%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:45 PM UTC 2026
% Result : Theorem 10.26s 1.98s
% Output : CNFRefutation 10.26s
% 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/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
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/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
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/sandbox/benchmark/theBenchmark.p',dt_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/sandbox/benchmark/theBenchmark.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,
! [X36,X37] :
( complements_of_subsets(X36,complements_of_subsets(X36,X37)) = X37
| ~ element(X37,powerset(powerset(X36))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])])]) ).
fof(c_0_6,negated_conjecture,
( ( 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)
| ~ open_subsets(esk2_0,esk1_0) )
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& top_str(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X34,X35] :
( element(complements_of_subsets(X34,X35),powerset(powerset(X34)))
| ~ element(X35,powerset(powerset(X34))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])])]) ).
fof(c_0_8,lemma,
! [X27,X28] :
( ( ~ top_str(X27)
| ~ element(X28,powerset(powerset(the_carrier(X27))))
| closed_subsets(X28,X27)
| ~ open_subsets(complements_of_subsets(the_carrier(X27),X28),X27) )
& ( ~ top_str(X27)
| ~ element(X28,powerset(powerset(the_carrier(X27))))
| open_subsets(complements_of_subsets(the_carrier(X27),X28),X27)
| ~ closed_subsets(X28,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
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,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
( ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ open_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| closed_subsets(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,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_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
element(complements_of_subsets(the_carrier(esk1_0),esk2_0),powerset(powerset(the_carrier(esk1_0)))),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0)
| open_subsets(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ closed_subsets(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk1_0)
| ~ open_subsets(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,
( ~ top_str(X2)
| ~ element(X1,powerset(powerset(the_carrier(X2))))
| ~ closed_subsets(X1,X2)
| open_subsets(complements_of_subsets(the_carrier(X2),X1),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_13]),c_0_14]),c_0_15])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 06:14:46 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 10.26/1.98 % Version: 3.5.1
% 10.26/1.98 % Preprocessing class: FSLMSMSSSSSNFFN.
% 10.26/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.26/1.98 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 10.26/1.98 % Starting new_bool_3 with 600s (2) cores
% 10.26/1.98 % Starting new_bool_1 with 600s (2) cores
% 10.26/1.98 % Starting sh5l with 300s (1) cores
% 10.26/1.98 % new_bool_3 with pid 3587715 completed with status 0
% 10.26/1.98 % Result found by new_bool_3
% 10.26/1.98 % Preprocessing class: FSLMSMSSSSSNFFN.
% 10.26/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.26/1.98 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 10.26/1.98 % Starting new_bool_3 with 600s (2) cores
% 10.26/1.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 10.26/1.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.26/1.98 % Search class: FGHSM-SMLM32-MFFFFFNN
% 10.26/1.98 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 10.26/1.98 % Starting SubtermCWHack with 55s (1) cores
% 10.26/1.98 % Starting new_bool_3 with 61s (1) cores
% 10.26/1.98 % new_bool_3 with pid 3587720 completed with status 0
% 10.26/1.98 % Result found by new_bool_3
% 10.26/1.98 % Preprocessing class: FSLMSMSSSSSNFFN.
% 10.26/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.26/1.98 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 10.26/1.98 % Starting new_bool_3 with 600s (2) cores
% 10.26/1.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 10.26/1.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 10.26/1.98 % Search class: FGHSM-SMLM32-MFFFFFNN
% 10.26/1.98 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 10.26/1.98 % Starting SubtermCWHack with 55s (1) cores
% 10.26/1.98 % Starting new_bool_3 with 61s (1) cores
% 10.26/1.98 % Preprocessing time : 0.048 s
% 10.26/1.98 % Presaturation interreduction done
% 10.26/1.98
% 10.26/1.98 % Proof found!
% 10.26/1.98 % SZS status Theorem
% 10.26/1.98 % SZS output start CNFRefutation
% See solution above
% 10.26/1.98 % Parsed axioms : 556
% 10.26/1.98 % Removed by relevancy pruning/SinE : 344
% 10.26/1.98 % Initial clauses : 1452
% 10.26/1.98 % Removed in clause preprocessing : 2
% 10.26/1.98 % Initial clauses in saturation : 1450
% 10.26/1.98 % Processed clauses : 2844
% 10.26/1.98 % ...of these trivial : 20
% 10.26/1.98 % ...subsumed : 498
% 10.26/1.98 % ...remaining for further processing : 2326
% 10.26/1.98 % Other redundant clauses eliminated : 753
% 10.26/1.98 % Clauses deleted for lack of memory : 0
% 10.26/1.98 % Backward-subsumed : 15
% 10.26/1.98 % Backward-rewritten : 29
% 10.26/1.98 % Generated clauses : 3201
% 10.26/1.98 % ...of the previous two non-redundant : 2856
% 10.26/1.98 % ...aggressively subsumed : 0
% 10.26/1.98 % Contextual simplify-reflections : 270
% 10.26/1.98 % Paramodulations : 2635
% 10.26/1.98 % Factorizations : 0
% 10.26/1.98 % NegExts : 0
% 10.26/1.98 % Equation resolutions : 755
% 10.26/1.98 % Disequality decompositions : 0
% 10.26/1.98 % Total rewrite steps : 518
% 10.26/1.98 % ...of those cached : 394
% 10.26/1.98 % Propositional unsat checks : 0
% 10.26/1.98 % Propositional check models : 0
% 10.26/1.98 % Propositional check unsatisfiable : 0
% 10.26/1.98 % Propositional clauses : 0
% 10.26/1.98 % Propositional clauses after purity: 0
% 10.26/1.98 % Propositional unsat core size : 0
% 10.26/1.98 % Propositional preprocessing time : 0.000
% 10.26/1.98 % Propositional encoding time : 0.000
% 10.26/1.98 % Propositional solver time : 0.000
% 10.26/1.98 % Success case prop preproc time : 0.000
% 10.26/1.98 % Success case prop encoding time : 0.000
% 10.26/1.98 % Success case prop solver time : 0.000
% 10.26/1.98 % Current number of processed clauses : 423
% 10.26/1.98 % Positive orientable unit clauses : 107
% 10.26/1.98 % Positive unorientable unit clauses: 3
% 10.26/1.98 % Negative unit clauses : 75
% 10.26/1.98 % Non-unit-clauses : 238
% 10.26/1.98 % Current number of unprocessed clauses: 2804
% 10.26/1.98 % ...number of literals in the above : 10807
% 10.26/1.98 % Current number of archived formulas : 0
% 10.26/1.98 % Current number of archived clauses : 1395
% 10.26/1.98 % Clause-clause subsumption calls (NU) : 1196155
% 10.26/1.98 % Rec. Clause-clause subsumption calls : 51659
% 10.26/1.98 % Non-unit clause-clause subsumptions : 513
% 10.26/1.98 % Unit Clause-clause subsumption calls : 1205
% 10.26/1.98 % Rewrite failures with RHS unbound : 0
% 10.26/1.98 % BW rewrite match attempts : 105
% 10.26/1.98 % BW rewrite match successes : 49
% 10.26/1.98 % Condensation attempts : 0
% 10.26/1.98 % Condensation successes : 0
% 10.26/1.98 % Termbank termtop insertions : 165469
% 10.26/1.98 % Search garbage collected termcells : 19918
% 10.26/1.98
% 10.26/1.98 % -------------------------------------------------
% 10.26/1.98 % User time : 1.366 s
% 10.26/1.98 % System time : 0.025 s
% 10.26/1.98 % Total time : 1.391 s
% 10.26/1.98 % Maximum resident set size: 7204 pages
% 10.26/1.98
% 10.26/1.98 % -------------------------------------------------
% 10.26/1.98 % User time : 2.649 s
% 10.26/1.98 % System time : 0.075 s
% 10.26/1.98 % Total time : 2.724 s
% 10.26/1.98 % Maximum resident set size: 5376 pages
% 10.26/1.98 % E exiting
%------------------------------------------------------------------------------