%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU323+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 : n007.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 02:24:42 PM UTC 2026
% Result : Theorem 33.18s 6.17s
% Output : CNFRefutation 33.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 87 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 90 ( 37 ~; 30 |; 10 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t51_tops_1,conjecture,
! [X1] :
( ( top_str(X1)
& topological_space(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(t29_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(fc2_tops_1,axiom,
! [X1,X2] :
( ( element(X2,powerset(the_carrier(X1)))
& top_str(X1)
& topological_space(X1) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( element(X2,powerset(the_carrier(X1)))
& top_str(X1) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
inference(assume_negation,[status(cth)],[t51_tops_1]) ).
fof(c_0_9,negated_conjecture,
( ~ open_subset(interior(esk333_0,esk334_0),esk333_0)
& element(esk334_0,powerset(the_carrier(esk333_0)))
& top_str(esk333_0)
& topological_space(esk333_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_10,plain,
! [X252,X253] :
( interior(X252,X253) = subset_complement(the_carrier(X252),topstr_closure(X252,subset_complement(the_carrier(X252),X253)))
| ~ element(X253,powerset(the_carrier(X252)))
| ~ top_str(X252) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])])]) ).
cnf(c_0_11,negated_conjecture,
~ open_subset(interior(esk333_0,esk334_0),esk333_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
top_str(esk333_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
element(esk334_0,powerset(the_carrier(esk333_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,lemma,
! [X1413,X1414] :
( ( ~ top_str(X1413)
| ~ element(X1414,powerset(the_carrier(X1413)))
| closed_subset(X1414,X1413)
| ~ open_subset(subset_complement(the_carrier(X1413),X1414),X1413) )
& ( ~ top_str(X1413)
| ~ element(X1414,powerset(the_carrier(X1413)))
| open_subset(subset_complement(the_carrier(X1413),X1414),X1413)
| ~ closed_subset(X1414,X1413) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_tops_1])])])])]) ).
cnf(c_0_16,negated_conjecture,
~ open_subset(subset_complement(the_carrier(esk333_0),topstr_closure(esk333_0,subset_complement(the_carrier(esk333_0),esk334_0))),esk333_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_17,lemma,
( ~ top_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ closed_subset(X1,X2)
| open_subset(subset_complement(the_carrier(X2),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X654,X655] :
( closed_subset(topstr_closure(X654,X655),X654)
| ~ element(X655,powerset(the_carrier(X654)))
| ~ top_str(X654)
| ~ topological_space(X654) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])])]) ).
cnf(c_0_19,lemma,
( ~ element(topstr_closure(esk333_0,subset_complement(the_carrier(esk333_0),esk334_0)),powerset(the_carrier(esk333_0)))
| ~ closed_subset(topstr_closure(esk333_0,subset_complement(the_carrier(esk333_0),esk334_0)),esk333_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_13])]) ).
cnf(c_0_20,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| closed_subset(topstr_closure(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
topological_space(esk333_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X581,X582] :
( element(topstr_closure(X581,X582),powerset(the_carrier(X581)))
| ~ element(X582,powerset(the_carrier(X581)))
| ~ top_str(X581) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])])]) ).
fof(c_0_23,plain,
! [X1473,X1474] :
( ( element(X1473,powerset(X1474))
| ~ subset(X1473,X1474) )
& ( subset(X1473,X1474)
| ~ element(X1473,powerset(X1474)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_24,lemma,
! [X1453,X1454] : subset(set_difference(X1453,X1454),X1453),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_25,lemma,
( ~ element(subset_complement(the_carrier(esk333_0),esk334_0),powerset(the_carrier(esk333_0)))
| ~ element(topstr_closure(esk333_0,subset_complement(the_carrier(esk333_0),esk334_0)),powerset(the_carrier(esk333_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_13])]) ).
cnf(c_0_26,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X459,X460] :
( subset_complement(X459,X460) = set_difference(X459,X460)
| ~ element(X460,powerset(X459)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
cnf(c_0_28,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,lemma,
~ element(subset_complement(the_carrier(esk333_0),esk334_0),powerset(the_carrier(esk333_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13])]) ).
cnf(c_0_31,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,lemma,
element(set_difference(X1,X2),powerset(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 06:09:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 33.18/6.17 % Version: 3.5.1
% 33.18/6.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 33.18/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.18/6.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 33.18/6.17 % Starting new_bool_3 with 600s (2) cores
% 33.18/6.17 % Starting new_bool_1 with 600s (2) cores
% 33.18/6.17 % Starting sh5l with 300s (1) cores
% 33.18/6.17 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 348611 completed with status 0
% 33.18/6.17 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 33.18/6.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 33.18/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.18/6.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 33.18/6.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.18/6.17 % No SInE strategy applied
% 33.18/6.17 % Search class: FGHSM-SMLM32-MFFFFFNN
% 33.18/6.17 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 33.18/6.17 % Starting SubtermCWHack with 82s (1) cores
% 33.18/6.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 33.18/6.17 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 33.18/6.17 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 348621 completed with status 0
% 33.18/6.17 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 33.18/6.17 % Preprocessing class: FSLMSMSSSSSNFFN.
% 33.18/6.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.18/6.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 33.18/6.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.18/6.17 % No SInE strategy applied
% 33.18/6.17 % Search class: FGHSM-SMLM32-MFFFFFNN
% 33.18/6.17 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 33.18/6.17 % Starting SubtermCWHack with 82s (1) cores
% 33.18/6.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 33.18/6.17 % Preprocessing time : 0.039 s
% 33.18/6.17 % Presaturation interreduction done
% 33.18/6.17
% 33.18/6.17 % Proof found!
% 33.18/6.17 % SZS status Theorem
% 33.18/6.17 % SZS output start CNFRefutation
% See solution above
% 33.18/6.17 % Parsed axioms : 532
% 33.18/6.17 % Removed by relevancy pruning/SinE : 0
% 33.18/6.17 % Initial clauses : 2082
% 33.18/6.17 % Removed in clause preprocessing : 40
% 33.18/6.17 % Initial clauses in saturation : 2042
% 33.18/6.17 % Processed clauses : 18525
% 33.18/6.17 % ...of these trivial : 83
% 33.18/6.17 % ...subsumed : 11101
% 33.18/6.17 % ...remaining for further processing : 7341
% 33.18/6.17 % Other redundant clauses eliminated : 742
% 33.18/6.17 % Clauses deleted for lack of memory : 0
% 33.18/6.17 % Backward-subsumed : 390
% 33.18/6.17 % Backward-rewritten : 71
% 33.18/6.17 % Generated clauses : 118775
% 33.18/6.17 % ...of the previous two non-redundant : 112574
% 33.18/6.17 % ...aggressively subsumed : 0
% 33.18/6.17 % Contextual simplify-reflections : 296
% 33.18/6.17 % Paramodulations : 118151
% 33.18/6.17 % Factorizations : 14
% 33.18/6.17 % NegExts : 0
% 33.18/6.17 % Equation resolutions : 748
% 33.18/6.17 % Disequality decompositions : 0
% 33.18/6.17 % Total rewrite steps : 14942
% 33.18/6.17 % ...of those cached : 14356
% 33.18/6.17 % Propositional unsat checks : 1
% 33.18/6.17 % Propositional check models : 0
% 33.18/6.17 % Propositional check unsatisfiable : 0
% 33.18/6.17 % Propositional clauses : 0
% 33.18/6.17 % Propositional clauses after purity: 0
% 33.18/6.17 % Propositional unsat core size : 0
% 33.18/6.17 % Propositional preprocessing time : 0.000
% 33.18/6.17 % Propositional encoding time : 0.066
% 33.18/6.17 % Propositional solver time : 0.087
% 33.18/6.17 % Success case prop preproc time : 0.000
% 33.18/6.17 % Success case prop encoding time : 0.000
% 33.18/6.17 % Success case prop solver time : 0.000
% 33.18/6.17 % Current number of processed clauses : 4594
% 33.18/6.17 % Positive orientable unit clauses : 208
% 33.18/6.17 % Positive unorientable unit clauses: 3
% 33.18/6.17 % Negative unit clauses : 997
% 33.18/6.17 % Non-unit-clauses : 3386
% 33.18/6.17 % Current number of unprocessed clauses: 97142
% 33.18/6.17 % ...number of literals in the above : 526760
% 33.18/6.17 % Current number of archived formulas : 0
% 33.18/6.17 % Current number of archived clauses : 2360
% 33.18/6.17 % Clause-clause subsumption calls (NU) : 6140525
% 33.18/6.17 % Rec. Clause-clause subsumption calls : 1586663
% 33.18/6.17 % Non-unit clause-clause subsumptions : 4950
% 33.18/6.17 % Unit Clause-clause subsumption calls : 239289
% 33.18/6.17 % Rewrite failures with RHS unbound : 0
% 33.18/6.17 % BW rewrite match attempts : 126
% 33.18/6.17 % BW rewrite match successes : 85
% 33.18/6.17 % Condensation attempts : 0
% 33.18/6.17 % Condensation successes : 0
% 33.18/6.17 % Termbank termtop insertions : 2510476
% 33.18/6.17 % Search garbage collected termcells : 28811
% 33.18/6.17
% 33.18/6.17 % -------------------------------------------------
% 33.18/6.17 % User time : 5.165 s
% 33.18/6.17 % System time : 0.123 s
% 33.18/6.17 % Total time : 5.288 s
% 33.18/6.17 % Maximum resident set size: 9144 pages
% 33.18/6.17
% 33.18/6.17 % -------------------------------------------------
% 33.18/6.17 % User time : 15.858 s
% 33.18/6.17 % System time : 0.400 s
% 33.18/6.17 % Total time : 16.258 s
% 33.18/6.17 % Maximum resident set size: 5376 pages
% 33.18/6.17 % E exiting
%------------------------------------------------------------------------------