%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 103 ( 8 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 117 ( 48 ~; 45 |; 12 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_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/sandbox2/benchmark/theBenchmark.p',d1_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/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(fc3_tops_1,axiom,
! [X1,X2] :
( ( element(X2,powerset(the_carrier(X1)))
& closed_subset(X2,X1)
& top_str(X1)
& topological_space(X1) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_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/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
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/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(dt_k1_tops_1,axiom,
! [X1,X2] :
( ( element(X2,powerset(the_carrier(X1)))
& top_str(X1) )
=> element(interior(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(c_0_8,plain,
! [X20,X21] :
( subset_complement(X20,subset_complement(X20,X21)) = X21
| ~ element(X21,powerset(X20)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
fof(c_0_9,plain,
! [X13,X14] :
( interior(X13,X14) = subset_complement(the_carrier(X13),topstr_closure(X13,subset_complement(the_carrier(X13),X14)))
| ~ element(X14,powerset(the_carrier(X13)))
| ~ top_str(X13) ),
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_10,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,subset_complement(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,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_9]) ).
fof(c_0_12,plain,
! [X26,X27] :
( element(topstr_closure(X26,X27),powerset(the_carrier(X26)))
| ~ element(X27,powerset(the_carrier(X26)))
| ~ top_str(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])])]) ).
fof(c_0_13,plain,
! [X22,X23] :
( element(subset_complement(X22,X23),powerset(X22))
| ~ element(X23,powerset(X22)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])])]) ).
fof(c_0_14,plain,
! [X5,X6] :
( open_subset(subset_complement(the_carrier(X5),X6),X5)
| ~ element(X6,powerset(the_carrier(X5)))
| ~ closed_subset(X6,X5)
| ~ top_str(X5)
| ~ topological_space(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_tops_1])])]) ).
fof(c_0_15,plain,
! [X24,X25] :
( closed_subset(topstr_closure(X24,X25),X24)
| ~ element(X25,powerset(the_carrier(X24)))
| ~ top_str(X24)
| ~ topological_space(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])])]) ).
cnf(c_0_16,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| topstr_closure(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),interior(X1,X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,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_12]) ).
cnf(c_0_18,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,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]) ).
cnf(c_0_20,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| open_subset(subset_complement(the_carrier(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,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_15]) ).
cnf(c_0_22,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| topstr_closure(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),interior(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
fof(c_0_23,plain,
! [X11,X12] :
( element(interior(X11,X12),powerset(the_carrier(X11)))
| ~ element(X12,powerset(the_carrier(X11)))
| ~ top_str(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_tops_1])])]) ).
fof(c_0_24,negated_conjecture,
( ~ open_subset(interior(esk1_0,esk2_0),esk1_0)
& element(esk2_0,powerset(the_carrier(esk1_0)))
& top_str(esk1_0)
& topological_space(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_25,plain,
( ~ topological_space(X2)
| ~ top_str(X2)
| ~ closed_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ element(X1,powerset(the_carrier(X2)))
| open_subset(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_18]) ).
cnf(c_0_26,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| closed_subset(subset_complement(the_carrier(X1),interior(X1,X2)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18]) ).
cnf(c_0_27,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| element(interior(X1,X2),powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ open_subset(interior(esk1_0,esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| open_subset(interior(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n008.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Mon Sep 21 06:12:38 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.56 Running first-order theorem proving
% 0.23/0.56 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/benchmark/theBenchmark.p
% 0.23/0.61 % Version: 3.5.1
% 0.23/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.61 % Starting sh5l with 300s (1) cores
% 0.23/0.61 % new_bool_3 with pid 313721 completed with status 0
% 0.23/0.61 % Result found by new_bool_3
% 0.23/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.61 % Search class: FHUSF-FFSS21-MFFFFFNN
% 0.23/0.61 % partial match(1): FHUSF-FFSS21-SFFFFFNN
% 0.23/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.61 % SubtermCWHack with pid 313724 completed with status 0
% 0.23/0.61 % Result found by SubtermCWHack
% 0.23/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.61 % Search class: FHUSF-FFSS21-MFFFFFNN
% 0.23/0.61 % partial match(1): FHUSF-FFSS21-SFFFFFNN
% 0.23/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.61 % Preprocessing time : 0.002 s
% 0.23/0.61
% 0.23/0.61 % Proof found!
% 0.23/0.61 % SZS status Theorem
% 0.23/0.61 % SZS output start CNFRefutation
% See solution above
% 0.23/0.61 % Parsed axioms : 21
% 0.23/0.61 % Removed by relevancy pruning/SinE : 8
% 0.23/0.61 % Initial clauses : 18
% 0.23/0.61 % Removed in clause preprocessing : 0
% 0.23/0.61 % Initial clauses in saturation : 18
% 0.23/0.61 % Processed clauses : 32
% 0.23/0.61 % ...of these trivial : 0
% 0.23/0.61 % ...subsumed : 5
% 0.23/0.61 % ...remaining for further processing : 27
% 0.23/0.61 % Other redundant clauses eliminated : 0
% 0.23/0.61 % Clauses deleted for lack of memory : 0
% 0.23/0.61 % Backward-subsumed : 1
% 0.23/0.61 % Backward-rewritten : 0
% 0.23/0.61 % Generated clauses : 41
% 0.23/0.61 % ...of the previous two non-redundant : 36
% 0.23/0.61 % ...aggressively subsumed : 0
% 0.23/0.61 % Contextual simplify-reflections : 7
% 0.23/0.61 % Paramodulations : 41
% 0.23/0.61 % Factorizations : 0
% 0.23/0.61 % NegExts : 0
% 0.23/0.61 % Equation resolutions : 0
% 0.23/0.61 % Disequality decompositions : 0
% 0.23/0.61 % Total rewrite steps : 3
% 0.23/0.61 % ...of those cached : 0
% 0.23/0.61 % Propositional unsat checks : 0
% 0.23/0.61 % Propositional check models : 0
% 0.23/0.61 % Propositional check unsatisfiable : 0
% 0.23/0.61 % Propositional clauses : 0
% 0.23/0.61 % Propositional clauses after purity: 0
% 0.23/0.61 % Propositional unsat core size : 0
% 0.23/0.61 % Propositional preprocessing time : 0.000
% 0.23/0.61 % Propositional encoding time : 0.000
% 0.23/0.61 % Propositional solver time : 0.000
% 0.23/0.61 % Success case prop preproc time : 0.000
% 0.23/0.61 % Success case prop encoding time : 0.000
% 0.23/0.61 % Success case prop solver time : 0.000
% 0.23/0.61 % Current number of processed clauses : 26
% 0.23/0.61 % Positive orientable unit clauses : 5
% 0.23/0.61 % Positive unorientable unit clauses: 0
% 0.23/0.61 % Negative unit clauses : 1
% 0.23/0.61 % Non-unit-clauses : 20
% 0.23/0.61 % Current number of unprocessed clauses: 22
% 0.23/0.61 % ...number of literals in the above : 107
% 0.23/0.61 % Current number of archived formulas : 0
% 0.23/0.61 % Current number of archived clauses : 1
% 0.23/0.61 % Clause-clause subsumption calls (NU) : 116
% 0.23/0.61 % Rec. Clause-clause subsumption calls : 58
% 0.23/0.61 % Non-unit clause-clause subsumptions : 13
% 0.23/0.61 % Unit Clause-clause subsumption calls : 0
% 0.23/0.61 % Rewrite failures with RHS unbound : 0
% 0.23/0.61 % BW rewrite match attempts : 0
% 0.23/0.61 % BW rewrite match successes : 0
% 0.23/0.61 % Condensation attempts : 0
% 0.23/0.61 % Condensation successes : 0
% 0.23/0.61 % Termbank termtop insertions : 2679
% 0.23/0.61 % Search garbage collected termcells : 293
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.006 s
% 0.23/0.61 % System time : 0.006 s
% 0.23/0.61 % Total time : 0.012 s
% 0.23/0.61 % Maximum resident set size: 3596 pages
% 0.23/0.61
% 0.23/0.61 % -------------------------------------------------
% 0.23/0.61 % User time : 0.010 s
% 0.23/0.61 % System time : 0.010 s
% 0.23/0.61 % Total time : 0.020 s
% 0.23/0.61 % Maximum resident set size: 4864 pages
% 0.23/0.61 % E exiting
%------------------------------------------------------------------------------