%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU320+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 : n006.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 1.42s 0.67s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 70 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 24 |; 4 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_tops_1,conjecture,
! [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(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(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(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(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(c_0_5,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t30_tops_1]) ).
fof(c_0_6,plain,
! [X57,X58] :
( subset_complement(X57,subset_complement(X57,X58)) = X58
| ~ element(X58,powerset(X57)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
fof(c_0_7,negated_conjecture,
( ( closed_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
| open_subset(esk2_0,esk1_0) )
& ( ~ closed_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
| ~ open_subset(esk2_0,esk1_0) )
& element(esk2_0,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_5])])])]) ).
fof(c_0_8,plain,
! [X53,X54] :
( subset_complement(X53,X54) = set_difference(X53,X54)
| ~ element(X54,powerset(X53)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
fof(c_0_9,plain,
! [X55,X56] :
( element(subset_complement(X55,X56),powerset(X55))
| ~ element(X56,powerset(X55)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_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_6]) ).
cnf(c_0_11,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,lemma,
! [X81,X82] :
( ( ~ top_str(X81)
| ~ element(X82,powerset(the_carrier(X81)))
| closed_subset(X82,X81)
| ~ open_subset(subset_complement(the_carrier(X81),X82),X81) )
& ( ~ top_str(X81)
| ~ element(X82,powerset(the_carrier(X81)))
| open_subset(subset_complement(the_carrier(X81),X82),X81)
| ~ closed_subset(X82,X81) ) ),
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_15,negated_conjecture,
subset_complement(the_carrier(esk1_0),subset_complement(the_carrier(esk1_0),esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
subset_complement(the_carrier(esk1_0),esk2_0) = set_difference(the_carrier(esk1_0),esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
element(subset_complement(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0))),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( closed_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
| open_subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(esk1_0),esk2_0),esk1_0)
| ~ open_subset(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,lemma,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(subset_complement(the_carrier(X1),X2),X1)
| closed_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
subset_complement(the_carrier(esk1_0),set_difference(the_carrier(esk1_0),esk2_0)) = esk2_0,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
element(set_difference(the_carrier(esk1_0),esk2_0),powerset(the_carrier(esk1_0))),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( open_subset(esk2_0,esk1_0)
| closed_subset(set_difference(the_carrier(esk1_0),esk2_0),esk1_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( ~ open_subset(esk2_0,esk1_0)
| ~ closed_subset(set_difference(the_carrier(esk1_0),esk2_0),esk1_0) ),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,lemma,
closed_subset(set_difference(the_carrier(esk1_0),esk2_0),esk1_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23])]),c_0_24]) ).
cnf(c_0_27,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_14]) ).
cnf(c_0_28,negated_conjecture,
~ open_subset(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_29,lemma,
$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_27,c_0_26]),c_0_21]),c_0_22]),c_0_23])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 06:11:13 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 1.42/0.67 % Version: 3.5.1
% 1.42/0.67 % Preprocessing class: FSLMSMSSSSSNFFN.
% 1.42/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.42/0.67 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 1.42/0.67 % Starting new_bool_3 with 600s (2) cores
% 1.42/0.67 % Starting new_bool_1 with 600s (2) cores
% 1.42/0.67 % Starting sh5l with 300s (1) cores
% 1.42/0.67 % new_bool_3 with pid 2161163 completed with status 0
% 1.42/0.67 % Result found by new_bool_3
% 1.42/0.67 % Preprocessing class: FSLMSMSSSSSNFFN.
% 1.42/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.42/0.67 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 1.42/0.67 % Starting new_bool_3 with 600s (2) cores
% 1.42/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.42/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.42/0.67 % Search class: FGHSM-FSLM31-MFFFFFNN
% 1.42/0.67 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 1.42/0.67 % Starting SubtermCWHack with 55s (1) cores
% 1.42/0.67 % Starting new_bool_3 with 61s (1) cores
% 1.42/0.67 % new_bool_3 with pid 2161167 completed with status 0
% 1.42/0.67 % Result found by new_bool_3
% 1.42/0.67 % Preprocessing class: FSLMSMSSSSSNFFN.
% 1.42/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.42/0.67 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 1.42/0.67 % Starting new_bool_3 with 600s (2) cores
% 1.42/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.42/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.42/0.67 % Search class: FGHSM-FSLM31-MFFFFFNN
% 1.42/0.67 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 1.42/0.67 % Starting SubtermCWHack with 55s (1) cores
% 1.42/0.67 % Starting new_bool_3 with 61s (1) cores
% 1.42/0.67 % Preprocessing time : 0.013 s
% 1.42/0.67 % Presaturation interreduction done
% 1.42/0.67
% 1.42/0.67 % Proof found!
% 1.42/0.67 % SZS status Theorem
% 1.42/0.67 % SZS output start CNFRefutation
% See solution above
% 1.42/0.67 % Parsed axioms : 522
% 1.42/0.67 % Removed by relevancy pruning/SinE : 360
% 1.42/0.67 % Initial clauses : 657
% 1.42/0.67 % Removed in clause preprocessing : 2
% 1.42/0.67 % Initial clauses in saturation : 655
% 1.42/0.67 % Processed clauses : 1414
% 1.42/0.67 % ...of these trivial : 18
% 1.42/0.67 % ...subsumed : 330
% 1.42/0.67 % ...remaining for further processing : 1066
% 1.42/0.67 % Other redundant clauses eliminated : 208
% 1.42/0.67 % Clauses deleted for lack of memory : 0
% 1.42/0.67 % Backward-subsumed : 4
% 1.42/0.67 % Backward-rewritten : 44
% 1.42/0.67 % Generated clauses : 1867
% 1.42/0.67 % ...of the previous two non-redundant : 1634
% 1.42/0.67 % ...aggressively subsumed : 0
% 1.42/0.67 % Contextual simplify-reflections : 55
% 1.42/0.67 % Paramodulations : 1689
% 1.42/0.67 % Factorizations : 0
% 1.42/0.67 % NegExts : 0
% 1.42/0.67 % Equation resolutions : 210
% 1.42/0.67 % Disequality decompositions : 0
% 1.42/0.67 % Total rewrite steps : 671
% 1.42/0.67 % ...of those cached : 585
% 1.42/0.67 % Propositional unsat checks : 0
% 1.42/0.67 % Propositional check models : 0
% 1.42/0.67 % Propositional check unsatisfiable : 0
% 1.42/0.67 % Propositional clauses : 0
% 1.42/0.67 % Propositional clauses after purity: 0
% 1.42/0.67 % Propositional unsat core size : 0
% 1.42/0.67 % Propositional preprocessing time : 0.000
% 1.42/0.67 % Propositional encoding time : 0.000
% 1.42/0.67 % Propositional solver time : 0.000
% 1.42/0.67 % Success case prop preproc time : 0.000
% 1.42/0.67 % Success case prop encoding time : 0.000
% 1.42/0.67 % Success case prop solver time : 0.000
% 1.42/0.67 % Current number of processed clauses : 300
% 1.42/0.67 % Positive orientable unit clauses : 70
% 1.42/0.67 % Positive unorientable unit clauses: 1
% 1.42/0.67 % Negative unit clauses : 30
% 1.42/0.67 % Non-unit-clauses : 199
% 1.42/0.67 % Current number of unprocessed clauses: 1442
% 1.42/0.67 % ...number of literals in the above : 4947
% 1.42/0.67 % Current number of archived formulas : 0
% 1.42/0.67 % Current number of archived clauses : 647
% 1.42/0.67 % Clause-clause subsumption calls (NU) : 228406
% 1.42/0.67 % Rec. Clause-clause subsumption calls : 39372
% 1.42/0.67 % Non-unit clause-clause subsumptions : 258
% 1.42/0.67 % Unit Clause-clause subsumption calls : 456
% 1.42/0.67 % Rewrite failures with RHS unbound : 0
% 1.42/0.67 % BW rewrite match attempts : 78
% 1.42/0.67 % BW rewrite match successes : 26
% 1.42/0.67 % Condensation attempts : 0
% 1.42/0.67 % Condensation successes : 0
% 1.42/0.67 % Termbank termtop insertions : 73288
% 1.42/0.67 % Search garbage collected termcells : 11020
% 1.42/0.67
% 1.42/0.67 % -------------------------------------------------
% 1.42/0.67 % User time : 0.204 s
% 1.42/0.67 % System time : 0.010 s
% 1.42/0.67 % Total time : 0.214 s
% 1.42/0.67 % Maximum resident set size: 5604 pages
% 1.42/0.67
% 1.42/0.67 % -------------------------------------------------
% 1.42/0.67 % User time : 0.406 s
% 1.42/0.67 % System time : 0.017 s
% 1.42/0.67 % Total time : 0.423 s
% 1.42/0.67 % Maximum resident set size: 5632 pages
% 1.42/0.67 % E exiting
%------------------------------------------------------------------------------