%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n003.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 09:17:08 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 23 unt; 0 def)
% Number of atoms : 146 ( 62 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 50 ~; 57 |; 10 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 14 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l4_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l4_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l32_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d10_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_boole) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t48_xboole_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t28_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t36_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l2_zfmisc_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r1_tarski) ).
fof(t33_xboole_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t33_xboole_1) ).
fof(l3_zfmisc_1,lemma,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l3_zfmisc_1) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
fof(c_0_15,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk4_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).
fof(c_0_16,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
fof(c_0_17,lemma,
! [X3,X4,X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])])]) ).
fof(c_0_18,negated_conjecture,
( ( esk1_0 != empty_set
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( esk1_0 != singleton(esk2_0)
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( subset(esk1_0,singleton(esk2_0))
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_19,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])])]) ).
fof(c_0_22,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_23,lemma,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_24,lemma,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_25,lemma,
! [X3,X4] : subset(set_difference(X3,X4),X3),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_26,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( esk1_0 = singleton(esk2_0)
| esk1_0 = empty_set
| subset(esk1_0,singleton(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(esk1_0,singleton(esk2_0))
| esk1_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| X1 != empty_set ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,lemma,
! [X3,X4,X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])])]) ).
cnf(c_0_32,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_34,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_35,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_36,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_37,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = empty_set
| singleton(esk2_0) = esk1_0
| empty_set = esk1_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_39,negated_conjecture,
empty_set != esk1_0,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_40,negated_conjecture,
( singleton(esk2_0) = esk1_0
| empty_set = esk1_0
| ~ subset(singleton(esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_41,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_42,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_xboole_1])])])]) ).
cnf(c_0_43,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_46,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,lemma,
( set_difference(X1,X2) = X1
| ~ subset(X1,set_difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_49,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) = empty_set
| singleton(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,negated_conjecture,
( ~ subset(esk1_0,singleton(esk2_0))
| esk1_0 != singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,lemma,
( singleton(esk2_0) = esk1_0
| ~ in(esk2_0,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_19]) ).
cnf(c_0_52,lemma,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( set_difference(esk1_0,set_difference(esk1_0,singleton(esk2_0))) = esk1_0
| singleton(esk2_0) = esk1_0
| empty_set = esk1_0 ),
inference(spm,[status(thm)],[c_0_45,c_0_27]) ).
cnf(c_0_55,lemma,
in(X1,singleton(X1)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( singleton(esk2_0) = esk1_0
| ~ subset(esk1_0,empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39]) ).
cnf(c_0_57,negated_conjecture,
~ in(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47])]) ).
cnf(c_0_58,lemma,
( subset(set_difference(X1,X2),empty_set)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( set_difference(esk1_0,set_difference(esk1_0,singleton(esk2_0))) = esk1_0
| singleton(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[c_0_54,c_0_39]) ).
cnf(c_0_60,lemma,
~ subset(esk1_0,empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
fof(c_0_61,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| in(X6,X4)
| subset(X4,set_difference(X5,singleton(X6))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])])])]) ).
cnf(c_0_62,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_63,negated_conjecture,
( singleton(esk2_0) = esk1_0
| ~ subset(esk1_0,set_difference(esk1_0,singleton(esk2_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_64,lemma,
( subset(X1,set_difference(X2,singleton(X3)))
| in(X3,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) != empty_set
| singleton(esk2_0) != esk1_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_62]) ).
cnf(c_0_66,lemma,
singleton(esk2_0) = esk1_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_47])]),c_0_57]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_53]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n003.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 Jun 19 01:04:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.019 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 68
% 0.24/1.42 # Proof object clause steps : 39
% 0.24/1.42 # Proof object formula steps : 29
% 0.24/1.42 # Proof object conjectures : 17
% 0.24/1.42 # Proof object clause conjectures : 14
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 18
% 0.24/1.42 # Proof object initial formulas used : 14
% 0.24/1.42 # Proof object generating inferences : 15
% 0.24/1.42 # Proof object simplifying inferences : 18
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 67
% 0.24/1.42 # Removed by relevancy pruning/SinE : 27
% 0.24/1.42 # Initial clauses : 69
% 0.24/1.42 # Removed in clause preprocessing : 1
% 0.24/1.42 # Initial clauses in saturation : 68
% 0.24/1.42 # Processed clauses : 479
% 0.24/1.42 # ...of these trivial : 17
% 0.24/1.42 # ...subsumed : 272
% 0.24/1.42 # ...remaining for further processing : 190
% 0.24/1.42 # Other redundant clauses eliminated : 43
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 7
% 0.24/1.42 # Backward-rewritten : 39
% 0.24/1.42 # Generated clauses : 2364
% 0.24/1.42 # ...of the previous two non-trivial : 1768
% 0.24/1.42 # Contextual simplify-reflections : 70
% 0.24/1.42 # Paramodulations : 2289
% 0.24/1.42 # Factorizations : 14
% 0.24/1.42 # Equation resolutions : 57
% 0.24/1.42 # Current number of processed clauses : 137
% 0.24/1.42 # Positive orientable unit clauses : 32
% 0.24/1.42 # Positive unorientable unit clauses: 2
% 0.24/1.42 # Negative unit clauses : 8
% 0.24/1.42 # Non-unit-clauses : 95
% 0.24/1.42 # Current number of unprocessed clauses: 1019
% 0.24/1.42 # ...number of literals in the above : 2825
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 51
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 2982
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 2547
% 0.24/1.42 # Non-unit clause-clause subsumptions : 233
% 0.24/1.42 # Unit Clause-clause subsumption calls : 127
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 28
% 0.24/1.42 # BW rewrite match successes : 14
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 24481
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.066 s
% 0.24/1.42 # System time : 0.008 s
% 0.24/1.42 # Total time : 0.074 s
% 0.24/1.42 # Maximum resident set size: 4408 pages
%------------------------------------------------------------------------------