TSTP Solution File: SET098+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SET098+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% 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 : 600s
% DateTime : Tue Jul 19 00:09:26 EDT 2022
% Result : Theorem 10.00s 2.80s
% Output : CNFRefutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 20 unt; 0 def)
% Number of atoms : 208 ( 49 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 213 ( 85 ~; 92 |; 28 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 10 sgn 49 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_1_to_number_of_elements_in_class,conjecture,
! [X1] :
( X1 = null_class
| ? [X2] : singleton(X2) = X1
| ? [X4] :
( member(X4,X1)
& ? [X7] :
( member(X7,intersection(complement(singleton(X4)),X1))
& member(X7,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_number_of_elements_in_class) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(complement,axiom,
! [X1,X5] :
( member(X5,complement(X1))
<=> ( member(X5,universal_class)
& ~ member(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',complement) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ! [X3] :
~ ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',disjoint_defn) ).
fof(intersection,axiom,
! [X1,X2,X5] :
( member(X5,intersection(X1,X2))
<=> ( member(X5,X1)
& member(X5,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',intersection) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(null_class_defn,axiom,
! [X1] : ~ member(X1,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X1,X2)
& subclass(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( X1 = null_class
| ? [X2] : singleton(X2) = X1
| ? [X4] :
( member(X4,X1)
& ? [X7] :
( member(X7,intersection(complement(singleton(X4)),X1))
& member(X7,X1) ) ) ),
inference(assume_negation,[status(cth)],[corollary_1_to_number_of_elements_in_class]) ).
fof(c_0_12,negated_conjecture,
! [X108,X109,X110] :
( esk8_0 != null_class
& singleton(X108) != esk8_0
& ( ~ member(X109,esk8_0)
| ~ member(X110,intersection(complement(singleton(X109)),esk8_0))
| ~ member(X110,esk8_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_13,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_14,plain,
! [X41,X42] :
( ( member(X42,universal_class)
| ~ member(X42,complement(X41)) )
& ( ~ member(X42,X41)
| ~ member(X42,complement(X41)) )
& ( ~ member(X42,universal_class)
| member(X42,X41)
| member(X42,complement(X41)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[complement])])])]) ).
fof(c_0_15,plain,
! [X101] :
( ( member(esk6_1(X101),universal_class)
| X101 = null_class )
& ( member(esk6_1(X101),X101)
| X101 = null_class )
& ( disjoint(esk6_1(X101),X101)
| X101 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[regularity])])])]) ).
fof(c_0_16,plain,
! [X95,X96,X97,X98,X99] :
( ( ~ disjoint(X95,X96)
| ~ member(X97,X95)
| ~ member(X97,X96) )
& ( member(esk5_2(X98,X99),X98)
| disjoint(X98,X99) )
& ( member(esk5_2(X98,X99),X99)
| disjoint(X98,X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[disjoint_defn])])])])])]) ).
fof(c_0_17,plain,
! [X38,X39,X40] :
( ( member(X40,X38)
| ~ member(X40,intersection(X38,X39)) )
& ( member(X40,X39)
| ~ member(X40,intersection(X38,X39)) )
& ( ~ member(X40,X38)
| ~ member(X40,X39)
| member(X40,intersection(X38,X39)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(X1,esk8_0)
| ~ member(X2,intersection(complement(singleton(X1)),esk8_0))
| ~ member(X2,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ subclass(X10,X11)
| ~ member(X12,X10)
| member(X12,X11) )
& ( member(esk1_2(X13,X14),X13)
| subclass(X13,X14) )
& ( ~ member(esk1_2(X13,X14),X14)
| subclass(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subclass_defn])])])])])]) ).
fof(c_0_21,plain,
! [X16] : subclass(X16,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( member(esk5_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( member(esk5_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X2,esk8_0)
| ~ member(X1,esk8_0)
| ~ member(X2,intersection(complement(unordered_pair(X1,X1)),esk8_0)) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,plain,
! [X46] : ~ member(X46,null_class),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[null_class_defn])]) ).
cnf(c_0_32,plain,
( complement(X1) = null_class
| ~ member(esk6_1(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,plain,
( member(esk6_1(X1),universal_class)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,plain,
( disjoint(complement(X1),X2)
| ~ member(esk5_2(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_36,plain,
( disjoint(X1,intersection(X2,X3))
| member(esk5_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_38,plain,
! [X19,X20,X21] :
( ( member(X19,universal_class)
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 = X20
| X19 = X21
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 != X20
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) )
& ( X19 != X21
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,complement(unordered_pair(X2,X2)))
| ~ member(X1,esk8_0)
| ~ member(X2,esk8_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_40,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
( complement(complement(X1)) = null_class
| member(esk6_1(complement(complement(X1))),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_43,plain,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_44,plain,
disjoint(complement(X1),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( intersection(X1,X2) = null_class
| member(esk6_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_46,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( member(X1,unordered_pair(X2,X2))
| ~ member(X1,esk8_0)
| ~ member(X2,esk8_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_40]) ).
cnf(c_0_48,plain,
complement(complement(null_class)) = null_class,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,complement(X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( intersection(complement(X1),X2) = null_class
| ~ member(esk6_1(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( X1 = X2
| ~ member(X1,esk8_0)
| ~ member(X2,esk8_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
esk8_0 != null_class,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_53,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_54,plain,
( member(X1,complement(null_class))
| ~ member(X1,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_41]) ).
cnf(c_0_55,plain,
( intersection(X1,X2) = null_class
| ~ member(esk6_1(intersection(X1,X2)),complement(X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_56,plain,
( intersection(complement(complement(X1)),X2) = null_class
| member(esk6_1(intersection(complement(complement(X1)),X2)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_34]) ).
cnf(c_0_57,negated_conjecture,
( esk6_1(esk8_0) = X1
| ~ member(X1,esk8_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_23]),c_0_52]) ).
fof(c_0_58,plain,
! [X17,X18] :
( ( subclass(X17,X18)
| X17 != X18 )
& ( subclass(X18,X17)
| X17 != X18 )
& ( ~ subclass(X17,X18)
| ~ subclass(X18,X17)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])]) ).
cnf(c_0_59,plain,
( subclass(X1,complement(null_class))
| ~ member(esk1_2(X1,complement(null_class)),universal_class) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_61,plain,
intersection(complement(complement(complement(X1))),X1) = null_class,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( esk6_1(complement(complement(esk8_0))) = esk6_1(esk8_0)
| complement(complement(esk8_0)) = null_class ),
inference(spm,[status(thm)],[c_0_57,c_0_42]) ).
cnf(c_0_63,plain,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,plain,
subclass(universal_class,complement(null_class)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( ~ member(X1,complement(complement(complement(X2))))
| ~ member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_61]),c_0_41]) ).
cnf(c_0_66,negated_conjecture,
( complement(complement(esk8_0)) = null_class
| member(esk6_1(esk8_0),esk8_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_62]) ).
cnf(c_0_67,plain,
complement(null_class) = universal_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_30])]) ).
cnf(c_0_68,negated_conjecture,
( esk1_2(esk8_0,X1) = esk6_1(esk8_0)
| subclass(esk8_0,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( member(esk6_1(esk8_0),esk8_0)
| ~ member(X1,esk8_0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_40]) ).
cnf(c_0_70,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X1
| esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( subclass(esk8_0,X1)
| ~ member(esk6_1(esk8_0),X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
member(esk6_1(esk8_0),esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_23]),c_0_52]) ).
cnf(c_0_73,negated_conjecture,
singleton(X1) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_74,plain,
( esk1_2(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_70])]) ).
cnf(c_0_75,negated_conjecture,
( subclass(esk8_0,unordered_pair(X1,X1))
| ~ member(X1,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_47]),c_0_72])]) ).
cnf(c_0_76,negated_conjecture,
unordered_pair(X1,X1) != esk8_0,
inference(rw,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_77,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
~ member(X1,esk8_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_75]),c_0_76]),c_0_77]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_72,c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET098+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 11:12:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.46 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 10.00/2.80 # ENIGMATIC: Solved by autoschedule:
% 10.00/2.80 # No SInE strategy applied
% 10.00/2.80 # Trying AutoSched0 for 150 seconds
% 10.00/2.80 # AutoSched0-Mode selected heuristic G_E___042_C18_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 10.00/2.80 # and selection function SelectMaxLComplexAvoidPosPred.
% 10.00/2.80 #
% 10.00/2.80 # Preprocessing time : 0.030 s
% 10.00/2.80 # Presaturation interreduction done
% 10.00/2.80
% 10.00/2.80 # Proof found!
% 10.00/2.80 # SZS status Theorem
% 10.00/2.80 # SZS output start CNFRefutation
% See solution above
% 10.00/2.81 # Training examples: 0 positive, 0 negative
% 10.00/2.81
% 10.00/2.81 # -------------------------------------------------
% 10.00/2.81 # User time : 0.415 s
% 10.00/2.81 # System time : 0.020 s
% 10.00/2.81 # Total time : 0.435 s
% 10.00/2.81 # Maximum resident set size: 7112 pages
% 10.00/2.81
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