%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU341+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 : n002.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 02:29:02 PM UTC 2026
% Result : Theorem 28.15s 4.74s
% Output : CNFRefutation 28.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 139 ( 11 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 160 ( 58 ~; 46 |; 25 &)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_connsp_2,conjecture,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
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(t30_tops_1,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(t52_pre_topc,lemma,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( ( topstr_closure(X1,X2) = X2
& topological_space(X1) )
=> closed_subset(X2,X1) )
& ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t5_connsp_2]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( in(X3,X2)
& open_subset(X2,X1) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_9,plain,
! [X1] :
( ( top_str(X1)
& topological_space(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_connsp_2]) ).
fof(c_0_10,negated_conjecture,
( ~ point_neighbourhood(esk417_0,esk416_0,esk418_0)
& in(esk418_0,esk417_0)
& open_subset(esk417_0,esk416_0)
& element(esk418_0,the_carrier(esk416_0))
& element(esk417_0,powerset(the_carrier(esk416_0)))
& top_str(esk416_0)
& topological_space(esk416_0)
& ~ empty_carrier(esk416_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_11,plain,
! [X169,X170,X171] :
( ( ~ top_str(X169)
| ~ topological_space(X169)
| empty_carrier(X169)
| ~ element(X170,the_carrier(X169))
| ~ element(X171,powerset(the_carrier(X169)))
| point_neighbourhood(X171,X169,X170)
| ~ in(X170,interior(X169,X171)) )
& ( ~ top_str(X169)
| ~ topological_space(X169)
| empty_carrier(X169)
| ~ element(X170,the_carrier(X169))
| ~ element(X171,powerset(the_carrier(X169)))
| in(X170,interior(X169,X171))
| ~ point_neighbourhood(X171,X169,X170) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_12,negated_conjecture,
~ point_neighbourhood(esk417_0,esk416_0,esk418_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( ~ top_str(X2)
| ~ topological_space(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ in(X1,interior(X2,X3))
| empty_carrier(X2)
| point_neighbourhood(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
topological_space(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
top_str(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
element(esk417_0,powerset(the_carrier(esk416_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
element(esk418_0,the_carrier(esk416_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
~ empty_carrier(esk416_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,plain,
! [X255,X256] :
( interior(X255,X256) = subset_complement(the_carrier(X255),topstr_closure(X255,subset_complement(the_carrier(X255),X256)))
| ~ element(X256,powerset(the_carrier(X255)))
| ~ top_str(X255) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])])]) ).
fof(c_0_20,lemma,
! [X1645,X1646] :
( ( ~ top_str(X1645)
| ~ element(X1646,powerset(the_carrier(X1645)))
| open_subset(X1646,X1645)
| ~ closed_subset(subset_complement(the_carrier(X1645),X1646),X1645) )
& ( ~ top_str(X1645)
| ~ element(X1646,powerset(the_carrier(X1645)))
| closed_subset(subset_complement(the_carrier(X1645),X1646),X1645)
| ~ open_subset(X1646,X1645) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_tops_1])])])])]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk418_0,interior(esk416_0,esk417_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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]),c_0_17])]),c_0_18]) ).
cnf(c_0_22,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_19]) ).
fof(c_0_23,lemma,
! [X1773,X1774] :
( ( ~ top_str(X1773)
| ~ element(X1774,powerset(the_carrier(X1773)))
| closed_subset(X1774,X1773)
| topstr_closure(X1773,X1774) != X1774
| ~ topological_space(X1773) )
& ( ~ top_str(X1773)
| ~ element(X1774,powerset(the_carrier(X1773)))
| topstr_closure(X1773,X1774) = X1774
| ~ closed_subset(X1774,X1773) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t52_pre_topc])])])])]) ).
cnf(c_0_24,lemma,
( ~ top_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ open_subset(X1,X2)
| closed_subset(subset_complement(the_carrier(X2),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
open_subset(esk417_0,esk416_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk418_0,subset_complement(the_carrier(esk416_0),topstr_closure(esk416_0,subset_complement(the_carrier(esk416_0),esk417_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15]),c_0_16])]) ).
cnf(c_0_27,lemma,
( ~ top_str(X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ closed_subset(X1,X2)
| topstr_closure(X2,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
closed_subset(subset_complement(the_carrier(esk416_0),esk417_0),esk416_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]),c_0_16])]) ).
fof(c_0_29,plain,
! [X754,X755] :
( subset_complement(X754,subset_complement(X754,X755)) = X755
| ~ element(X755,powerset(X754)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
cnf(c_0_30,lemma,
( ~ in(esk418_0,subset_complement(the_carrier(esk416_0),subset_complement(the_carrier(esk416_0),esk417_0)))
| ~ element(subset_complement(the_carrier(esk416_0),esk417_0),powerset(the_carrier(esk416_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_15])]) ).
cnf(c_0_31,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,subset_complement(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
in(esk418_0,esk417_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_33,plain,
! [X589,X590] :
( element(subset_complement(X589,X590),powerset(X589))
| ~ element(X590,powerset(X589)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])])]) ).
cnf(c_0_34,lemma,
~ element(subset_complement(the_carrier(esk416_0),esk417_0),powerset(the_carrier(esk416_0))),
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_16])]) ).
cnf(c_0_35,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU341+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n002.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 06:16:32 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 28.15/4.74 % Version: 3.5.1
% 28.15/4.74 % Preprocessing class: FSLMSMSSSSSNFFN.
% 28.15/4.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.15/4.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 28.15/4.74 % Starting new_bool_3 with 600s (2) cores
% 28.15/4.74 % Starting new_bool_1 with 600s (2) cores
% 28.15/4.74 % Starting sh5l with 300s (1) cores
% 28.15/4.74 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2605092 completed with status 0
% 28.15/4.74 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 28.15/4.74 % Preprocessing class: FSLMSMSSSSSNFFN.
% 28.15/4.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.15/4.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 28.15/4.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 28.15/4.74 % No SInE strategy applied
% 28.15/4.74 % Search class: FGHSM-SMLM32-MFFFFFNN
% 28.15/4.74 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 28.15/4.74 % Starting SubtermCWHack with 82s (1) cores
% 28.15/4.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 28.15/4.74 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 28.15/4.74 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2605102 completed with status 0
% 28.15/4.74 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 28.15/4.74 % Preprocessing class: FSLMSMSSSSSNFFN.
% 28.15/4.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.15/4.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 28.15/4.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 28.15/4.74 % No SInE strategy applied
% 28.15/4.74 % Search class: FGHSM-SMLM32-MFFFFFNN
% 28.15/4.74 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 28.15/4.74 % Starting SubtermCWHack with 82s (1) cores
% 28.15/4.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 28.15/4.74 % Preprocessing time : 0.051 s
% 28.15/4.74 % Presaturation interreduction done
% 28.15/4.74
% 28.15/4.74 % Proof found!
% 28.15/4.74 % SZS status Theorem
% 28.15/4.74 % SZS output start CNFRefutation
% See solution above
% 28.15/4.74 % Parsed axioms : 573
% 28.15/4.74 % Removed by relevancy pruning/SinE : 0
% 28.15/4.74 % Initial clauses : 2561
% 28.15/4.74 % Removed in clause preprocessing : 40
% 28.15/4.74 % Initial clauses in saturation : 2521
% 28.15/4.74 % Processed clauses : 10014
% 28.15/4.74 % ...of these trivial : 104
% 28.15/4.74 % ...subsumed : 4219
% 28.15/4.74 % ...remaining for further processing : 5691
% 28.15/4.74 % Other redundant clauses eliminated : 928
% 28.15/4.74 % Clauses deleted for lack of memory : 0
% 28.15/4.74 % Backward-subsumed : 32
% 28.15/4.74 % Backward-rewritten : 61
% 28.15/4.74 % Generated clauses : 27938
% 28.15/4.74 % ...of the previous two non-redundant : 25212
% 28.15/4.74 % ...aggressively subsumed : 0
% 28.15/4.74 % Contextual simplify-reflections : 290
% 28.15/4.74 % Paramodulations : 27236
% 28.15/4.74 % Factorizations : 2
% 28.15/4.74 % NegExts : 0
% 28.15/4.74 % Equation resolutions : 933
% 28.15/4.74 % Disequality decompositions : 0
% 28.15/4.74 % Total rewrite steps : 5845
% 28.15/4.74 % ...of those cached : 5387
% 28.15/4.74 % Propositional unsat checks : 1
% 28.15/4.74 % Propositional check models : 1
% 28.15/4.74 % Propositional check unsatisfiable : 0
% 28.15/4.74 % Propositional clauses : 0
% 28.15/4.74 % Propositional clauses after purity: 0
% 28.15/4.74 % Propositional unsat core size : 0
% 28.15/4.74 % Propositional preprocessing time : 0.000
% 28.15/4.74 % Propositional encoding time : 0.038
% 28.15/4.74 % Propositional solver time : 0.042
% 28.15/4.74 % Success case prop preproc time : 0.000
% 28.15/4.74 % Success case prop encoding time : 0.000
% 28.15/4.74 % Success case prop solver time : 0.000
% 28.15/4.74 % Current number of processed clauses : 2621
% 28.15/4.74 % Positive orientable unit clauses : 238
% 28.15/4.74 % Positive unorientable unit clauses: 4
% 28.15/4.74 % Negative unit clauses : 583
% 28.15/4.74 % Non-unit-clauses : 1796
% 28.15/4.74 % Current number of unprocessed clauses: 19924
% 28.15/4.74 % ...number of literals in the above : 69157
% 28.15/4.74 % Current number of archived formulas : 0
% 28.15/4.74 % Current number of archived clauses : 2444
% 28.15/4.74 % Clause-clause subsumption calls (NU) : 4214446
% 28.15/4.74 % Rec. Clause-clause subsumption calls : 642013
% 28.15/4.74 % Non-unit clause-clause subsumptions : 1702
% 28.15/4.74 % Unit Clause-clause subsumption calls : 41826
% 28.15/4.74 % Rewrite failures with RHS unbound : 3
% 28.15/4.74 % BW rewrite match attempts : 128
% 28.15/4.74 % BW rewrite match successes : 84
% 28.15/4.74 % Condensation attempts : 0
% 28.15/4.74 % Condensation successes : 0
% 28.15/4.74 % Termbank termtop insertions : 592409
% 28.15/4.74 % Search garbage collected termcells : 34984
% 28.15/4.74
% 28.15/4.74 % -------------------------------------------------
% 28.15/4.74 % User time : 3.704 s
% 28.15/4.74 % System time : 0.085 s
% 28.15/4.74 % Total time : 3.788 s
% 28.15/4.74 % Maximum resident set size: 10552 pages
% 28.15/4.74
% 28.15/4.74 % -------------------------------------------------
% 28.15/4.74 % User time : 11.255 s
% 28.15/4.74 % System time : 0.266 s
% 28.15/4.74 % Total time : 11.522 s
% 28.15/4.74 % Maximum resident set size: 5376 pages
% 28.15/4.74 % E exiting
%------------------------------------------------------------------------------