%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET004-1 : 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/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 : n010.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 08:37:25 PM UTC 2025
% Result : Unsatisfiable 4.05s 2.00s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ union > subset > member > equal_sets > g > member_of_1_not_of_2 > #nlpp > b > aUb > 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(b,type,
b: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(aUb,type,
aUb: $i ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(f_156,axiom,
~ subset(a,aUb),
file(unknown,unknown) ).
tff(f_154,axiom,
union(a,b,aUb),
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_119,axiom,
! [Set1,Set2,Union,Element] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| 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(c_28,plain,
~ subset(a,aUb),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_26,plain,
union(a,b,aUb),
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_102,plain,
! [Element_64,Union_65,Set1_66,Set2_67] :
( member(Element_64,Union_65)
| ~ member(Element_64,Set1_66)
| ~ union(Set1_66,Set2_67,Union_65) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_599,plain,
! [Subset_111,Superset_112,Union_113,Set2_114] :
( member(member_of_1_not_of_2(Subset_111,Superset_112),Union_113)
| ~ union(Subset_111,Set2_114,Union_113)
| subset(Subset_111,Superset_112) ),
inference(resolution,[status(thm)],[c_4,c_102]) ).
tff(c_603,plain,
! [Superset_115] :
( member(member_of_1_not_of_2(a,Superset_115),aUb)
| subset(a,Superset_115) ),
inference(resolution,[status(thm)],[c_26,c_599]) ).
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_619,plain,
subset(a,aUb),
inference(resolution,[status(thm)],[c_603,c_6]) ).
tff(c_629,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_28,c_619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET004-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.13 % 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
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 19:39:33 EDT 2025
% 0.14/0.35 % CPUTime :
% 4.05/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.05/2.01
% 4.05/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------