%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET002-1 : 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 : n031.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 08:37:24 PM UTC 2025
% Result : Unsatisfiable 5.42s 2.29s
% Output : CNFRefutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 29 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 52 ( 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ union > subset > member > equal_sets > g > member_of_1_not_of_2 > #nlpp > aUa > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i * $i ) > $o ).
tff(member_of_1_not_of_2,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(g,type,
g: ( $i * $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(aUa,type,
aUa: $i ).
tff(f_156,axiom,
~ equal_sets(aUa,a),
file(unknown,unknown) ).
tff(f_154,axiom,
union(a,a,aUa),
file(unknown,unknown) ).
tff(f_56,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file(unknown,unknown) ).
tff(f_127,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set2)
| member(Element,Union) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [Subset,Superset] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [Set1,Set2] :
( ~ subset(Set1,Set2)
| ~ subset(Set2,Set1)
| equal_sets(Set2,Set1) ),
file(unknown,unknown) ).
tff(f_111,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Union)
| member(Element,Set1)
| member(Element,Set2) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [Subset,Superset] :
( ~ equal_sets(Subset,Superset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [Superset,Subset] :
( ~ equal_sets(Superset,Subset)
| subset(Subset,Superset) ),
file(unknown,unknown) ).
tff(c_28,plain,
~ equal_sets(aUa,a),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_26,plain,
union(a,a,aUa),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_4,plain,
! [Subset_4,Superset_5] :
( member(member_of_1_not_of_2(Subset_4,Superset_5),Subset_4)
| subset(Subset_4,Superset_5) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_90,plain,
! [Element_60,Union_61,Set2_62,Set1_63] :
( member(Element_60,Union_61)
| ~ member(Element_60,Set2_62)
| ~ union(Set1_63,Set2_62,Union_61) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_134,plain,
! [Subset_74,Superset_75,Union_76,Set1_77] :
( member(member_of_1_not_of_2(Subset_74,Superset_75),Union_76)
| ~ union(Set1_77,Subset_74,Union_76)
| subset(Subset_74,Superset_75) ),
inference(resolution,[status(thm)],[c_4,c_90]) ).
tff(c_148,plain,
! [Superset_82] :
( member(member_of_1_not_of_2(a,Superset_82),aUa)
| subset(a,Superset_82) ),
inference(resolution,[status(thm)],[c_26,c_134]) ).
tff(c_6,plain,
! [Subset_6,Superset_7] :
( subset(Subset_6,Superset_7)
| ~ member(member_of_1_not_of_2(Subset_6,Superset_7),Superset_7) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_168,plain,
subset(a,aUa),
inference(resolution,[status(thm)],[c_148,c_6]) ).
tff(c_12,plain,
! [Set2_13,Set1_12] :
( equal_sets(Set2_13,Set1_12)
| ~ subset(Set2_13,Set1_12)
| ~ subset(Set1_12,Set2_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_174,plain,
( equal_sets(a,aUa)
| ~ subset(aUa,a) ),
inference(resolution,[status(thm)],[c_168,c_12]) ).
tff(c_196,plain,
~ subset(aUa,a),
inference(splitLeft,[status(thm)],[c_174]) ).
tff(c_138,plain,
! [Element_78,Set2_79,Set1_80,Union_81] :
( member(Element_78,Set2_79)
| member(Element_78,Set1_80)
| ~ member(Element_78,Union_81)
| ~ union(Set1_80,Set2_79,Union_81) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_1932,plain,
! [Subset_264,Superset_265,Set2_266,Set1_267] :
( member(member_of_1_not_of_2(Subset_264,Superset_265),Set2_266)
| member(member_of_1_not_of_2(Subset_264,Superset_265),Set1_267)
| ~ union(Set1_267,Set2_266,Subset_264)
| subset(Subset_264,Superset_265) ),
inference(resolution,[status(thm)],[c_4,c_138]) ).
tff(c_1939,plain,
! [Superset_268] :
( member(member_of_1_not_of_2(aUa,Superset_268),a)
| subset(aUa,Superset_268) ),
inference(resolution,[status(thm)],[c_26,c_1932]) ).
tff(c_1973,plain,
subset(aUa,a),
inference(resolution,[status(thm)],[c_1939,c_6]) ).
tff(c_2004,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_196,c_196,c_1973]) ).
tff(c_2005,plain,
equal_sets(a,aUa),
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_8,plain,
! [Subset_8,Superset_9] :
( subset(Subset_8,Superset_9)
| ~ equal_sets(Subset_8,Superset_9) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_10,plain,
! [Subset_11,Superset_10] :
( subset(Subset_11,Superset_10)
| ~ equal_sets(Superset_10,Subset_11) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_39,plain,
! [Set2_44,Set1_45] :
( equal_sets(Set2_44,Set1_45)
| ~ subset(Set2_44,Set1_45)
| ~ subset(Set1_45,Set2_44) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_62,plain,
! [Subset_50,Superset_51] :
( equal_sets(Subset_50,Superset_51)
| ~ subset(Superset_51,Subset_50)
| ~ equal_sets(Superset_51,Subset_50) ),
inference(resolution,[status(thm)],[c_10,c_39]) ).
tff(c_75,plain,
! [Superset_9,Subset_8] :
( equal_sets(Superset_9,Subset_8)
| ~ equal_sets(Subset_8,Superset_9) ),
inference(resolution,[status(thm)],[c_8,c_62]) ).
tff(c_2008,plain,
equal_sets(aUa,a),
inference(resolution,[status(thm)],[c_2005,c_75]) ).
tff(c_2012,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_2008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % 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
% 0.12/0.31 % Computer : n031.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Apr 8 19:37:52 EDT 2025
% 0.16/0.32 % CPUTime :
% 5.42/2.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.42/2.29
% 5.42/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------