TSTP Solution File: TOP001-2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : TOP001-2 : TPTP v8.1.2. 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 : n013.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 : Tue Aug 22 11:18:39 EDT 2023
% Result : Unsatisfiable 6.73s 2.58s
% Output : CNFRefutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 53 ( 10 unt; 12 typ; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 97 ( 47 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 81 (; 81 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset_sets > equal_sets > element_of_set > element_of_collection > basis > f10 > in_1st_set > f1 > #nlpp > union_of_members > top_of_basis > f > cx
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_sets,type,
subset_sets: ( $i * $i ) > $o ).
tff(basis,type,
basis: ( $i * $i ) > $o ).
tff(element_of_collection,type,
element_of_collection: ( $i * $i ) > $o ).
tff(union_of_members,type,
union_of_members: $i > $i ).
tff(f,type,
f: $i ).
tff(element_of_set,type,
element_of_set: ( $i * $i ) > $o ).
tff(cx,type,
cx: $i ).
tff(top_of_basis,type,
top_of_basis: $i > $i ).
tff(in_1st_set,type,
in_1st_set: ( $i * $i ) > $i ).
tff(equal_sets,type,
equal_sets: ( $i * $i ) > $o ).
tff(f10,type,
f10: ( $i * $i * $i ) > $i ).
tff(f1,type,
f1: ( $i * $i ) > $i ).
tff(f_93,axiom,
basis(cx,f),
file(unknown,unknown) ).
tff(f_51,axiom,
! [X,Vf] :
( ~ basis(X,Vf)
| equal_sets(union_of_members(Vf),X) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [X,Y] :
( ~ equal_sets(X,Y)
| subset_sets(X,Y) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X] : subset_sets(X,X),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] :
( subset_sets(X,Y)
| element_of_set(in_1st_set(X,Y),X) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X,Y,U] :
( ~ subset_sets(X,Y)
| ~ element_of_set(U,X)
| element_of_set(U,Y) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [U,Vf] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [U,Vf] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [U,Vf,X] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [U,Vf,X] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) ),
file(unknown,unknown) ).
tff(f_45,axiom,
! [U,Vf,Uu1] :
( element_of_set(U,union_of_members(Vf))
| ~ element_of_set(U,Uu1)
| ~ element_of_collection(Uu1,Vf) ),
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y] :
( subset_sets(X,Y)
| ~ element_of_set(in_1st_set(X,Y),Y) ),
file(unknown,unknown) ).
tff(f_95,axiom,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file(unknown,unknown) ).
tff(c_24,plain,
basis(cx,f),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_8,plain,
! [Vf_9,X_8] :
( equal_sets(union_of_members(Vf_9),X_8)
| ~ basis(X_8,Vf_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_18,plain,
! [X_20,Y_21] :
( subset_sets(X_20,Y_21)
| ~ equal_sets(X_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_14,plain,
! [X_16] : subset_sets(X_16,X_16),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_20,plain,
! [X_22,Y_23] :
( element_of_set(in_1st_set(X_22,Y_23),X_22)
| subset_sets(X_22,Y_23) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_46,plain,
! [U_35,Y_36,X_37] :
( element_of_set(U_35,Y_36)
| ~ element_of_set(U_35,X_37)
| ~ subset_sets(X_37,Y_36) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_60,plain,
! [X_45,Y_46,Y_47] :
( element_of_set(in_1st_set(X_45,Y_46),Y_47)
| ~ subset_sets(X_45,Y_47)
| subset_sets(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_20,c_46]) ).
tff(c_4,plain,
! [Vf_4,U_3] :
( element_of_collection(f1(Vf_4,U_3),Vf_4)
| ~ element_of_set(U_3,union_of_members(Vf_4)) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_70,plain,
! [Vf_4,X_45,Y_46] :
( element_of_collection(f1(Vf_4,in_1st_set(X_45,Y_46)),Vf_4)
| ~ subset_sets(X_45,union_of_members(Vf_4))
| subset_sets(X_45,Y_46) ),
inference(resolution,[status(thm)],[c_60,c_4]) ).
tff(c_2,plain,
! [U_1,Vf_2] :
( element_of_set(U_1,f1(Vf_2,U_1))
| ~ element_of_set(U_1,union_of_members(Vf_2)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_10,plain,
! [X_12,Vf_11,U_10] :
( element_of_set(X_12,f10(Vf_11,U_10,X_12))
| ~ element_of_set(X_12,U_10)
| ~ element_of_collection(U_10,top_of_basis(Vf_11)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_77,plain,
! [Vf_50,U_51,X_52] :
( element_of_collection(f10(Vf_50,U_51,X_52),Vf_50)
| ~ element_of_set(X_52,U_51)
| ~ element_of_collection(U_51,top_of_basis(Vf_50)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_6,plain,
! [Uu1_7,Vf_6,U_5] :
( ~ element_of_collection(Uu1_7,Vf_6)
| ~ element_of_set(U_5,Uu1_7)
| element_of_set(U_5,union_of_members(Vf_6)) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_181,plain,
! [U_102,Vf_103,U_104,X_105] :
( ~ element_of_set(U_102,f10(Vf_103,U_104,X_105))
| element_of_set(U_102,union_of_members(Vf_103))
| ~ element_of_set(X_105,U_104)
| ~ element_of_collection(U_104,top_of_basis(Vf_103)) ),
inference(resolution,[status(thm)],[c_77,c_6]) ).
tff(c_201,plain,
! [X_106,Vf_107,U_108] :
( element_of_set(X_106,union_of_members(Vf_107))
| ~ element_of_set(X_106,U_108)
| ~ element_of_collection(U_108,top_of_basis(Vf_107)) ),
inference(resolution,[status(thm)],[c_10,c_181]) ).
tff(c_252,plain,
! [U_114,Vf_115,Vf_116] :
( element_of_set(U_114,union_of_members(Vf_115))
| ~ element_of_collection(f1(Vf_116,U_114),top_of_basis(Vf_115))
| ~ element_of_set(U_114,union_of_members(Vf_116)) ),
inference(resolution,[status(thm)],[c_2,c_201]) ).
tff(c_3106,plain,
! [X_488,Y_489,Vf_490] :
( element_of_set(in_1st_set(X_488,Y_489),union_of_members(Vf_490))
| ~ element_of_set(in_1st_set(X_488,Y_489),union_of_members(top_of_basis(Vf_490)))
| ~ subset_sets(X_488,union_of_members(top_of_basis(Vf_490)))
| subset_sets(X_488,Y_489) ),
inference(resolution,[status(thm)],[c_70,c_252]) ).
tff(c_3158,plain,
! [Vf_490,Y_23] :
( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_490)),Y_23),union_of_members(Vf_490))
| ~ subset_sets(union_of_members(top_of_basis(Vf_490)),union_of_members(top_of_basis(Vf_490)))
| subset_sets(union_of_members(top_of_basis(Vf_490)),Y_23) ),
inference(resolution,[status(thm)],[c_20,c_3106]) ).
tff(c_3174,plain,
! [Vf_491,Y_492] :
( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_491)),Y_492),union_of_members(Vf_491))
| subset_sets(union_of_members(top_of_basis(Vf_491)),Y_492) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_3158]) ).
tff(c_16,plain,
! [U_19,Y_18,X_17] :
( element_of_set(U_19,Y_18)
| ~ element_of_set(U_19,X_17)
| ~ subset_sets(X_17,Y_18) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_3474,plain,
! [Vf_502,Y_503,Y_504] :
( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_502)),Y_503),Y_504)
| ~ subset_sets(union_of_members(Vf_502),Y_504)
| subset_sets(union_of_members(top_of_basis(Vf_502)),Y_503) ),
inference(resolution,[status(thm)],[c_3174,c_16]) ).
tff(c_22,plain,
! [X_24,Y_25] :
( ~ element_of_set(in_1st_set(X_24,Y_25),Y_25)
| subset_sets(X_24,Y_25) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_3550,plain,
! [Vf_505,Y_506] :
( ~ subset_sets(union_of_members(Vf_505),Y_506)
| subset_sets(union_of_members(top_of_basis(Vf_505)),Y_506) ),
inference(resolution,[status(thm)],[c_3474,c_22]) ).
tff(c_26,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_3602,plain,
~ subset_sets(union_of_members(f),cx),
inference(resolution,[status(thm)],[c_3550,c_26]) ).
tff(c_3620,plain,
~ equal_sets(union_of_members(f),cx),
inference(resolution,[status(thm)],[c_18,c_3602]) ).
tff(c_3623,plain,
~ basis(cx,f),
inference(resolution,[status(thm)],[c_8,c_3620]) ).
tff(c_3627,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_3623]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : TOP001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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
% 0.14/0.34 % Computer : n013.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 : Thu Aug 3 17:42:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.73/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.73/2.59
% 6.73/2.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.92/2.62
% 6.92/2.62 Inference rules
% 6.92/2.62 ----------------------
% 6.92/2.62 #Ref : 0
% 6.92/2.62 #Sup : 925
% 6.92/2.62 #Fact : 0
% 6.92/2.62 #Define : 0
% 6.92/2.62 #Split : 0
% 6.92/2.62 #Chain : 0
% 6.92/2.62 #Close : 0
% 6.92/2.62
% 6.92/2.62 Ordering : KBO
% 6.92/2.62
% 6.92/2.62 Simplification rules
% 6.92/2.62 ----------------------
% 6.92/2.62 #Subsume : 125
% 6.92/2.62 #Demod : 5
% 6.92/2.62 #Tautology : 2
% 6.92/2.62 #SimpNegUnit : 0
% 6.92/2.62 #BackRed : 0
% 6.92/2.62
% 6.92/2.62 #Partial instantiations: 0
% 6.92/2.62 #Strategies tried : 1
% 6.92/2.62
% 6.92/2.62 Timing (in seconds)
% 6.92/2.62 ----------------------
% 6.92/2.62 Preprocessing : 0.41
% 6.92/2.62 Parsing : 0.23
% 6.92/2.62 CNF conversion : 0.02
% 6.92/2.62 Main loop : 1.18
% 6.92/2.62 Inferencing : 0.41
% 6.92/2.62 Reduction : 0.24
% 6.92/2.62 Demodulation : 0.15
% 6.92/2.62 BG Simplification : 0.03
% 6.92/2.62 Subsumption : 0.42
% 6.92/2.62 Abstraction : 0.04
% 6.92/2.62 MUC search : 0.00
% 6.92/2.62 Cooper : 0.00
% 6.92/2.62 Total : 1.64
% 6.92/2.62 Index Insertion : 0.00
% 6.92/2.62 Index Deletion : 0.00
% 6.92/2.62 Index Matching : 0.00
% 6.92/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------