%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU324+1 : 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 : n009.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 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 132 ( 28 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 148 ( 54 ~; 52 |; 18 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t52_pre_topc,axiom,
! [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(t55_tops_1,conjecture,
! [X1] :
( ( top_str(X1)
& topological_space(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( interior(X1,X3) = X3
=> open_subset(X3,X1) )
& ( open_subset(X4,X2)
=> interior(X2,X4) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(t30_tops_1,axiom,
! [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(fc6_tops_1,axiom,
! [X1,X2] :
( ( element(X2,powerset(the_carrier(X1)))
& top_str(X1)
& topological_space(X1) )
=> open_subset(interior(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(c_0_7,plain,
! [X19,X20] :
( interior(X19,X20) = subset_complement(the_carrier(X19),topstr_closure(X19,subset_complement(the_carrier(X19),X20)))
| ~ element(X20,powerset(the_carrier(X19)))
| ~ top_str(X19) ),
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_8,plain,
! [X32,X33] :
( subset_complement(X32,subset_complement(X32,X33)) = X33
| ~ element(X33,powerset(X32)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
fof(c_0_9,plain,
! [X30,X31] :
( element(subset_complement(X30,X31),powerset(X30))
| ~ element(X31,powerset(X30)) ),
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(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_7]) ).
cnf(c_0_11,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,subset_complement(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ element(X1,powerset(X2))
| element(subset_complement(X2,X1),powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X38,X39] :
( ( ~ top_str(X38)
| ~ element(X39,powerset(the_carrier(X38)))
| closed_subset(X39,X38)
| topstr_closure(X38,X39) != X39
| ~ topological_space(X38) )
& ( ~ top_str(X38)
| ~ element(X39,powerset(the_carrier(X38)))
| topstr_closure(X38,X39) = X39
| ~ closed_subset(X39,X38) ) ),
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_14,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,plain,
( ~ 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_13]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( top_str(X1)
& topological_space(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( interior(X1,X3) = X3
=> open_subset(X3,X1) )
& ( open_subset(X4,X2)
=> interior(X2,X4) = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t55_tops_1]) ).
cnf(c_0_17,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1)
| interior(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X17,X18] :
( ( ~ top_str(X17)
| ~ element(X18,powerset(the_carrier(X17)))
| open_subset(X18,X17)
| ~ closed_subset(subset_complement(the_carrier(X17),X18),X17) )
& ( ~ top_str(X17)
| ~ element(X18,powerset(the_carrier(X17)))
| closed_subset(subset_complement(the_carrier(X17),X18),X17)
| ~ open_subset(X18,X17) ) ),
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])])])])]) ).
fof(c_0_19,plain,
! [X23,X24] :
( open_subset(interior(X23,X24),X23)
| ~ element(X24,powerset(the_carrier(X23)))
| ~ top_str(X23)
| ~ topological_space(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_tops_1])])]) ).
fof(c_0_20,negated_conjecture,
( ( interior(esk2_0,esk4_0) != esk4_0
| ~ open_subset(esk3_0,esk1_0) )
& ( interior(esk2_0,esk4_0) != esk4_0
| interior(esk1_0,esk3_0) = esk3_0 )
& ( open_subset(esk4_0,esk2_0)
| ~ open_subset(esk3_0,esk1_0) )
& ( open_subset(esk4_0,esk2_0)
| interior(esk1_0,esk3_0) = esk3_0 )
& element(esk4_0,powerset(the_carrier(esk2_0)))
& element(esk3_0,powerset(the_carrier(esk1_0)))
& top_str(esk2_0)
& top_str(esk1_0)
& topological_space(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
cnf(c_0_21,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| interior(X1,X2) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_12]) ).
cnf(c_0_22,plain,
( ~ 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_18]) ).
cnf(c_0_23,plain,
( ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| open_subset(interior(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( open_subset(esk4_0,esk2_0)
| interior(esk1_0,esk3_0) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
topological_space(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
element(esk3_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
top_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ open_subset(esk3_0,esk1_0)
| open_subset(esk4_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( interior(esk2_0,esk4_0) != esk4_0
| interior(esk1_0,esk3_0) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(X2,X1)
| interior(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
open_subset(esk4_0,esk2_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
element(esk4_0,powerset(the_carrier(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
top_str(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,negated_conjecture,
( interior(esk2_0,esk4_0) != esk4_0
| ~ open_subset(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
interior(esk1_0,esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
~ open_subset(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_37,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_23,c_0_35]),c_0_25]),c_0_26]),c_0_27])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n009.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 06:11:42 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.57 % Version: 3.5.1
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % Starting sh5l with 300s (1) cores
% 0.22/0.57 % new_bool_3 with pid 1017270 completed with status 0
% 0.22/0.57 % Result found by new_bool_3
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % SubtermCWHack with pid 1017273 completed with status 0
% 0.22/0.57 % Result found by SubtermCWHack
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % Preprocessing time : 0.002 s
% 0.22/0.57
% 0.22/0.57 % Proof found!
% 0.22/0.57 % SZS status Theorem
% 0.22/0.57 % SZS output start CNFRefutation
% See solution above
% 0.22/0.57 % Parsed axioms : 25
% 0.22/0.57 % Removed by relevancy pruning/SinE : 8
% 0.22/0.57 % Initial clauses : 31
% 0.22/0.57 % Removed in clause preprocessing : 0
% 0.22/0.57 % Initial clauses in saturation : 31
% 0.22/0.57 % Processed clauses : 48
% 0.22/0.57 % ...of these trivial : 0
% 0.22/0.57 % ...subsumed : 7
% 0.22/0.57 % ...remaining for further processing : 41
% 0.22/0.57 % Other redundant clauses eliminated : 0
% 0.22/0.57 % Clauses deleted for lack of memory : 0
% 0.22/0.57 % Backward-subsumed : 3
% 0.22/0.57 % Backward-rewritten : 2
% 0.22/0.57 % Generated clauses : 57
% 0.22/0.57 % ...of the previous two non-redundant : 44
% 0.22/0.57 % ...aggressively subsumed : 0
% 0.22/0.57 % Contextual simplify-reflections : 6
% 0.22/0.57 % Paramodulations : 57
% 0.22/0.57 % Factorizations : 0
% 0.22/0.57 % NegExts : 0
% 0.22/0.57 % Equation resolutions : 0
% 0.22/0.57 % Disequality decompositions : 0
% 0.22/0.57 % Total rewrite steps : 14
% 0.22/0.57 % ...of those cached : 7
% 0.22/0.57 % Propositional unsat checks : 0
% 0.22/0.57 % Propositional check models : 0
% 0.22/0.57 % Propositional check unsatisfiable : 0
% 0.22/0.57 % Propositional clauses : 0
% 0.22/0.57 % Propositional clauses after purity: 0
% 0.22/0.57 % Propositional unsat core size : 0
% 0.22/0.57 % Propositional preprocessing time : 0.000
% 0.22/0.57 % Propositional encoding time : 0.000
% 0.22/0.57 % Propositional solver time : 0.000
% 0.22/0.57 % Success case prop preproc time : 0.000
% 0.22/0.57 % Success case prop encoding time : 0.000
% 0.22/0.57 % Success case prop solver time : 0.000
% 0.22/0.57 % Current number of processed clauses : 36
% 0.22/0.57 % Positive orientable unit clauses : 9
% 0.22/0.57 % Positive unorientable unit clauses: 0
% 0.22/0.57 % Negative unit clauses : 1
% 0.22/0.57 % Non-unit-clauses : 26
% 0.22/0.57 % Current number of unprocessed clauses: 26
% 0.22/0.57 % ...number of literals in the above : 124
% 0.22/0.57 % Current number of archived formulas : 0
% 0.22/0.57 % Current number of archived clauses : 5
% 0.22/0.57 % Clause-clause subsumption calls (NU) : 180
% 0.22/0.57 % Rec. Clause-clause subsumption calls : 70
% 0.22/0.57 % Non-unit clause-clause subsumptions : 14
% 0.22/0.57 % Unit Clause-clause subsumption calls : 29
% 0.22/0.57 % Rewrite failures with RHS unbound : 0
% 0.22/0.57 % BW rewrite match attempts : 2
% 0.22/0.57 % BW rewrite match successes : 2
% 0.22/0.57 % Condensation attempts : 0
% 0.22/0.57 % Condensation successes : 0
% 0.22/0.57 % Termbank termtop insertions : 3921
% 0.22/0.57 % Search garbage collected termcells : 504
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.008 s
% 0.22/0.57 % System time : 0.001 s
% 0.22/0.57 % Total time : 0.010 s
% 0.22/0.57 % Maximum resident set size: 3652 pages
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.010 s
% 0.22/0.57 % System time : 0.006 s
% 0.22/0.57 % Total time : 0.016 s
% 0.22/0.57 % Maximum resident set size: 4864 pages
% 0.22/0.57 % E exiting
%------------------------------------------------------------------------------