TSTP Solution File: SEU189+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU189+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 : n001.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 10:57:57 EDT 2023
% Result : Theorem 10.19s 3.35s
% Output : CNFRefutation 10.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 104
% Syntax : Number of formulae : 151 ( 38 unt; 98 typ; 0 def)
% Number of atoms : 75 ( 57 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 23 ~; 15 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 194 ( 92 >; 102 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 90 ( 90 usr; 6 con; 0-5 aty)
% Number of variables : 11 (; 9 !; 2 ?; 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 > relation_composition > ordered_pair > meet_of_subsets > complements_of_subsets > cartesian_product2 > #nlpp > union > singleton > set_meet > relation_rng > relation_inverse > relation_field > relation_dom > powerset > cast_to_subset > empty_set > #skF_13 > #skF_49 > #skF_24 > #skF_37 > #skF_62 > #skF_11 > #skF_41 > #skF_44 > #skF_6 > #skF_17 > #skF_33 > #skF_26 > #skF_30 > #skF_1 > #skF_18 > #skF_47 > #skF_55 > #skF_63 > #skF_32 > #skF_56 > #skF_60 > #skF_31 > #skF_38 > #skF_4 > #skF_3 > #skF_39 > #skF_29 > #skF_64 > #skF_12 > #skF_53 > #skF_48 > #skF_45 > #skF_10 > #skF_35 > #skF_19 > #skF_42 > #skF_8 > #skF_36 > #skF_57 > #skF_59 > #skF_20 > #skF_28 > #skF_34 > #skF_15 > #skF_23 > #skF_14 > #skF_67 > #skF_54 > #skF_52 > #skF_50 > #skF_46 > #skF_2 > #skF_21 > #skF_66 > #skF_40 > #skF_68 > #skF_25 > #skF_43 > #skF_7 > #skF_27 > #skF_61 > #skF_9 > #skF_5 > #skF_22 > #skF_58 > #skF_65 > #skF_16 > #skF_51
%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_49',type,
'#skF_49': ( $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_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $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_41',type,
'#skF_41': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i * $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(relation_inverse,type,
relation_inverse: $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('#skF_47',type,
'#skF_47': ( $i * $i * $i ) > $i ).
tff(meet_of_subsets,type,
meet_of_subsets: ( $i * $i ) > $i ).
tff('#skF_55',type,
'#skF_55': $i ).
tff('#skF_63',type,
'#skF_63': ( $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_56',type,
'#skF_56': $i ).
tff('#skF_60',type,
'#skF_60': ( $i * $i ) > $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_64',type,
'#skF_64': $i > $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(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(relation_composition,type,
relation_composition: ( $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('#skF_57',type,
'#skF_57': $i > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_59',type,
'#skF_59': $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_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff('#skF_67',type,
'#skF_67': $i > $i ).
tff('#skF_54',type,
'#skF_54': $i > $i ).
tff('#skF_52',type,
'#skF_52': ( $i * $i ) > $i ).
tff('#skF_50',type,
'#skF_50': ( $i * $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i * $i ) > $i ).
tff('#skF_66',type,
'#skF_66': $i ).
tff(union_of_subsets,type,
union_of_subsets: ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $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_68',type,
'#skF_68': ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': ( $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_61',type,
'#skF_61': ( $i * $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_58',type,
'#skF_58': $i ).
tff('#skF_65',type,
'#skF_65': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff('#skF_51',type,
'#skF_51': $i > $i ).
tff(f_462,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_880,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_473,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_869,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_dom(A) = empty_set )
<=> ( relation_rng(A) = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
tff(f_862,lemma,
! [A] :
( relation(A)
=> ( ( ( relation_dom(A) = empty_set )
| ( relation_rng(A) = empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
tff(f_843,lemma,
( ( relation_dom(empty_set) = empty_set )
& ( relation_rng(empty_set) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
tff(c_424,plain,
empty('#skF_53'),
inference(cnfTransformation,[status(thm)],[f_462]) ).
tff(c_3165,plain,
! [A_898] :
( ( empty_set = A_898 )
| ~ empty(A_898) ),
inference(cnfTransformation,[status(thm)],[f_880]) ).
tff(c_3180,plain,
empty_set = '#skF_53',
inference(resolution,[status(thm)],[c_424,c_3165]) ).
tff(c_430,plain,
empty('#skF_55'),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_3179,plain,
empty_set = '#skF_55',
inference(resolution,[status(thm)],[c_430,c_3165]) ).
tff(c_3203,plain,
'#skF_55' = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_3180,c_3179]) ).
tff(c_624,plain,
( ( relation_rng('#skF_66') != empty_set )
| ( relation_dom('#skF_66') != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_683,plain,
relation_dom('#skF_66') != empty_set,
inference(splitLeft,[status(thm)],[c_624]) ).
tff(c_748,plain,
! [A_701] :
( ( empty_set = A_701 )
| ~ empty(A_701) ),
inference(cnfTransformation,[status(thm)],[f_880]) ).
tff(c_763,plain,
empty_set = '#skF_53',
inference(resolution,[status(thm)],[c_424,c_748]) ).
tff(c_762,plain,
empty_set = '#skF_55',
inference(resolution,[status(thm)],[c_430,c_748]) ).
tff(c_785,plain,
'#skF_55' = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_763,c_762]) ).
tff(c_630,plain,
( ( relation_dom('#skF_66') = empty_set )
| ( relation_rng('#skF_66') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_699,plain,
relation_rng('#skF_66') = empty_set,
inference(splitLeft,[status(thm)],[c_630]) ).
tff(c_771,plain,
relation_rng('#skF_66') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_762,c_699]) ).
tff(c_794,plain,
relation_rng('#skF_66') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_785,c_771]) ).
tff(c_622,plain,
relation('#skF_66'),
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_618,plain,
! [A_614] :
( ( relation_rng(A_614) != empty_set )
| ( empty_set = A_614 )
| ~ relation(A_614) ),
inference(cnfTransformation,[status(thm)],[f_862]) ).
tff(c_2854,plain,
! [A_870] :
( ( relation_rng(A_870) != '#skF_53' )
| ( A_870 = '#skF_53' )
| ~ relation(A_870) ),
inference(demodulation,[status(thm),theory(equality)],[c_763,c_763,c_618]) ).
tff(c_2875,plain,
( ( relation_rng('#skF_66') != '#skF_53' )
| ( '#skF_53' = '#skF_66' ) ),
inference(resolution,[status(thm)],[c_622,c_2854]) ).
tff(c_2887,plain,
'#skF_53' = '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_794,c_2875]) ).
tff(c_770,plain,
relation_dom('#skF_66') != '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_762,c_683]) ).
tff(c_831,plain,
relation_dom('#skF_66') != '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_785,c_770]) ).
tff(c_2930,plain,
relation_dom('#skF_66') != '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_2887,c_831]) ).
tff(c_612,plain,
relation_dom(empty_set) = empty_set,
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_772,plain,
relation_dom('#skF_55') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_762,c_762,c_612]) ).
tff(c_815,plain,
relation_dom('#skF_53') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_785,c_785,c_772]) ).
tff(c_2935,plain,
relation_dom('#skF_66') = '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_2887,c_2887,c_815]) ).
tff(c_3040,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2930,c_2935]) ).
tff(c_3041,plain,
relation_dom('#skF_66') = empty_set,
inference(splitRight,[status(thm)],[c_630]) ).
tff(c_3057,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_683,c_3041]) ).
tff(c_3059,plain,
relation_dom('#skF_66') = empty_set,
inference(splitRight,[status(thm)],[c_624]) ).
tff(c_3194,plain,
relation_dom('#skF_66') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3059]) ).
tff(c_3219,plain,
relation_dom('#skF_66') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3194]) ).
tff(c_620,plain,
! [A_614] :
( ( relation_dom(A_614) != empty_set )
| ( empty_set = A_614 )
| ~ relation(A_614) ),
inference(cnfTransformation,[status(thm)],[f_862]) ).
tff(c_7028,plain,
! [A_1139] :
( ( relation_dom(A_1139) != '#skF_53' )
| ( A_1139 = '#skF_53' )
| ~ relation(A_1139) ),
inference(demodulation,[status(thm),theory(equality)],[c_3180,c_3180,c_620]) ).
tff(c_7049,plain,
( ( relation_dom('#skF_66') != '#skF_53' )
| ( '#skF_53' = '#skF_66' ) ),
inference(resolution,[status(thm)],[c_622,c_7028]) ).
tff(c_7061,plain,
'#skF_53' = '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_3219,c_7049]) ).
tff(c_3058,plain,
relation_rng('#skF_66') != empty_set,
inference(splitRight,[status(thm)],[c_624]) ).
tff(c_3190,plain,
relation_rng('#skF_66') != '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3058]) ).
tff(c_3209,plain,
relation_rng('#skF_66') != '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3190]) ).
tff(c_7116,plain,
relation_rng('#skF_66') != '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_7061,c_3209]) ).
tff(c_610,plain,
relation_rng(empty_set) = empty_set,
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_3188,plain,
relation_rng('#skF_55') = '#skF_55',
inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3179,c_610]) ).
tff(c_3245,plain,
relation_rng('#skF_53') = '#skF_53',
inference(demodulation,[status(thm),theory(equality)],[c_3203,c_3203,c_3188]) ).
tff(c_7113,plain,
relation_rng('#skF_66') = '#skF_66',
inference(demodulation,[status(thm),theory(equality)],[c_7061,c_7061,c_3245]) ).
tff(c_7204,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7116,c_7113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU189+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
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 12:17:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 10.19/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.19/3.35
% 10.19/3.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.31/3.39
% 10.31/3.39 Inference rules
% 10.31/3.39 ----------------------
% 10.31/3.39 #Ref : 1
% 10.31/3.39 #Sup : 1530
% 10.31/3.39 #Fact : 0
% 10.31/3.39 #Define : 0
% 10.31/3.39 #Split : 3
% 10.31/3.39 #Chain : 0
% 10.31/3.39 #Close : 0
% 10.31/3.39
% 10.31/3.39 Ordering : KBO
% 10.31/3.39
% 10.31/3.39 Simplification rules
% 10.31/3.39 ----------------------
% 10.31/3.39 #Subsume : 301
% 10.31/3.39 #Demod : 834
% 10.31/3.39 #Tautology : 925
% 10.31/3.39 #SimpNegUnit : 22
% 10.31/3.39 #BackRed : 155
% 10.31/3.39
% 10.31/3.39 #Partial instantiations: 0
% 10.31/3.39 #Strategies tried : 1
% 10.31/3.39
% 10.31/3.39 Timing (in seconds)
% 10.31/3.39 ----------------------
% 10.31/3.39 Preprocessing : 0.95
% 10.31/3.39 Parsing : 0.45
% 10.31/3.39 CNF conversion : 0.10
% 10.31/3.39 Main loop : 1.36
% 10.31/3.39 Inferencing : 0.39
% 10.31/3.39 Reduction : 0.51
% 10.31/3.39 Demodulation : 0.35
% 10.31/3.39 BG Simplification : 0.08
% 10.31/3.39 Subsumption : 0.26
% 10.31/3.39 Abstraction : 0.05
% 10.31/3.39 MUC search : 0.00
% 10.31/3.39 Cooper : 0.00
% 10.31/3.39 Total : 2.36
% 10.31/3.39 Index Insertion : 0.00
% 10.31/3.39 Index Deletion : 0.00
% 10.31/3.39 Index Matching : 0.00
% 10.31/3.39 BG Taut test : 0.00
%------------------------------------------------------------------------------