%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET008-1 : 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 : n028.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 4.45s 2.04s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 16 |; 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ intersection > difference > subset > member > equal_sets > k > h > member_of_1_not_of_2 > #nlpp > bDa > b > aI_bDa > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: ( $i * $i * $i ) > $i ).
tff(member_of_1_not_of_2,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(k,type,
k: ( $i * $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(intersection,type,
intersection: ( $i * $i * $i ) > $o ).
tff(difference,type,
difference: ( $i * $i * $i ) > $o ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(bDa,type,
bDa: $i ).
tff(aI_bDa,type,
aI_bDa: $i ).
tff(f_229,axiom,
~ intersection(a,bDa,aI_bDa),
file(unknown,unknown) ).
tff(f_135,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set1) ),
file(unknown,unknown) ).
tff(f_232,axiom,
! [A] : ~ member(A,aI_bDa),
file(unknown,unknown) ).
tff(f_141,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set2) ),
file(unknown,unknown) ).
tff(f_227,axiom,
difference(b,a,bDa),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Element,Set1,Set2,A_set] :
( ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ difference(A_set,Set1,Set2) ),
file(unknown,unknown) ).
tff(c_40,plain,
~ intersection(a,bDa,aI_bDa),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_718,plain,
! [Set1_151,Set2_152,Intersection_153] :
( member(h(Set1_151,Set2_152,Intersection_153),Set1_151)
| intersection(Set1_151,Set2_152,Intersection_153)
| member(h(Set1_151,Set2_152,Intersection_153),Intersection_153) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_42,plain,
! [A_56] : ~ member(A_56,aI_bDa),
inference(cnfTransformation,[status(thm)],[f_232]) ).
tff(c_780,plain,
! [Set1_151,Set2_152] :
( member(h(Set1_151,Set2_152,aI_bDa),Set1_151)
| intersection(Set1_151,Set2_152,aI_bDa) ),
inference(resolution,[status(thm)],[c_718,c_42]) ).
tff(c_575,plain,
! [Set1_143,Set2_144,Intersection_145] :
( member(h(Set1_143,Set2_144,Intersection_145),Set2_144)
| intersection(Set1_143,Set2_144,Intersection_145)
| member(h(Set1_143,Set2_144,Intersection_145),Intersection_145) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_781,plain,
! [Set1_154,Set2_155] :
( member(h(Set1_154,Set2_155,aI_bDa),Set2_155)
| intersection(Set1_154,Set2_155,aI_bDa) ),
inference(resolution,[status(thm)],[c_575,c_42]) ).
tff(c_38,plain,
difference(b,a,bDa),
inference(cnfTransformation,[status(thm)],[f_227]) ).
tff(c_137,plain,
! [A_set_78,Set1_79,Set2_80,Element_81] :
( ~ difference(A_set_78,Set1_79,Set2_80)
| ~ member(Element_81,Set2_80)
| ~ member(Element_81,Set1_79) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_140,plain,
! [Element_81] :
( ~ member(Element_81,bDa)
| ~ member(Element_81,a) ),
inference(resolution,[status(thm)],[c_38,c_137]) ).
tff(c_994,plain,
! [Set1_173] :
( ~ member(h(Set1_173,bDa,aI_bDa),a)
| intersection(Set1_173,bDa,aI_bDa) ),
inference(resolution,[status(thm)],[c_781,c_140]) ).
tff(c_998,plain,
intersection(a,bDa,aI_bDa),
inference(resolution,[status(thm)],[c_780,c_994]) ).
tff(c_1004,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_40,c_998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 19:39:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.45/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.52/2.05
% 4.52/2.05 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------