TSTP Solution File: SEU147+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n005.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 09:17:09 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 99 ( 26 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 94 ( 37 ~; 41 |; 9 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 76 ( 17 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_zfmisc_1) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_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(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(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_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(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(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t1_zfmisc_1) ).
fof(c_0_8,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| ~ subset(esk3_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk3_2(X4,X5),X5)
| subset(esk3_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_9,lemma,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_10,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_11,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,lemma,
( in(empty_set,X1)
| X1 != powerset(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,lemma,
( in(singleton(X1),X2)
| X2 != powerset(X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_16,lemma,
in(empty_set,powerset(X1)),
inference(er,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk5_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])])])])])])]) ).
cnf(c_0_18,lemma,
( in(singleton(empty_set),X1)
| X1 != powerset(powerset(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,lemma,
in(singleton(empty_set),powerset(powerset(X1))),
inference(er,[status(thm)],[c_0_18]) ).
fof(c_0_22,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_23,plain,
( subset(esk5_2(X1,X2),X3)
| subset(X1,X2)
| X1 != powerset(X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,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])])])])]) ).
cnf(c_0_25,lemma,
( subset(singleton(empty_set),X1)
| powerset(powerset(X2)) != powerset(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_26,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( subset(esk5_2(powerset(X1),X2),X1)
| subset(powerset(X1),X2) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_29,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[t1_zfmisc_1]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,lemma,
subset(singleton(empty_set),powerset(X1)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,lemma,
( esk5_2(powerset(empty_set),X1) = empty_set
| subset(powerset(empty_set),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,lemma,
( in(X1,X2)
| ~ subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
cnf(c_0_37,lemma,
( powerset(X1) = singleton(empty_set)
| ~ subset(powerset(X1),singleton(empty_set)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,lemma,
( subset(powerset(empty_set),X1)
| ~ in(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,lemma,
in(X1,singleton(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,lemma,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 05:01:08 EDT 2022
% 0.13/0.35 % 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 : 42
% 0.24/1.42 # Proof object clause steps : 25
% 0.24/1.42 # Proof object formula steps : 17
% 0.24/1.42 # Proof object conjectures : 4
% 0.24/1.42 # Proof object clause conjectures : 1
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 11
% 0.24/1.42 # Proof object initial formulas used : 8
% 0.24/1.42 # Proof object generating inferences : 14
% 0.24/1.42 # Proof object simplifying inferences : 3
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 70
% 0.24/1.42 # Removed by relevancy pruning/SinE : 28
% 0.24/1.42 # Initial clauses : 74
% 0.24/1.42 # Removed in clause preprocessing : 1
% 0.24/1.42 # Initial clauses in saturation : 73
% 0.24/1.42 # Processed clauses : 4519
% 0.24/1.42 # ...of these trivial : 242
% 0.24/1.42 # ...subsumed : 3324
% 0.24/1.42 # ...remaining for further processing : 953
% 0.24/1.42 # Other redundant clauses eliminated : 284
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 28
% 0.24/1.42 # Backward-rewritten : 18
% 0.24/1.42 # Generated clauses : 46650
% 0.24/1.42 # ...of the previous two non-trivial : 37670
% 0.24/1.42 # Contextual simplify-reflections : 401
% 0.24/1.42 # Paramodulations : 46175
% 0.24/1.42 # Factorizations : 64
% 0.24/1.42 # Equation resolutions : 411
% 0.24/1.42 # Current number of processed clauses : 904
% 0.24/1.42 # Positive orientable unit clauses : 118
% 0.24/1.42 # Positive unorientable unit clauses: 2
% 0.24/1.42 # Negative unit clauses : 76
% 0.24/1.42 # Non-unit-clauses : 708
% 0.24/1.42 # Current number of unprocessed clauses: 29891
% 0.24/1.42 # ...number of literals in the above : 100110
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 47
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 207327
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 142177
% 0.24/1.42 # Non-unit clause-clause subsumptions : 2093
% 0.24/1.42 # Unit Clause-clause subsumption calls : 12081
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 157
% 0.24/1.42 # BW rewrite match successes : 22
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 509636
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.645 s
% 0.24/1.42 # System time : 0.019 s
% 0.24/1.42 # Total time : 0.664 s
% 0.24/1.42 # Maximum resident set size: 27916 pages
%------------------------------------------------------------------------------