TSTP Solution File: SEU180+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n002.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 10:57:56 EDT 2023
% Result : Theorem 56.37s 39.47s
% Output : CNFRefutation 56.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 92
% Syntax : Number of formulae : 126 ( 15 unt; 85 typ; 0 def)
% Number of atoms : 74 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 28 ~; 24 |; 2 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 161 ( 78 >; 83 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 77 ( 77 usr; 7 con; 0-4 aty)
% Number of variables : 52 (; 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > disjoint > are_equipotent > relation > empty > subset_difference > unordered_pair > union_of_subsets > subset_complement > set_union2 > set_intersection2 > set_difference > ordered_pair > meet_of_subsets > complements_of_subsets > cartesian_product2 > #nlpp > union > singleton > set_meet > relation_rng > relation_field > relation_dom > powerset > cast_to_subset > empty_set > #skF_13 > #skF_24 > #skF_37 > #skF_11 > #skF_52 > #skF_44 > #skF_6 > #skF_17 > #skF_33 > #skF_57 > #skF_26 > #skF_30 > #skF_1 > #skF_18 > #skF_32 > #skF_43 > #skF_31 > #skF_38 > #skF_4 > #skF_3 > #skF_39 > #skF_29 > #skF_47 > #skF_12 > #skF_53 > #skF_56 > #skF_51 > #skF_45 > #skF_10 > #skF_41 > #skF_35 > #skF_49 > #skF_19 > #skF_54 > #skF_42 > #skF_8 > #skF_36 > #skF_20 > #skF_28 > #skF_34 > #skF_15 > #skF_40 > #skF_23 > #skF_14 > #skF_50 > #skF_55 > #skF_2 > #skF_21 > #skF_48 > #skF_25 > #skF_7 > #skF_27 > #skF_46 > #skF_9 > #skF_5 > #skF_22 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff(are_equipotent,type,
are_equipotent: ( $i * $i ) > $o ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(complements_of_subsets,type,
complements_of_subsets: ( $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(relation_field,type,
relation_field: $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cast_to_subset,type,
cast_to_subset: $i > $i ).
tff(union,type,
union: $i > $i ).
tff('#skF_44',type,
'#skF_44': $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_53',type,
'#skF_53': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff('#skF_56',type,
'#skF_56': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_51',type,
'#skF_51': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_41',type,
'#skF_41': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff(set_meet,type,
set_meet: $i > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i * $i ) > $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff('#skF_48',type,
'#skF_48': $i > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_556,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
tff(f_210,axiom,
! [A] :
( relation(A)
=> ( relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
tff(f_744,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_511,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
tff(f_147,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_428,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(c_458,plain,
( ~ in('#skF_52',relation_field('#skF_53'))
| ~ in('#skF_51',relation_field('#skF_53')) ),
inference(cnfTransformation,[status(thm)],[f_556]) ).
tff(c_617,plain,
~ in('#skF_51',relation_field('#skF_53')),
inference(splitLeft,[status(thm)],[c_458]) ).
tff(c_462,plain,
relation('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_556]) ).
tff(c_7905,plain,
! [A_970] :
( ( set_union2(relation_dom(A_970),relation_rng(A_970)) = relation_field(A_970) )
| ~ relation(A_970) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_556,plain,
! [A_478,B_479] : subset(A_478,set_union2(A_478,B_479)),
inference(cnfTransformation,[status(thm)],[f_744]) ).
tff(c_7968,plain,
! [A_970] :
( subset(relation_dom(A_970),relation_field(A_970))
| ~ relation(A_970) ),
inference(superposition,[status(thm),theory(equality)],[c_7905,c_556]) ).
tff(c_434,plain,
! [A_380] :
( subset(A_380,cartesian_product2(relation_dom(A_380),relation_rng(A_380)))
| ~ relation(A_380) ),
inference(cnfTransformation,[status(thm)],[f_511]) ).
tff(c_460,plain,
in(ordered_pair('#skF_51','#skF_52'),'#skF_53'),
inference(cnfTransformation,[status(thm)],[f_556]) ).
tff(c_8318,plain,
! [C_990,B_991,A_992] :
( in(C_990,B_991)
| ~ in(C_990,A_992)
| ~ subset(A_992,B_991) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_8387,plain,
! [B_991] :
( in(ordered_pair('#skF_51','#skF_52'),B_991)
| ~ subset('#skF_53',B_991) ),
inference(resolution,[status(thm)],[c_460,c_8318]) ).
tff(c_10960,plain,
! [A_1065,C_1066,B_1067,D_1068] :
( in(A_1065,C_1066)
| ~ in(ordered_pair(A_1065,B_1067),cartesian_product2(C_1066,D_1068)) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_11255,plain,
! [C_1071,D_1072] :
( in('#skF_51',C_1071)
| ~ subset('#skF_53',cartesian_product2(C_1071,D_1072)) ),
inference(resolution,[status(thm)],[c_8387,c_10960]) ).
tff(c_11259,plain,
( in('#skF_51',relation_dom('#skF_53'))
| ~ relation('#skF_53') ),
inference(resolution,[status(thm)],[c_434,c_11255]) ).
tff(c_11274,plain,
in('#skF_51',relation_dom('#skF_53')),
inference(demodulation,[status(thm),theory(equality)],[c_462,c_11259]) ).
tff(c_142,plain,
! [C_116,B_113,A_112] :
( in(C_116,B_113)
| ~ in(C_116,A_112)
| ~ subset(A_112,B_113) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_114195,plain,
! [B_753919] :
( in('#skF_51',B_753919)
| ~ subset(relation_dom('#skF_53'),B_753919) ),
inference(resolution,[status(thm)],[c_11274,c_142]) ).
tff(c_114211,plain,
( in('#skF_51',relation_field('#skF_53'))
| ~ relation('#skF_53') ),
inference(resolution,[status(thm)],[c_7968,c_114195]) ).
tff(c_114263,plain,
in('#skF_51',relation_field('#skF_53')),
inference(demodulation,[status(thm),theory(equality)],[c_462,c_114211]) ).
tff(c_114265,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_617,c_114263]) ).
tff(c_114266,plain,
~ in('#skF_52',relation_field('#skF_53')),
inference(splitRight,[status(thm)],[c_458]) ).
tff(c_121342,plain,
! [A_754764] :
( ( set_union2(relation_dom(A_754764),relation_rng(A_754764)) = relation_field(A_754764) )
| ~ relation(A_754764) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_114870,plain,
! [B_754441,A_754442] : ( set_union2(B_754441,A_754442) = set_union2(A_754442,B_754441) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_114906,plain,
! [B_754441,A_754442] : subset(B_754441,set_union2(A_754442,B_754441)),
inference(superposition,[status(thm),theory(equality)],[c_114870,c_556]) ).
tff(c_121393,plain,
! [A_754764] :
( subset(relation_rng(A_754764),relation_field(A_754764))
| ~ relation(A_754764) ),
inference(superposition,[status(thm),theory(equality)],[c_121342,c_114906]) ).
tff(c_121767,plain,
! [C_754786,B_754787,A_754788] :
( in(C_754786,B_754787)
| ~ in(C_754786,A_754788)
| ~ subset(A_754788,B_754787) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_121836,plain,
! [B_754787] :
( in(ordered_pair('#skF_51','#skF_52'),B_754787)
| ~ subset('#skF_53',B_754787) ),
inference(resolution,[status(thm)],[c_460,c_121767]) ).
tff(c_123786,plain,
! [B_754864,D_754865,A_754866,C_754867] :
( in(B_754864,D_754865)
| ~ in(ordered_pair(A_754866,B_754864),cartesian_product2(C_754867,D_754865)) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_123822,plain,
! [D_754870,C_754871] :
( in('#skF_52',D_754870)
| ~ subset('#skF_53',cartesian_product2(C_754871,D_754870)) ),
inference(resolution,[status(thm)],[c_121836,c_123786]) ).
tff(c_123826,plain,
( in('#skF_52',relation_rng('#skF_53'))
| ~ relation('#skF_53') ),
inference(resolution,[status(thm)],[c_434,c_123822]) ).
tff(c_123841,plain,
in('#skF_52',relation_rng('#skF_53')),
inference(demodulation,[status(thm),theory(equality)],[c_462,c_123826]) ).
tff(c_237393,plain,
! [B_1550443] :
( in('#skF_52',B_1550443)
| ~ subset(relation_rng('#skF_53'),B_1550443) ),
inference(resolution,[status(thm)],[c_123841,c_142]) ).
tff(c_237401,plain,
( in('#skF_52',relation_field('#skF_53'))
| ~ relation('#skF_53') ),
inference(resolution,[status(thm)],[c_121393,c_237393]) ).
tff(c_237457,plain,
in('#skF_52',relation_field('#skF_53')),
inference(demodulation,[status(thm),theory(equality)],[c_462,c_237401]) ).
tff(c_237459,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_114266,c_237457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % 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
% 0.15/0.34 % Computer : n002.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu Aug 3 12:02:31 EDT 2023
% 0.15/0.34 % CPUTime :
% 56.37/39.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.41/39.48
% 56.41/39.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 56.41/39.51
% 56.41/39.51 Inference rules
% 56.41/39.51 ----------------------
% 56.41/39.51 #Ref : 10
% 56.41/39.51 #Sup : 43167
% 56.41/39.51 #Fact : 24
% 56.41/39.51 #Define : 0
% 56.41/39.51 #Split : 34
% 56.41/39.51 #Chain : 0
% 56.41/39.51 #Close : 0
% 56.41/39.51
% 56.41/39.51 Ordering : KBO
% 56.41/39.51
% 56.41/39.51 Simplification rules
% 56.41/39.51 ----------------------
% 56.41/39.51 #Subsume : 16746
% 56.41/39.51 #Demod : 9185
% 56.41/39.51 #Tautology : 6802
% 56.41/39.51 #SimpNegUnit : 1771
% 56.41/39.51 #BackRed : 203
% 56.41/39.51
% 56.41/39.51 #Partial instantiations: 809809
% 56.41/39.51 #Strategies tried : 1
% 56.41/39.51
% 56.41/39.51 Timing (in seconds)
% 56.41/39.51 ----------------------
% 56.41/39.52 Preprocessing : 0.93
% 56.41/39.52 Parsing : 0.42
% 56.41/39.52 CNF conversion : 0.10
% 56.41/39.52 Main loop : 37.52
% 56.41/39.52 Inferencing : 9.23
% 56.41/39.52 Reduction : 15.07
% 56.41/39.52 Demodulation : 10.08
% 56.41/39.52 BG Simplification : 0.27
% 56.41/39.52 Subsumption : 11.06
% 56.41/39.52 Abstraction : 0.37
% 56.41/39.52 MUC search : 0.00
% 56.41/39.52 Cooper : 0.00
% 56.41/39.52 Total : 38.51
% 56.41/39.52 Index Insertion : 0.00
% 56.41/39.52 Index Deletion : 0.00
% 56.41/39.52 Index Matching : 0.00
% 56.41/39.52 BG Taut test : 0.00
%------------------------------------------------------------------------------