),union(bs,as)),
file(unknown,unknown) ).
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_199,plain,
! [X_100,Ys_101,Xs_102] :
( member(X_100,Ys_101)
| member(X_100,Xs_102)
| ~ member(X_100,union(Xs_102,Ys_101)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_1185,plain,
! [Xs_203,Ys_204,Superset_205] :
( member(member_of_1_not_of_2(union(Xs_203,Ys_204),Superset_205),Ys_204)
| member(member_of_1_not_of_2(union(Xs_203,Ys_204),Superset_205),Xs_203)
| subset(union(Xs_203,Ys_204),Superset_205) ),
inference(resolution,[status(thm)],[c_6,c_199]) ).
tff(c_96,plain,
! [X_73,Xs_74,Ys_75] :
( member(X_73,union(Xs_74,Ys_75))
| ~ member(X_73,Xs_74) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
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_101,plain,
! [Subset_7,Xs_74,Ys_75] :
( subset(Subset_7,union(Xs_74,Ys_75))
| ~ member(member_of_1_not_of_2(Subset_7,union(Xs_74,Ys_75)),Xs_74) ),
inference(resolution,[status(thm)],[c_96,c_8]) ).
tff(c_12961,plain,
! [Xs_744,Ys_745,Ys_746] :
( member(member_of_1_not_of_2(union(Xs_744,Ys_745),union(Ys_745,Ys_746)),Xs_744)
| subset(union(Xs_744,Ys_745),union(Ys_745,Ys_746)) ),
inference(resolution,[status(thm)],[c_1185,c_101]) ).
tff(c_108,plain,
! [X_79,Xs_80,Ys_81] :
( member(X_79,union(Xs_80,Ys_81))
| ~ member(X_79,Ys_81) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_113,plain,
! [Subset_7,Xs_80,Ys_81] :
( subset(Subset_7,union(Xs_80,Ys_81))
| ~ member(member_of_1_not_of_2(Subset_7,union(Xs_80,Ys_81)),Ys_81) ),
inference(resolution,[status(thm)],[c_108,c_8]) ).
tff(c_13047,plain,
! [Xs_744,Ys_745] : subset(union(Xs_744,Ys_745),union(Ys_745,Xs_744)),
inference(resolution,[status(thm)],[c_12961,c_113]) ).
tff(c_13057,plain,
! [Xs_747,Ys_748] : subset(union(Xs_747,Ys_748),union(Ys_748,Xs_747)),
inference(resolution,[status(thm)],[c_12961,c_113]) ).
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_13067,plain,
! [Xs_747,Ys_748] :
( equal_sets(union(Xs_747,Ys_748),union(Ys_748,Xs_747))
| ~ subset(union(Ys_748,Xs_747),union(Xs_747,Ys_748)) ),
inference(resolution,[status(thm)],[c_13057,c_30]) ).
tff(c_13073,plain,
! [Xs_747,Ys_748] : equal_sets(union(Xs_747,Ys_748),union(Ys_748,Xs_747)),
inference(demodulation,[status(thm),theory(equality)],[c_13047,c_13067]) ).
tff(c_44,plain,
~ equal_sets(union(as,bs),union(bs,as)),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_13076,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13073,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET015-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 19:41:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 12.27/4.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.27/4.25
% 12.27/4.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------