TSTP Solution File: SEU337+2 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:26:03 EDT 2023
% Result : Theorem 5.15s 1.34s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 57 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 20 |; 4 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn; 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t17_tops_2,conjecture,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2zv1y7RdMs/E---3.1_18444.p',t17_tops_2) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.2zv1y7RdMs/E---3.1_18444.p',dt_k7_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.2zv1y7RdMs/E---3.1_18444.p',involutiveness_k7_setfam_1) ).
fof(t16_tops_2,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( closed_subsets(X2,X1)
<=> open_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2zv1y7RdMs/E---3.1_18444.p',t16_tops_2) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( open_subsets(X2,X1)
<=> closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t17_tops_2]) ).
fof(c_0_5,plain,
! [X34,X35] :
( ~ element(X35,powerset(powerset(X34)))
| element(complements_of_subsets(X34,X35),powerset(powerset(X34))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(c_0_6,negated_conjecture,
( top_str(esk1_0)
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& ( ~ open_subsets(esk2_0,esk1_0)
| ~ closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) )
& ( open_subsets(esk2_0,esk1_0)
| closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X36,X37] :
( ~ element(X37,powerset(powerset(X36)))
| complements_of_subsets(X36,complements_of_subsets(X36,X37)) = X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
fof(c_0_8,lemma,
! [X27,X28] :
( ( ~ closed_subsets(X28,X27)
| open_subsets(complements_of_subsets(the_carrier(X27),X28),X27)
| ~ element(X28,powerset(powerset(the_carrier(X27))))
| ~ top_str(X27) )
& ( ~ open_subsets(complements_of_subsets(the_carrier(X27),X28),X27)
| closed_subsets(X28,X27)
| ~ element(X28,powerset(powerset(the_carrier(X27))))
| ~ top_str(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_tops_2])])])]) ).
cnf(c_0_9,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
( closed_subsets(X2,X1)
| ~ open_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
complements_of_subsets(the_carrier(esk1_0),complements_of_subsets(the_carrier(esk1_0),esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( open_subsets(esk2_0,esk1_0)
| closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ open_subsets(esk2_0,esk1_0)
| ~ closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_19,lemma,
( open_subsets(complements_of_subsets(the_carrier(X2),X1),X2)
| ~ closed_subsets(X1,X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
~ open_subsets(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_14]),c_0_15]),c_0_13])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.19 % Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.20 % Command : run_E %s %d THM
% 0.19/0.42 % Computer : n022.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8042.1875MB
% 0.19/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.42 % CPULimit : 2400
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Mon Oct 2 09:10:39 EDT 2023
% 0.19/0.42 % CPUTime :
% 0.40/0.62 Running first-order theorem proving
% 0.40/0.62 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.2zv1y7RdMs/E---3.1_18444.p
% 5.15/1.34 # Version: 3.1pre001
% 5.15/1.34 # Preprocessing class: FSLMSMSSSSSNFFN.
% 5.15/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.34 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.15/1.34 # Starting new_bool_3 with 600s (2) cores
% 5.15/1.34 # Starting new_bool_1 with 600s (2) cores
% 5.15/1.34 # Starting sh5l with 300s (1) cores
% 5.15/1.34 # new_bool_1 with pid 18524 completed with status 0
% 5.15/1.34 # Result found by new_bool_1
% 5.15/1.34 # Preprocessing class: FSLMSMSSSSSNFFN.
% 5.15/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.34 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.15/1.34 # Starting new_bool_3 with 600s (2) cores
% 5.15/1.34 # Starting new_bool_1 with 600s (2) cores
% 5.15/1.34 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.15/1.34 # Search class: FGHSM-SMLM32-MFFFFFNN
% 5.15/1.34 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 5.15/1.34 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 5.15/1.34 # Starting new_bool_1 with 61s (1) cores
% 5.15/1.34 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 18526 completed with status 0
% 5.15/1.34 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 5.15/1.34 # Preprocessing class: FSLMSMSSSSSNFFN.
% 5.15/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.34 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 5.15/1.34 # Starting new_bool_3 with 600s (2) cores
% 5.15/1.34 # Starting new_bool_1 with 600s (2) cores
% 5.15/1.34 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.15/1.34 # Search class: FGHSM-SMLM32-MFFFFFNN
% 5.15/1.34 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 5.15/1.34 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 5.15/1.34 # Preprocessing time : 0.024 s
% 5.15/1.34 # Presaturation interreduction done
% 5.15/1.34
% 5.15/1.34 # Proof found!
% 5.15/1.34 # SZS status Theorem
% 5.15/1.34 # SZS output start CNFRefutation
% See solution above
% 5.15/1.34 # Parsed axioms : 556
% 5.15/1.34 # Removed by relevancy pruning/SinE : 344
% 5.15/1.34 # Initial clauses : 1452
% 5.15/1.34 # Removed in clause preprocessing : 2
% 5.15/1.34 # Initial clauses in saturation : 1450
% 5.15/1.34 # Processed clauses : 2679
% 5.15/1.34 # ...of these trivial : 5
% 5.15/1.34 # ...subsumed : 311
% 5.15/1.34 # ...remaining for further processing : 2363
% 5.15/1.34 # Other redundant clauses eliminated : 700
% 5.15/1.34 # Clauses deleted for lack of memory : 0
% 5.15/1.34 # Backward-subsumed : 20
% 5.15/1.34 # Backward-rewritten : 13
% 5.15/1.34 # Generated clauses : 2144
% 5.15/1.34 # ...of the previous two non-redundant : 1863
% 5.15/1.34 # ...aggressively subsumed : 0
% 5.15/1.34 # Contextual simplify-reflections : 270
% 5.15/1.34 # Paramodulations : 1631
% 5.15/1.34 # Factorizations : 0
% 5.15/1.34 # NegExts : 0
% 5.15/1.34 # Equation resolutions : 702
% 5.15/1.34 # Total rewrite steps : 394
% 5.15/1.34 # Propositional unsat checks : 0
% 5.15/1.34 # Propositional check models : 0
% 5.15/1.34 # Propositional check unsatisfiable : 0
% 5.15/1.34 # Propositional clauses : 0
% 5.15/1.34 # Propositional clauses after purity: 0
% 5.15/1.34 # Propositional unsat core size : 0
% 5.15/1.34 # Propositional preprocessing time : 0.000
% 5.15/1.34 # Propositional encoding time : 0.000
% 5.15/1.34 # Propositional solver time : 0.000
% 5.15/1.34 # Success case prop preproc time : 0.000
% 5.15/1.34 # Success case prop encoding time : 0.000
% 5.15/1.34 # Success case prop solver time : 0.000
% 5.15/1.34 # Current number of processed clauses : 471
% 5.15/1.34 # Positive orientable unit clauses : 145
% 5.15/1.34 # Positive unorientable unit clauses: 3
% 5.15/1.34 # Negative unit clauses : 102
% 5.15/1.34 # Non-unit-clauses : 221
% 5.15/1.34 # Current number of unprocessed clauses: 1974
% 5.15/1.34 # ...number of literals in the above : 7741
% 5.15/1.34 # Current number of archived formulas : 0
% 5.15/1.34 # Current number of archived clauses : 1384
% 5.15/1.34 # Clause-clause subsumption calls (NU) : 1026791
% 5.15/1.34 # Rec. Clause-clause subsumption calls : 37640
% 5.15/1.34 # Non-unit clause-clause subsumptions : 445
% 5.15/1.34 # Unit Clause-clause subsumption calls : 1329
% 5.15/1.34 # Rewrite failures with RHS unbound : 0
% 5.15/1.34 # BW rewrite match attempts : 86
% 5.15/1.34 # BW rewrite match successes : 51
% 5.15/1.34 # Condensation attempts : 0
% 5.15/1.34 # Condensation successes : 0
% 5.15/1.34 # Termbank termtop insertions : 147979
% 5.15/1.34
% 5.15/1.34 # -------------------------------------------------
% 5.15/1.34 # User time : 0.585 s
% 5.15/1.34 # System time : 0.015 s
% 5.15/1.34 # Total time : 0.600 s
% 5.15/1.34 # Maximum resident set size: 5516 pages
% 5.15/1.34
% 5.15/1.34 # -------------------------------------------------
% 5.15/1.34 # User time : 1.224 s
% 5.15/1.34 # System time : 0.022 s
% 5.15/1.34 # Total time : 1.246 s
% 5.15/1.34 # Maximum resident set size: 2448 pages
% 5.15/1.34 % E---3.1 exiting
% 5.15/1.34 % E---3.1 exiting
%------------------------------------------------------------------------------